data/chunks/chunk_a71f59bd_20.jsonl

{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 377, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\nEurocodes 2: Design of concrete structures\n356\nExample 8.11 continued\nEFFECTIVE SPAN\nFrom Cl 5.3.2.2. of EC 2, effective span of slab, leff, is\nleff = ln + a1 + a2\nwhere\nln\nclear distance between the face of supports\na1, a2\nare the lesser of half the width of the support, t/2, (= 150/2 = 75 mm) or half the overall depth of the slab,\nh/2 (= 150/2 = 75 mm) at the ends of the slab\n⇒ \n    \nleff\nmm\n=\n+\n+\n=\n \n  \n  \n  \n \n2850\n150\n2\n150\n2\n3000\nVARIABLE LOAD CAPACITY\nThis can only really be estimated by trial and error. Try qk = 11.4 kNm−1.\nCheck bending\nSelf weight of slab (gk) = 0.15 × 25 kNm−3 = 3.75 kNm−2\nUltimate load (ω)\n= 1.35gk + 1.5qk\n= 1.35 × 3.75 + 1.5 × 11.4\nDesign moment, \n      \nM\ng\nq\n  \n  ( .\n  \n  .\n)\n  ( .\n  .\n  .   \n. )\n  \n.  \n=\n=\n×\n+\n=\n×\n+\n×\n=\nωB\nB\n2\n2\n2\n8\n1 35\n1 5\n8\n1 35\n3 75\n1 5\n11 4 3\n8\n24 9\nk\nk\nkNm\nEffective depth of slab (d) = h − cover − Φ/2 = 150 − 25 − 10/2 = 120 mm\n    \nK\nM\nf bd\no\nck\n  \n  \n.   \n  \n  \n  .\n=\n=\n×\n×\n×\n=\n2\n6\n2\n24 9\n10\n25\n1000\n120\n0 0692\n    z\nd\nK\n  ( .   ( .\n  \n/ . ))  \n( .   ( .\n    .\n/ . ))  \n \n=\n+\n−\n=\n+\n−\n×\n=\n0 5\n0 25\n3\n3 4\n120 0 5\n0 25\n3\n0 0692 3 4\n112\no\nmm\n    \nA\nM\nf z\ns\ny\nmm\nprovided\nmm\n1\n6\n2\n2\n0 87\n24 9\n10\n0 87\n500\n112\n511\n628\n  \n.\n  \n.   \n.\n  \n  \n  \n \n  \n  \n \n=\n=\n×\n×\n×\n=\n<\n=\nCheck deflection\nDesign service stress, \n    \nσs\nyk\ns,req\ns,prov\nNmm\n    \n  \n    \n  \n  \n.  \n≈\n×\n×\n=\n×\n×\n=\n−\n5\n8\n5\n8\n500\n511\n628\n254 3\n2\nf\nA\nA\nModification factor = \n  \n310\n310\n254 3\n1 22\nσs\n  \n.   .\n=\n=\n    \nρ\nρ\n  \n  \n  \n  .\n  .\n  \n  \n  \n  \n  \n  \n=\n=\n×\n=\n=\n×\n<\n=\n×\n=\n×\n−\n−\n−\nA\nbd\nf\ns1\no\nck\n511\n1000\n120\n0 00426\n4 26\n10\n10\n25\n10\n3\n3\n3\nThe basic span/effective depth ratio is given by\n      \nB\n \nd\nK\nf\nf\n  \n  .\n  .\n  \n/\n=\n+\n\n\n\n+\n−\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n11\n1 5\n3 2\n1\n3 2\nck\no\nck\no\nρ\nρ\nρ\nρ\n  \n=\n+\n×\n×\n\n\n\n+\n×\n×\n−\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n=\n−\n−\n−\n−\n .\n  .\n  \n.\n  \n  .\n  \n.\n  \n  \n  \n \n/\n1 0 11\n1 5 25\n25\n10\n4 26\n10\n3 2 25\n25\n10\n4 26\n10\n1\n21\n3\n3\n3\n3\n3 2\nAllowable span/effective depth ratio = basic ratio × modification factor\n= 21 × 1.22 = 25.6 > actual (3000/120 = 25)\nOK\n\n[TABLES]\n[[{\"0\": \"Eurocodes 2: Design of concrete structures\"}, {\"0\": \"Example 8.11 continued\"}, {\"0\": \"EFFECTIVE SPAN\"}, {\"0\": \"From Cl 5.3.2.2. of EC 2, effective span of slab, leff, is\"}, {\"0\": \"leff = ln + a1 + a2\"}, {\"0\": \"where\"}, {\"0\": \"clear distance between the face of supportsln\"}, {\"0\": \"are the lesser of half the width of the support, t/2, (= 150/2 = 75 mm) or half the overall depth of the slab,a1, a2\"}, {\"0\": \"h/2 (= 150/2 = 75 mm) at the ends of the slab\"}, {\"0\": \"150150=++= 2850      3000 mm⇒ leff\"}, {\"0\": \"22\"}, {\"0\": \"VARIABLE LOAD CAPACITY\"}, {\"0\": \"This can only really be estimated by trial and error. Try qk = 11.4 kNm−1.\"}, {\"0\": \"Check bending\"}, {\"0\": \"Self weight of slab (gk) = 0.15 × 25 kNm−3 = 3.75 kNm−2\"}, {\"0\": \"Ultimate load (ω)= 1.35gk + 1.5qk\"}, {\"0\": \"= 1.35 × 3.75 + 1.5 × 11.4\"}, {\"0\": \"222×+×+×ωBB1 351 51 353 751 511 4 3(  g  q)(      kk====\"}, {\"0\": \"Design moment, 24 9M         kNm888\"}, {\"0\": \"Effective depth of slab (d) = h − cover − Φ/2 = 150 − 25 − 10/2 = 120 mm\"}, {\"0\": \"6×24 910M  ===\"}, {\"0\": \"0 0692K      o22××251000120fbd    ck\"}, {\"0\": \"=+−=+−×=  d(0 5  (0 25  3K/3 4))  120 0 5  (0 25  3  0 0692 3 4))  112 mmo    z\"}, {\"0\": \"6×24 9  10M22===<=\"}, {\"0\": \"511     628 Ammprovidedmms1××0 870 87  500  112f z\"}, {\"0\": \"Check deflection\"}, {\"0\": \"5 8A A5 8511s,req−2σ≈××=××=500254 3    f           NmmDesign service stress, syk\"}, {\"0\": \"628    310310\"}, {\"0\": \"==Modification factor = 1 22    σ254 3\"}, {\"0\": \"s\"}, {\"0\": \"A b511−−−s1333ρ====×<ρ=×=×0 004264 2610f102510                    ock\"}, {\"0\": \"×d1000120\"}, {\"0\": \"The basic span/effective depth ratio is given by\"}, {\"0\": \"3 2B\"}, {\"0\": \" ρ ρ  ρ ρ oo+−=+111 53 21  K  f  f  ckck\"}, {\"0\": \"d\"}, {\"0\": \"3 2−−3325  1025  10\"}, {\"0\": \" × ×  × × +−==+ 1 0 11  1 525  3 225  1  21 −−33\"}, {\"0\": \"4 26  104 26  10\"}, {\"0\": \"Allowable span/effective depth ratio = basic ratio × modification factor\"}, {\"0\": \"= 21 × 1.22 = 25.6 > actual (3000/120 = 25)OK\"}, {\"0\": \"356\"}], [], []]\n\n[FORMULAS]\n3 = 3; .22 = 25", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0377.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 378, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\n357\nExample 8.11 continued\nCheck shear capacity\nDesign shear force, VEd1, is\n      \nVEd\nkNm\n  \n  ( .\n  .\n  .   \n. )   \n.\n \n=\n=\n×\n+\n×\n=\nωB\n2\n1 35\n3 75\n1 5\n11 4 3\n2\n33 24\nShear resistance of concrete alone, VRd,c\nfck = 25 N mm−2\nCRd,c = 0.18/γc = 0.18/1.5 = 0.12 N mm−2\n    \nk\nd\n    \n    \n  .   .\n=\n+\n=\n+\n=\n≤\n1\n200\n1\n200\n120\n2 3\n2 0\nAssuming all bars are taken onto supports\n    \nρ1\n3\n628\n10\n120\n0 00523\n0 02\n  \n  \n  \n  .\n  .\n=\n=\n×\n=\n<\nA\nb d\ns1\nw\nOK\nσcp = 0\nνmin = 0.035k3/2f ck\n1/2 = 0.035 × 23/2 × 251/2 = 0.495\nVRd,c = [CRd,ck(100ρ1fck)1/3 + k1σcp]bwd\n= [0.12 × 2(100 × 0.00523 × 25)1/3]103 × 120\n= 67848 N ≥ (νmin + k1σcp)bwd = 0.495 × 103 × 120 = 59400 N\nVRd,c (= 67.85 kN) > VEd (= 33.24 kN)\nOK\nThus the slab is capable of supporting a uniformly distributed variable load of 11.4 kNm−2.\n8.10 Design of pad foundations\nThe design of pad foundations was discussed in\nsection 3.11.2.1 and found to be similar to that for\nslabs in respect of bending. However, the designer\nmust also check that the pad will not fail due to\nface, transverse or punching shear. EC 2 require-\nments in respect of these three modes of failure are\ndiscussed below.\n8.10.1 FACE SHEAR (CL. 6.4.5, EC 2)\nAccording to Cl. 6.4.5, adjacent to the column the\napplied ultimate shear stress, νEd, should not exceed\nthe maximum allowable shear resistance, νRd,max\nwhere νEd and νRd,max are given by, respectively,\nequations 8.43 and 8.44:\n    \nν\nβ\nEd\nEd\n0\n  \n=\nV\nu d\n(see Fig. 3.75, Chapter 3)\n(8.43)\nwhere\nVEd\napplied shear force\nd\nmean effective depth of the slab, which may\nbe taken as (dy + dz)/2 where dy, dz effective\ndepth of section in the y and z directions\nrespectively\nu0\nlength of column periphery\nβ\n= 1 where no eccentricity of loading exists\nνRd,max = 0.5νfcd\n(8.44)\nwhere\nν = 0.6[1 − ( fck/250)]\n    \nf\nf\ncd\ncc\nck\nc\n  \n= α\nγ\n8.10.2 TRANSVERSE SHEAR (CL. 6.4.4, EC 2)\nThe critical section for transverse shear failure nor-\nmally occurs a distance d from the face of the col-\numn. Shear reinforcement is not necessary provided\nthe ultimate design shear stress, νEd, is less that the\ndesign shear resistance, νRd where νEd and νRd are\ngiven by, respectively, equations 8.45 and 8.46:\n    \nνEd\nEd,red\n  \n= V\nud\n(8.45)\nDesign of pad foundations\n\n[TABLES]\n[[{\"0\": \"Design of pad foundations\"}, {\"0\": \"Example 8.11 continued\"}, {\"0\": \"Check shear capacity\"}, {\"0\": \"Design shear force, VEd1, is\"}, {\"0\": \"×+×ωB(1 35  3 75  1 5  11 4 3===      33 24 kNmVEd\"}, {\"0\": \"22\"}, {\"0\": \"Shear resistance of concrete alone, VRd,c\"}, {\"0\": \"fck = 25 N mm−2\"}, {\"0\": \"CRd,c = 0.18/γc = 0.18/1.5 = 0.12 N mm−2\"}, {\"0\": \"200200=+=+=≤k  1    1    2 3  2 0\"}, {\"0\": \"d120\"}, {\"0\": \"Assuming all bars are taken onto supports\"}, {\"0\": \"A bds6281===<ρ      0 00523  0 02OK1\"}, {\"0\": \"3×10  120w\"}, {\"0\": \"σcp = 0\"}, {\"0\": \"ν1/2 = 0.035 × 23/2 × 251/2 = 0.495min = 0.035k 3/2f ck\"}, {\"0\": \"σVRd,c = [CRd,ck(100ρ1fck)1/3 + k1cp]bwd\"}, {\"0\": \"= [0.12 × 2(100 × 0.00523 × 25)1/3]103 × 120\"}, {\"0\": \"σ= 67848 N ≥ (νmin + k1cp)bwd = 0.495 × 103 × 120 = 59400 N\"}, {\"0\": \"OKVRd,c (= 67.85 kN) > VEd (= 33.24 kN)\"}, {\"0\": \"Thus the slab is capable of supporting a uniformly distributed variable load of 11.4 kNm−2.\"}, {\"0\": \"depth of section in the y and z directions8.10 Design of pad foundations\"}, {\"0\": \"respectivelyThe  design  of  pad  foundations  was  discussed  in\"}, {\"0\": \"length of column peripheryu0section 3.11.2.1 and found to be similar to that for\"}, {\"0\": \"= 1 where no eccentricity of loading existsslabs in respect of bending. However, the designer\"}, {\"0\": \"ν(8.44)Rd,max = 0.5νfcdmust  also  check  that  the  pad  will  not  fail  due  to\"}, {\"0\": \"face,  transverse  or  punching  shear.  EC  2  require- where\"}, {\"0\": \"ments in respect of these three modes of failure are\"}, {\"0\": \"discussed below.ν = 0.6[1 − ( fck/250)]\"}, {\"0\": \"fck8.10.1FACE SHEAR (CL. 6.4.5, EC 2)f  = αcdcc\"}, {\"0\": \"γAccording to Cl. 6.4.5, adjacent to the column thec\"}, {\"0\": \"applied ultimate shear stress, νEd, should not exceed\"}, {\"0\": \"the  maximum  allowable  shear  resistance,  νRd,max8.10.2TRANSVERSE SHEAR (CL. 6.4.4, EC 2)\"}, {\"0\": \"where  νEd  and  νRd,max  are  given  by,  respectively,The critical section for transverse shear failure nor-\"}, {\"0\": \"equations 8.43 and 8.44:mally occurs a distance d from the face of the col-\"}, {\"0\": \"umn. Shear reinforcement is not necessary providedEdνβ =\"}, {\"0\": \"V u(see Fig. 3.75, Chapter 3)(8.43) Edthe ultimate design shear stress, νEd, is less that thed\"}, {\"0\": \"0    design  shear  resistance,  νRd  where  νEd  and  νRd  are\"}, {\"0\": \"given by, respectively, equations 8.45 and 8.46:where\"}, {\"0\": \"applied shear forceVEd\"}, {\"0\": \"Ed,reddmean effective depth of the slab, which mayν(8.45)  = VEd\"}], [], []]\n\n[FORMULAS]\nc = 0; .18/γc = 0; .18/1.5 = 0; νmin = 0; 251/2 = 0; max = 0; red\n  \n= V", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0378.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 379, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\nEurocodes 2: Design of concrete structures\n358\nwhere\nu\nis the perimeter being considered\nd\nis the mean effective depth of the section\nVEd,red\n= VEd − ∆VEd\nin which\nVEd\nis the applied shear force\n∆VEd\nis the net upward force within the control\nperimeter\nThe design shear resistance, νRd,c, is given by\nνRd = CRd,ck(100ρ1fck)1/3 × (2d/a)\n≥ νmin × (2d/a)\n(8.46)\nwhere\nCRd,c\n= 0.18/γC\nk\n= 1 + \n    \n200\nd  ≤ 2.0\nfck\ncharacteristic concrete strength\nνmin\n= 0.035k3/2f ck\n1/2\nd\nis the effective depth of the section\na\nis the distance from the periphery of the\ncolumn to the control perimeter considered\n    \nρ\nρ ρ\n1\n1\n1\n0 02\n  \n  \n  \n  .\n=\n=\n\n\n\n× \n\n\n≤\ny\nz\nsl,y\ny\nsl,z\nz\nA\nbd\nA\nbd\nin which\nρ1y, ρ1z\ntension steel ratio in the y and z\ndirections\ndy, dz\neffective depth of section in the y and z\ndirections\n8.10.3 PUNCHING SHEAR (CL. 6.4.3 & 6.4.4, EC 2)\nNo punching shear reinforcement is required if\nthe applied shear stress, νEd, is less than the design\npunching shear resistance of concrete, νRd, where\nνEd and νRd are calculated using, respectively, equa-\ntions 8.47 and 8.48:\n    \nν\nβ\nEd\nEd\n  \n=\nV\nu d\n1\n(8.47)\nwhere\nVEd\nultimate design shear force. For a\nfoundation this is normally calculated along\nthe perimeter of the base of the truncated\npunching shear cone, assumed to form at\n26.6° (Fig. 8.28)\nu1\nis the basic control perimeter (Fig. 8.29)\nβ\nis a coefficient which takes account of the\neffects of eccentricity of loading. In cases\nwhere no eccentricity of loading is possible,\nβ may be taken as 1.0.\n2d\n2d\n2d\n2d\nFig. 8.29 Critical perimeters (Fig. 6.13, EC 2).\nFig. 8.28 Design model for punching shear at ULS\n(Fig. 6.16, EC 2).\nLoaded area\nθ\nθ ≥ tan–1 (1/2)\nd\nPad foundation\nνRd = [CRd,ck(100ρfck)1/3 + k1σcp] × (2d/a)\n≥ [νmin + k1σcp] × (2d/a)\n(8.48)\nwhere\nCRd,c\n= 0.18/γC\nk\n= 1 + \n    \n200\nd  ≤ 2.0\nk1\n= 0.1\nfck\ncharacteristic concrete strength\nνmin\n= 0.035k3/2f ck\n1/2\n    \nρ\nρ ρ\n  \n  \n  \n  .\n=\n=\n\n\n\n× \n\n\n≤\n1\n1\n0 02\ny\nz\nsl,y\ny\nsl,z\nz\nA\nbd\nA\nbd\nin which\nρ1y, ρ1z\ntension steel ratio in the y and z\ndirections\ndy, dz\neffective depth of section in the y and z\ndirections\n\n[TABLES]\n[[{\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\"}], [{\"0\": \"2d\", \"1\": \"\"}, {\"0\": \"\", \"1\": \"\"}], [], [], []]\n\n[FORMULAS]\nc\n= 0; c\n= 0", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0379.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 380, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\n359\nWhere νEd exceeds νRd, shear reinforcement will\nneed to be provided such that νEd ≤ νRd,cs\nwhere\nνRd,cs\nis the design value of punching shear\nresistance of slab with shear reinforcement\ncalculated in accordance with Cl. 6.4.5 of\nEC 2.\nσcp = (σcy + σcz)/2\nin which\nσcy, σcz\nrespectively, NEdy/Acy and NEdz/Acz\nwhere\nNEd\nlongitudinal force\nAc\narea of concrete\nDesign of pad foundations\nShear failure could arise:\n(a) at the face of the column\n(b) at a distance d from the face of the column\n(c) punching failure of the slab\nFACE SHEAR\nLoad on footing due to column is 1.35 × 900 + 1.5 × 300 = 1665 kN\nDesign shear stress at the column perimeter, νEd, is\n    \nν\nβ\nEd\nEd\no\nNmm\n  \n  .   \n  \n(   \n)  \n  .\n \n=\n=\n×\n×\n×\n×\n=\n−\nV\nu d\n1 0\n1665\n10\n4\n350\n530\n2 24\n3\n2\nwhere d = h − cover − diameter of bar = 600 − 50 − 20 = 530 mm. Maximum punching shear resistance at the\ncolumn perimeter, νRd,max, is\nνRd,max = 0.5νfcd = 0.5 × 0.528 × 20 = 5.28 N mm−2 > νEd\nOK\nwhere\nH20 at 250c/c\neach way\nExample 8.12 Design of a pad foundation (EC 2)\nThe pad footing shown below supports a column which is subject to axial characteristic permanent and variable\nactions of 900 kN and 300 kN respectively. Assuming the following material strengths, check the suitability of the\ndesign in shear.\nfck = 30 N mm−2\nfyk = 500 N mm−2\n\n[TABLES]\n[[{\"0\": \"H20 at 250c/ceach way\", \"1\": \"\", \"2\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\"}], [], []]\n\n[FORMULAS]\nmax = 0; 20 = 5", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0380.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 381, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\nEurocodes 2: Design of concrete structures\n360\nExample 8.12 continued\nν = 0.6[1 − (fck/250)] = 0.6[1 − (30/250)] = 0.528\n    \nf\nf\ncd\ncc\nck\nc\nNmm\n  \n  .   \n.\n  \n \n=\n=\n×\n=\n−\nα\nγ\n1 0\n30\n1 5\n20\n2\nTRANSVERSE SHEAR\nFrom above, design shear force on footing, VEd = 1665 kN\nEarth pressure, \n    \np\nV\nE\nEd\nbase area\nkNm\n  \n  \n  \n \n=\n=\n=\n−\n1665\n3\n185\n2\n2\nUltimate load on shaded area is\n∆VEd = pE(3 × [3 − 0.795]) = 1223.8 kN\nApplied shear force is\nVEd,red = VEd − ∆VEd = 1665 − 1223.8 = 441.2 kN\nDesign transverse shear stress, νEd, is\n    \nνEd\nEd,red\nNmm\n  \n  \n.   \n  \n  .\n \n=\n=\n×\n×\n=\n−\nV\nbd\n441 2\n10\n3000\n530\n0 28\n3\n2\nwhere b = width of footing = 3 m\nfck = 30 N mm−2\nCRd,c = 0.18/γc = 0.18/1.5 = 0.12 N mm−2\n    \nk\nd\n    \n    \n  .\n  .\n=\n+\n=\n+\n=\n<\n1\n200\n1\n200\n530\n1 61\n2 0\nOK\n    \nρ\nρ ρ\n1\n1\n1\n3\n3\n1260\n10\n530\n1260\n10\n530\n0 00238\n0 02\n  \n  \n  \n \n  \n  \n  \n  .\n  .\n=\n=\n×\n=\n×\n×\n×\n=\n<\ny\nx\nsl,y\nsl,x\nA\nbd\nA\nbd\nOK\nσcp = 0\nνmin = 0.035k3/2f ck\n1/2 = 0.035 × 1.613/2 × 301/2 = 0.39\nDesign shear resistance of concrete, νRd,c, is given by\nνRd,c = [CRd,ck(100ρ1fck)1/3 + k1σcp] × (2d/a)\n= [0.12 × 1.61(100 × 0.00238 × 30)1/3 + 0] × 2\n= 0.74 N mm−2 ≥ [νmin + k1σcp] × (2d/a) = 0.39 × 2 = 0.78 Nmm−2\nSince νEd (= 0.28 Nmm−2) < νRd,c (= 0.78 Nmm−2) no shear reinforcement is required.\n530\nmm\n795 \nmm\n\n[TABLES]\n[[{\"0\": \"795 mm\", \"1\": \"530mm\"}], [], []]\n\n[FORMULAS]\n.8 = 441; c = 0; .18/γc = 0; .18/1.5 = 0; νmin = 0; 301/2 = 0; 2\n= 0; 2 = 0", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0381.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 382, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\n361\nExample 8.12 continued\nPUNCHING SHEAR\nDesign of columns\nlateral forces in that plane. Thus braced columns\nare assumed to not contribute to the overall hor-\nizontal stability of a structure and as such are only\ndesigned to resist axial load and bending due to\nvertical loading. For further information on braced\ncolumns refer to section 3.13.3. The design of\nbraced columns involves consideration of the follow-\ning aspects which are discussed individually below:\n(a) slenderness ratio, λ\n(b) threshold slenderness, λlim\n(c) first order effects\n(d) second order moments\n(e) reinforcement details.\n8.11.1 SLENDERNESS RATIO (CL. 5.8.3.2, EC 2)\nIn EC 2 the slenderness ratio, λ, is defined as:\n    \nλ  \n= l\ni\no\n(8.49)\nwhere\nlo\nis the effective length of the column\ni\nis the radius of gyration of the uncracked\nconcrete section\nNote that in BS 8110 the slenderness ratio is\nbased on the section depth (b or h) and not its\nradius of gyration.\n8.11 Design of columns\nColumn design is largely covered within sections\n5.8 and 6.1 of EC 2. The design procedures in EC\n2 are perhaps slightly more complex than those\nused in BS 8110, although the final result is simi-\nlar in both codes.\nColumn design generally involves determining\nthe slenderness ratio, λ, of the member. If it lies\nbelow a critical value, λlim, the column can simply\nbe designed to resist the axial action and moment\nobtained from an elastic analysis, but including the\neffect of geometric imperfections. These are termed\nfirst order effects. However, when the column slen-\nderness exceeds the critical value, additional (second\norder) moments caused by structural deformations\ncan occur and must also be taken into account. In\nEC 2, the slenderness ratio above which columns\nare subjected to second order effects has to be\nevaluated while in BS 8110 it is taken as 15 for\nbraced columns and 10 for unbraced columns.\nIn this chapter only the design of the most com-\nmon types of columns found in building structures,\nnamely braced columns, will be described. A col-\numn may be considered to be braced in a given\nplane if the bracing element or system (e.g. core\nor shear walls) is sufficiently stiff to resist all the\nCheck punching shear at 2d from face of column. Basic control perimeter, u1, is\nu1 = column perimeter + 2π(2d)\n= 4 × 350 + 2π(2 × 530) = 8060 mm\nArea within critical perimeter, A = 4 × 350(2 × 530) + 3502 + π(2 × 530)2 = 5.14 × 106 mm2\nUltimate load on shaded area, ∆VEd = pE × A = 185 × 5.14 = 950.9 kN\nApplied shear force, VEd,red = VEd − ∆VEd = 1665 − 950.9 = 714.1 kN\nPunching shear stress,\n    \nνEd\nEd,red\n  \n  \n.   \n  \n=\n=\n×\n×\nV\nu d\n1\n3\n714 1\n10\n8060\n530 = 0.17 Nmm−2 < νRd,c = 0.39 Nmm−2\nOK\nHence, no shear reinforcement is required.\n2d\n\n[TABLES]\n[[{\"0\": \"2d\", \"1\": \"\"}, {\"0\": \"\", \"1\": \"\"}], [], []]\n\n[FORMULAS]\nλ  \n= l; .14 = 950; .9 = 714; c = 0", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0382.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 383, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\nEurocodes 2: Design of concrete structures\n362\nbackground paper to the UK National Annex to\nEC 2, PD 6687, recommends that when calculat-\ning the effective height of a column in which the\nstiffness of adjacent columns do not vary signific-\nantly, k1 and k2 should be calculated ignoring the\ncontribution of the attached columns. Moreover,\nthe contribution of the attached beams should be\nmodelled as 2(EI/L), irrespective of end conditions\nat their remote ends, to allow for the effect of\ncracking. Calibration exercises suggest that use of\nthese recommendations will lead to effective lengths\nwhich are similar to those currently obtained using\nthe coefficients in Table 3.19 of BS 8110 (repro-\nduced as Table 3.27), and which could therefore\nbe used as an alternative method of estimating the\neffective lengths of braced columns, if desired.\n8.11.3 RADIUS OF GYRATION\nThe radius of gyration (i) is defined by:\n    i\nI A\n  (\n)\n=\n/\n(8.51)\nwhere\nI\nmoment of inertia of the uncracked concrete\nsection (see Table 2.4)\nA\narea of the uncracked concrete section\n8.11.4 THRESHOLD SLENDERNESS RATIO, λlim\n(CL. 5.8.3.1, EC 2)\nAs noted above, the threshold slenderness value,\nλlim, is a key element of the design procedure as it\nprovides a simple and convenient way of determin-\ning when to take account of first order effects only\nand when to include second order effects. The value\nof λlim is given by:\nλlim = 20ABC/  n\n(8.52)\nwhere\nA\n= 1/(1 + 0.2ϕef)(if ϕef is not known,\nA = 0.7 may be assumed)\nB\n=   (   \n)\n1\n2\n+\nω  (if ω is not known,\nB = 1.1 may be used)\nC\n= 1.7 − rm (if rm is not known,\nC = 0.7 may be used)\nϕef\neffective creep coefficient\nω\nmechanical reinforcement\nratio = As fyd/(Ac fcd)\nAs\ntotal area of longitudinal reinforcement\nn\nrelative normal force = NEd/(Ac fcd)\nrm\nmoment ratio = M01/M02 taken\npositive when moments produce\ntension on the same face, otherwise\nnegative\nM01,M02\nfirst order end moments, |M02| ≥ |M01|\n8.11.2 EFFECTIVE LENGTH\nFig. 5.7(f) from EC 2, reproduced as Fig. 8.30,\nsuggests that the effective length of a braced mem-\nber (lo) can vary between half and the full height of\nthe member depending on the degree of rotational\nrestraint at column ends i.e.\nl/2 < lo < l\nThe actual value of effective length can be esti-\nmated using the following expression\n    \nl\nl\nk\nk\nk\nk\no  .\n  \n.\n  \n  \n.\n  \n=\n+\n+\n\n\n\n\n+\n+\n\n\n\n\n0 5\n1\n0 45\n1\n0 45\n1\n1\n2\n2\n(8.50)\nwhere\nk1, k2\nare the relative flexibilities of rotational\nrestraints at ends 1 and 2 respectively\nin which\nk\n= (θ/M)/(EI/l)\nθ\nis the rotation of restraining members for\nbending moment M (see Fig. 8.30)\nEI\nis the bending stiffness of compression\nmembers\nl\nis the clear height of compression member\nbetween end restraints\nNote that in theory, k = 0 for fully rigid rota-\ntional restraint and k = ∞ for no restraint at all, i.e.\npinned support. Since fully rigid restraint is rare in\npractice, EC 2 recommends a minimum value of\n0.1 for k1 and k2.\nIt is not an easy matter to determine the values\nof k1 and k2 in practice because (a) the guidance\nin EC 2 is somewhat ambiguous with regard to the\neffect of stiffness of columns attached to the column\nunder consideration and (b) the effect of cracking\non the stiffness of the restraining member. The\nl\nθ\nl/2 < lo < l\nFig. 8.30 Effective length of columns partially restrained\nat both ends (based on Fig. 5.7f, EC 2).\n\n[TABLES]\n[[{\"0\": \"Eurocodes 2: Design of concrete structures\", \"1\": \"\"}, {\"0\": \"\", \"1\": \"background  paper  to  the  UK  National  Annex  to\"}, {\"0\": \"\", \"1\": \"EC 2, PD 6687, recommends that when calculat-\"}, {\"0\": \"\", \"1\": \"ing  the  effective  height  of  a  column  in  which  the\"}, {\"0\": \"\", \"1\": \"stiffness  of  adjacent  columns  do  not  vary  signific-\"}, {\"0\": \"\", \"1\": \"antly,  k1  and  k2  should  be  calculated  ignoring  thecontribution  of  the  attached  columns.  Moreover,\"}, {\"0\": \"l/2 < lo < ll\", \"1\": \"the  contribution  of  the  attached  beams  should  be\"}, {\"0\": \"θ\", \"1\": \"modelled as 2(EI/L), irrespective of end conditions\"}, {\"0\": \"\", \"1\": \"at  their  remote  ends,  to  allow  for  the  effect  of\"}, {\"0\": \"\", \"1\": \"cracking.  Calibration  exercises  suggest  that  use  of\"}, {\"0\": \"\", \"1\": \"these recommendations will lead to effective lengths\"}, {\"0\": \"\", \"1\": \"which are similar to those currently obtained using\"}, {\"0\": \"Fig. 8.30 Effective length of columns partially restrained\", \"1\": \"the  coefficients  in  Table  3.19  of  BS  8110  (repro-\"}, {\"0\": \"at both ends (based on Fig. 5.7f, EC 2).\", \"1\": \"duced  as  Table  3.27),  and  which  could  therefore\"}, {\"0\": \"\", \"1\": \"be used as an alternative method of estimating the\"}, {\"0\": \"\", \"1\": \"effective lengths of braced columns, if desired.\"}, {\"0\": \"8.11.2EFFECTIVE LENGTH\", \"1\": \"8.11.3 RADIUS OF GYRATION\"}, {\"0\": \"Fig.  5.7(f )  from  EC  2,  reproduced  as  Fig.  8.30,\", \"1\": \"The radius of gyration (i) is defined by:\"}, {\"0\": \"suggests that the effective length of a braced mem-\", \"1\": \"=(8.51)\"}, {\"0\": \"ber (lo) can vary between half and the full height of\", \"1\": \"i\"}, {\"0\": \"the member depending on the degree of rotational\", \"1\": \"where\"}, {\"0\": \"restraint at column ends i.e.\", \"1\": \"Imoment of inertia of the uncracked concrete\"}, {\"0\": \"l/2 < lo < l\", \"1\": \"section (see Table 2.4)\"}, {\"0\": \"\", \"1\": \"Aarea of the uncracked concrete section\"}, {\"0\": \"The actual value of effective length can be esti-\", \"1\": \"\"}, {\"0\": \"mated using the following expression\", \"1\": \"8.11.4THRESHOLD SLENDERNESS RATIO, λlim\"}, {\"0\": \"kk\", \"1\": \"(CL. 5.8.3.1, EC 2)\"}, {\"0\": \"    12+=+0 511(8.50)l l    o\", \"1\": \"As  noted  above,  the  threshold  slenderness  value,λ\"}, {\"0\": \"++0 450 45  k  k12\", \"1\": \"lim, is a key element of the design procedure as it\"}, {\"0\": \"\", \"1\": \"provides a simple and convenient way of determin-\"}, {\"0\": \"where\", \"1\": \"ing when to take account of first order effects only\"}, {\"0\": \"are the relative flexibilities of rotationalk1, k2\", \"1\": \"and when to include second order effects. The value\"}, {\"0\": \"restraints at ends 1 and 2 respectively\", \"1\": \"of λlim is given by:\"}, {\"0\": \"in which\", \"1\": \"λ(8.52)lim = 20ABC/   n\"}, {\"0\": \"k= (θ/M)/(EI/l )θ\", \"1\": \"\"}, {\"0\": \"is the rotation of restraining members for\", \"1\": \"where\"}, {\"0\": \"bending moment M (see Fig. 8.30)\", \"1\": \"A= 1/(1 + 0.2ϕef)(if ϕef is not known,\"}, {\"0\": \"EIis the bending stiffness of compression\", \"1\": \"A = 0.7 may be assumed)\"}, {\"0\": \"members\", \"1\": \"Bω  (if ω is not known,2+=    (\"}, {\"0\": \"lis the clear height of compression member\", \"1\": \"B = 1.1 may be used)\"}, {\"0\": \"between end restraints\", \"1\": \"C= 1.7 − rm (if rm is not known,\"}, {\"0\": \"Note  that  in  theory,  k  =  0  for  fully  rigid  rota-\", \"1\": \"C = 0.7 may be used)ϕ\"}, {\"0\": \"tional restraint and k = ∞ for no restraint at all, i.e.\", \"1\": \"effective creep coefficientefω\"}, {\"0\": \"pinned support. Since fully rigid restraint is rare in\", \"1\": \"mechanical reinforcement\"}, {\"0\": \"practice,  EC  2  recommends  a  minimum  value  of\", \"1\": \"ratio = As f yd/(A c f cd)\"}, {\"0\": \"0.1 for k1 and k2.\", \"1\": \"total area of longitudinal reinforcementAs\"}, {\"0\": \"It is not an easy matter to determine the values\", \"1\": \"nrelative normal force = NEd/(A c f cd)\"}, {\"0\": \"of  k1  and  k2  in  practice  because  (a)  the  guidancein EC 2 is somewhat ambiguous with regard to the\", \"1\": \"rmmoment ratio = M01/M02 takenpositive when moments produce\"}, {\"0\": \"effect of stiffness of columns attached to the column\", \"1\": \"tension on the same face, otherwise\"}, {\"0\": \"under consideration and (b) the effect of cracking\", \"1\": \"negative\"}, {\"0\": \"on  the  stiffness  of  the  restraining  member.  The\", \"1\": \"M01,M02first order end moments, |M02| ≥ |M01\"}], [], []]\n\n[FORMULAS]\nA = 0; B = 1; C\n= 1; C = 0", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0383.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 384, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\n363\nnumerically equal to the sum of the larger elastic\nend moment, M02, plus any moment due to geo-\nmetric imperfection, NEd.ei, as follows:\nMEd = M02 + NEd.ei\n(8.53)\nwhere\nei\nis the geometric imperfection = \n      \nθi\nB0\n2\n\n\n\n in\nwhich θi is the angle of inclination and can\nbe taken as 1/200 for isolated braced columns\nand l0 is the effective length (clause 5.2(7)).\nAccording to clause 6.1(4) the minimum\ndesign eccentricity, e0, is h/30 but not\nless than 20 mm where h is the depth of\nthe section. Note that in BS 8110 the\ncorresponding limit is h/20.\nOnce NEd and MEd have been determined, the area\nof longitudinal steel can be calculated by strain\ncompatibility using an iterative procedure as dis-\ncussed in example 3.19 of this book. However, this\napproach may not be practical for everyday design\nand therefore The Concrete Centre has produced\na series of design charts, similar to those in BS\n8110:Part 3, which can be used to determine the\narea of longitudinal steel. Two typical column\ndesign charts are shown in Fig. 8.32. Example 8.13\nillustrates the design procedure involved.\n8.11.5.2 Design of columns when λ > λlim\n(Cl. 5.8.8, EC 2)\nWhen λ > λlim, critical conditions may occur at\nthe top, middle or bottom of the column. The\nvalues of the design moments at these positions\nare, respectively:\n(i)\nM02\n(ii) M0Ed + M2\n(iii) M01 + 0.5M2\nM0Ed is the equivalent first order moment\nincluding the effect of imperfections at about mid-\nheight of the column and may be taken as M0e as\nfollows:\nM0e = (0.6M02 + 0.4M01) ≥ 0.4M02 (8.54)\nwhere M01 and M02 are the first order end moments\nincluding the effect of imperfections acting on the\ncolumn and M02 is the numerically larger of the\nelastic end moment acting on the column i.e.\n|M02| > |M01|.\nM2 is the nominal second order moment acting\non the column and is given by\nM2 = NEd.e2\n(8.55)\nDesign of columns\nFig. 8.31 Column buckling modes.\nThe value of the creep coefficient, ϕef, can be\ncalculated using the guidance in Cl. 5.8.4 of EC 2.\nHowever, in many cases the extra design effort\nrequired may not be justified and the recommended\nvalue of 0.7 for factor A should be used. Factor B\ndepends upon the area of longitudinal steel, which\nwill be unknown at the design stage. It would\nseem reasonable therefore to use the recommended\nvalue of 1.1, at least for the first iteration. Factor C\narguably has the largest influence on λlim and it is\nworthwhile calculating its value accurately rather\nthan simply assuming it is equal to 0.7. Factor C\ngives an indication of the column’s susceptibility\nto buckling under the action of applied moments.\nThus buckling is more likely where the end mo-\nments act in opposite senses as they will produce\ntension on the same face. Conversely, buckling is\nless likely when the end moments act in the same\nsense as the member will be in double curvature\n(Fig. 8.31).\n8.11.5 DESIGN OF BRACED COLUMNS\nHaving determined the value of λlim it is possible\nto design the column. The following sub-sections\ndiscuss the procedures recommended in EC 2 for\nthe design of braced columns when:\n(a) λ < λlim\n(b) λ > λlim\n8.11.5.1 Design of columns when λ < λlim\n(Cl. 6.1, EC 2)\nAccording to clause 5.8.3.1 of EC 2, if the slender-\nness, λ, is less than λlim the column should be\ndesigned for the applied axial action, NEd, and\nthe moment due to first order effects, MEd, being\n\n[TABLES]\n[[{\"0\": \"\", \"1\": \"Design of columns\"}, {\"0\": \"\", \"1\": \"numerically  equal  to  the  sum  of  the  larger  elastic\"}, {\"0\": \"\", \"1\": \"end  moment,  M02,  plus  any  moment  due  to  geo-\"}, {\"0\": \"\", \"1\": \"metric imperfection, NEd.ei, as follows:\"}, {\"0\": \"\", \"1\": \"(8.53)MEd = M02 + NEd.ei\"}, {\"0\": \"\", \"1\": \"where\"}, {\"0\": \"\", \"1\": \"  B 0θis the geometric imperfection =  iniei\"}, {\"0\": \"\", \"1\": \"2\"}, {\"0\": \"\", \"1\": \"which θi is the angle of inclination and can\"}, {\"0\": \"\", \"1\": \"be taken as 1/200 for isolated braced columns\"}, {\"0\": \"\", \"1\": \"and l0 is the effective length (clause 5.2(7)).According to clause 6.1(4) the minimum\"}, {\"0\": \"Fig. 8.31 Column buckling modes.\", \"1\": \"design eccentricity, e0, is h/30 but notless than 20 mm where h is the depth of\"}, {\"0\": \"\", \"1\": \"the section. Note that in BS 8110 the\"}, {\"0\": \"\", \"1\": \"corresponding limit is h/20.\"}, {\"0\": \"The  value  of  the  creep  coefficient,  ϕef,  can  be\", \"1\": \"Once NEd and MEd have been determined, the areaof  longitudinal  steel  can  be  calculated  by  strain\"}, {\"0\": \"calculated using the guidance in Cl. 5.8.4 of EC 2.\", \"1\": \"compatibility  using  an  iterative  procedure  as  dis-\"}, {\"0\": \"However, in  many  cases  the  extra  design  effort\", \"1\": \"cussed in example 3.19 of this book. However, this\"}, {\"0\": \"required may not be justified and the recommended\", \"1\": \"approach may not be practical for everyday design\"}, {\"0\": \"value of 0.7 for factor A should be used. Factor B\", \"1\": \"and  therefore  The  Concrete  Centre  has  produced\"}, {\"0\": \"depends upon the area of longitudinal steel, which\", \"1\": \"a  series  of  design  charts,  similar  to  those  in  BS\"}, {\"0\": \"will  be  unknown  at  the  design  stage.  It  would\", \"1\": \"8110:Part  3,  which  can  be  used  to  determine  the\"}, {\"0\": \"seem reasonable therefore to use the recommended\", \"1\": \"area  of longitudinal  steel.  Two typical  column\"}, {\"0\": \"value of 1.1, at least for the first iteration. Factor C\", \"1\": \"design charts are shown in Fig. 8.32. Example 8.13\"}, {\"0\": \"arguably  has  the  largest  influence  on  λlim  and  it  is\", \"1\": \"illustrates the design procedure involved.\"}, {\"0\": \"worthwhile  calculating  its  value  accurately  rather\", \"1\": \"\"}, {\"0\": \"than  simply  assuming  it  is  equal  to  0.7.  Factor  C\", \"1\": \"8.11.5.2 Design of columns when λ > λ\"}, {\"0\": \"gives  an  indication  of  the  column’s  susceptibility\", \"1\": \"lim(Cl. 5.8.8, EC 2)\"}, {\"0\": \"to buckling under the action of applied moments.\", \"1\": \"When  λ  >  λlim,  critical  conditions  may  occur  at\"}, {\"0\": \"Thus  buckling  is  more  likely  where  the  end  mo-\", \"1\": \"the  top,  middle  or  bottom  of  the  column.  The\"}, {\"0\": \"ments  act  in  opposite  senses  as  they  will  produce\", \"1\": \"values  of  the  design  moments  at  these  positions\"}, {\"0\": \"tension  on  the  same  face.  Conversely,  buckling  is\", \"1\": \"are, respectively:\"}, {\"0\": \"less likely when the end moments act in the same\", \"1\": \"\"}, {\"0\": \"sense  as  the  member  will  be  in  double  curvature\", \"1\": \"(i)M02\"}, {\"0\": \"(Fig. 8.31).\", \"1\": \"(ii) M0Ed + M2\"}, {\"0\": \"\", \"1\": \"(iii) M01 + 0.5M2\"}, {\"0\": \"8.11.5 DESIGN OF BRACED COLUMNS\", \"1\": \"is the equivalent  first order  momentM0Ed\"}, {\"0\": \"Having  determined  the  value  of  λlim  it  is  possible\", \"1\": \"including the effect of imperfections at about mid-\"}, {\"0\": \"to  design  the  column.  The  following  sub-sections\", \"1\": \"height  of  the  column  and  may  be  taken  as M0e  as\"}, {\"0\": \"discuss the procedures recommended in EC 2 for\", \"1\": \"follows:\"}, {\"0\": \"the design of braced columns when:\", \"1\": \"(8.54)M0e = (0.6M02 + 0.4M01) ≥ 0.4M02\"}, {\"0\": \"(a)λ < λlim\", \"1\": \"where M01 and M02 are the first order end moments\"}, {\"0\": \"(b) λ > λlim\", \"1\": \"including the effect of imperfections acting on the\"}, {\"0\": \"8.11.5.1 Design of columns when λ < λlim\", \"1\": \"column  and  M02  is  the  numerically  larger  of  theelastic  end  moment  acting  on the  column i.e.\"}, {\"0\": \"(Cl. 6.1, EC 2)\", \"1\": \"|.|M02| > |M01\"}, {\"0\": \"According to clause 5.8.3.1 of EC 2, if the slender-\", \"1\": \"M2  is  the  nominal  second  order  moment  acting\"}, {\"0\": \"ness,  λ, is less  than  λlim  the  column  should  be\", \"1\": \"on the column and is given by\"}, {\"0\": \"designed for  the  applied  axial  action,  NEd,  and\", \"1\": \"\"}, {\"0\": \"the  moment  due  to  first  order  effects,  MEd,  being\", \"1\": \"(8.55)M2 = NEd.e2\"}], [], [], [{\"\": \"\", \"None\": \"\"}]]\n\n[FORMULAS]\nMEd = M02 + NEd", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0384.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 385, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\nEurocodes 2: Design of concrete structures\n364\n(a) First order\n \n moments for\n \n ‘stocky’ columns\n(b) Additional second\n \norder moments for\n \n‘slender’ columns\n(c) Total moment\n \ndiagram for\n \n‘slender’ columns\nM01 + 0.5M2\n0.5M2\nM01\nM02\nM2 = NEde2\nM0e + M2\nM0e + M2\ne1NEd\nM\nM02\n+\n=\n0\n1.3\n1.2\n1.1\n1.0\n0.9\n0.8\n0.7\n0.6\n0.5\n0.4\n0.3\n0.2\n0.1\n0\nN/bhfck\nN/bhfck\n0.05\n(a)\n(b)\n0.10\n0.15\n0.2\n0.3\n0.4\n1.0\n0.9\n0.8\n0.5\n0.6\n0.7\n0.8\n0.9\nKt = 1\nM/bh2fck\nM/bh2fck\n0.20\n0.25\n0.30\n0.35\nd2/h = 0.20\nAsfyk/bhfyk\nAsfyk/bhfyk\n0.7\n0.6\n0.5\n0.4\n0.3\n0.2\n0.1\n0\n0\n1.3\n1.2\n1.1\n1.0\n0.9\n0.8\n0.7\n0.6\n0.5\n0.4\n0.3\n0.2\n0.1\n0\n0.05\n0.10\n0.15\n0.2\n0.3\n0.4\n1.0\n0.9\n0.8\n0.5\n0.6\n0.7\n0.8\n0.9\nKt = 1\n0.20\n0.25\n0.30\n0.40\n0.35\nd2/h = 0.15\n0.7\n0.6\n0.5\n0.4\n0.3\n0.2\n0.1\n0\nh\nb\nd2\nAs\n2\nAs\n2\nh\nb\nAs\n2\nAs\n2\nd2\nFig. 8.32 Typical column design charts for use with EC 2.\nwhere\nNEd\nis the design axial load at ULS\ne2\nis the deflection = \n      \n1\n10\n2\nr\n\n\n\nB0/\n(8.56)\nin which\n    \n1\n1\nr\nK K\nr\n  \n=\n\n\n\n\nr\no\nϕ\n(8.57)\nwhere\n    \nK\nn\nn\nn\nn\nr\nu\nu\nbal\n  \n  \n  \n  .\n=\n−\n−\n≤1 0\n(8.58)\nin which nu = 1 + ω\n(where ω = Asfyd/Ac fcd)\n(8.59)\nn\nrelative axial force = NEd/Ac fcd\n(8.60)\nnbal\n= 0.4\nKϕ\n= 1 + βϕef ≥ 1.0\n(8.61)\nin which\nϕef\neffective creep coefficient determined via\nclause 5.8.4\nβ = 0.35 + fck/200 − λ/150\n(8.62)\nλ\nslenderness ratio = \n      \nBo\ni\nand where\n    \n1\n0 45\nr\nd\no\nyd\n  .\n=\nε\n(8.63)\nin which\nεyd\ndesign yield strain of reinforcement: = \n    \nf\nE\nyd\ns\nd\neffective depth of section\nOnce NEd and MEd are known, the area of longi-\ntudinal steel can be evaluated using appropriate\ncolumn design charts (see Example 8.13).\n8.11.6 BIAXIAL BENDING (5.8.9, EC 2)\nColumns subjected to axial load and bi-axial bend-\ning can be checked using the following expression\n    \nM\nM\nM\nM\nEdz\nRdz\na\nEdy\nRdy\na\n\n\n\n\n+ \n\n\n\n≤\n  \n  .\n1 0\n(8.64)\nwhere\nMEdz/y\ndesign moment around the respective\naxis, including a 2nd order moment\nMRdz/y\nmoment of resistance in the respective\ndirection\nFig. 8.33\n\n[TABLES]\n[[{\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\"}, {\"0\": \"\", \"1\": \"Eurocodes 2: Design of concrete structures\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"d2/h = 0.20\", \"6\": \"\", \"7\": \"\", \"8\": \"\"}, {\"0\": \"1.3\", \"1\": \"0.2\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\"}, {\"0\": \"1.21.1\", \"1\": \"\", \"2\": \"0.3\", \"3\": \"Asfyk/bhfyk\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\"}, {\"0\": \"1.0\", \"1\": \"\", \"2\": \"\", \"3\": \"1.00.90.4\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"As2\", \"8\": \"\"}, {\"0\": \"0.9\", \"1\": \"\", \"2\": \"0.80.7\", \"3\": \"\", \"4\": \"0.5\", \"5\": \"h\", \"6\": \"\", \"7\": \"\", \"8\": \"\"}, {\"0\": \"0.8\", \"1\": \"\", \"2\": \"0.60.5\", \"3\": \"\", \"4\": \"0.6\", \"5\": \"\", \"6\": \"\", \"7\": \"As2d2\", \"8\": \"\"}, {\"0\": \"N/bhfck0.70.6\", \"1\": \"\", \"2\": \"0.40.3\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"b\", \"8\": \"\"}, {\"0\": \"0.5\", \"1\": \"0.1\", \"2\": \"0.2\", \"3\": \"\", \"4\": \"\", \"5\": \"0.7\", \"6\": \"\", \"7\": \"\", \"8\": \"\"}, {\"0\": \"0.4\", \"1\": \"0\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"0.8\", \"6\": \"\", \"7\": \"\", \"8\": \"\"}], [{\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"d2/h = 0.15\", \"7\": \"\", \"8\": \"\", \"9\": \"\"}, {\"0\": \"\", \"1\": \"0.2\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"0.3\", \"3\": \"Asfyk/bhfyk\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"1.00.9\", \"3\": \"0.4\", \"4\": \"\", \"5\": \"\", \"6\": \"As2\", \"7\": \"\", \"8\": \"\", \"9\": \"\"}, {\"0\": \"\", \"1\": \"0.7\", \"2\": \"0.8\", \"3\": \"0.5\", \"4\": \"\", \"5\": \"h\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\"}, {\"0\": \"\", \"1\": \"0.60.5\", \"2\": \"\", \"3\": \"\", \"4\": \"0.6\", \"5\": \"\", \"6\": \"As2\", \"7\": \"\", \"8\": \"d2\", \"9\": \"\"}, {\"0\": \"\", \"1\": \"0.40.30.2\", \"2\": \"\", \"3\": \"\", \"4\": \"0.7\", \"5\": \"\", \"6\": \"b\", \"7\": \"\", \"8\": \"\", \"9\": \"\"}, {\"0\": \"0.10\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"0.8\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\"}], [], [], [{\"0.2\": \"\", \"None\": \"\", \"\": \"\", \"d/h = 0.20\": \"2\\nA\\ns\\n2\\nh\\nA\\ns\\n2 d\\n2\\nb\"}, {\"0.2\": \"\", \"None\": \"\", \"\": \"\", \"d/h = 0.20\": \"\"}, {\"0.2\": \"\", \"None\": \"\", \"\": \"\", \"d/h = 0.20\": \"\"}, {\"0.2\": \"\", \"None\": \"\", \"\": \"5\", \"d/h = 0.20\": \"\"}, {\"0.2\": \"\", \"None\": \"\", \"\": \"0.6\", \"d/h = 0.20\": \"\"}, {\"0.2\": \"\", \"None\": \"\", \"\": \"\", \"d/h = 0.20\": \"\"}, {\"0.2\": \"\", \"None\": \"\", \"\": \"\", \"d/h = 0.20\": \"0.7\"}, {\"0.2\": \"0\", \"None\": \"\", \"\": \"\", \"d/h = 0.20\": \"0.8\"}, {\"0.2\": \"\", \"None\": \"0.9\", \"\": \"\", \"d/h = 0.20\": \"\"}, {\"0.2\": \"\", \"None\": \"\", \"\": \"\", \"d/h = 0.20\": \"\"}, {\"0.2\": \"\", \"None\": \"K = 1\\nt\", \"\": \"\", \"d/h = 0.20\": \"\"}, {\"0.2\": \"\", \"None\": \"\", \"\": \"\", \"d/h = 0.20\": \"\"}, {\"0.2\": \"\", \"None\": \"\", \"\": \"\", \"d/h = 0.20\": \"\"}], [{\"\": \"\", \"None\": \"\", \"0.2\": \"\", \"d/h = 0.15\": \"\"}, {\"\": \"\", \"None\": \"\", \"0.2\": \"\", \"d/h = 0.15\": \"\"}, {\"\": \"\", \"None\": \"\", \"0.2\": \"\", \"d/h = 0.15\": \"h\"}, {\"\": \"\", \"None\": \"\", \"0.2\": \"\", \"d/h = 0.15\": \"\"}, {\"\": \"\", \"None\": \"\", \"0.2\": \"\", \"d/h = 0.15\": \"\"}, {\"\": \"\", \"None\": \"\", \"0.2\": \"\", \"d/h = 0.15\": \"\"}, {\"\": \"\", \"None\": \"\", \"0.2\": \"\", \"d/h = 0.15\": \"\"}, {\"\": \"0.7\", \"None\": \"\", \"0.2\": \"0\\n0.1\", \"d/h = 0.15\": \"\"}, {\"\": \"\", \"None\": \"\", \"0.2\": \"\", \"d/h = 0.15\": \"0.8\"}, {\"\": \"\", \"None\": \".9\", \"0.2\": \"\", \"d/h = 0.15\": \"0\"}, {\"\": \"\", \"None\": \"K =\\nt\", \"0.2\": \"\", \"d/h = 0.15\": \"\"}, {\"\": \"\", \"None\": \"\", \"0.2\": \"\", \"d/h = 0.15\": \"\"}, {\"\": \"\", \"None\": \"\", \"0.2\": \"\", \"d/h = 0.15\": \"\"}, {\"\": \"\", \"None\": \"\", \"0.2\": \"\", \"d/h = 0.15\": \"\"}], [{\"d/h = 0.20\": \"2\"}, {\"d/h = 0.20\": \"A\\ns\\n2\\nA\\ns\\n2\"}]]\n\n[FORMULAS]\nnbal\n= 0", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0385.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 386, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\n365\nReinforcement percentages. The area of longi-\ntudinal reinforcement, As, should lie within the\nfollowing limits:\ngreater of \n    \n0 10\n.\nN\nf\nEd\nyd\n and 0.002 Ac < As < 0.04Ac\nwhere\nfyd\ndesign yield strength of the reinforcement\nNEd\ndesign axial compression force\nAc\ncross-section of the concrete\nNote that the upper limit should be increased to\n0.08Ac at laps.\n8.11.7.2 Transverse reinforcement (links)\n(Cl. 9.5.3, EC 2)\nSize and spacing of links. The diameter of the\nlinks should not be less than 6 mm or one quarter\nof the maximum diameter of the longitudinal bar,\nwhichever is the greater.\nThe spacing of links along the column should not\nexceed the least of the following three dimensions:\n(i)\n20 times the minimum diameter of the longi-\ntudinal bars\n(ii) the lesser lateral dimension of the column\n(iii) 400 mm\nArrangement of links. With regard to the\narrangement of links around the longitudinal\nreinforcement, EC 2 recommends that:\n(a) every longitudinal bar placed in a corner should\nbe supported by a link passing around the bar\nand\n(b) no bar within a compression zone should be\nfurther than 150 mm from a restrained bar.\nDesign of columns\nTable 8.17\nExponent a for rectangular\ncross-sections\nNEd/NRd\n0.1\n0.7\n1.0\na =\n1.0\n1.5\n2.0\na\nis the exponent; a = 2 for circular cross\nsections and for rectangular sections is\nobtained from Table 8.17 in which NRd\nis the design axial resistance of section\n= Ac fcd + As fyd where Ac is the gross area\nof the concrete section and As is the area\nof longitudinal steel\nFor rectangular sections, use of this equation\nassumes that the ratio of the relative first order\neccentricities, namely ey/h and ez/b, satisfies the fol-\nlowing relationship\n0.2 ≤ (ey/h) ÷ (ez/b) ≤ 5\n(8.65)\nUnlike BS 8110, the design procedure in EC 2\nis iterative and involves estimating an area of longi-\ntudinal steel which is then checked using expres-\nsion 8.64. To cut down the number of iterations it\nwould be sensible to use the approach currently\nrecommended in BS 8110 (section 3.13.5.2(ii)) to\nobtain an initial estimate of the required area of\nlongitudinal steel, which can be verified using equa-\ntion 8.64, as shown in example 8.17.\n8.11.7 REINFORCEMENT DETAILS FOR\nCOLUMNS\n8.11.7.1 Longitudinal reinforcement\n(Cl. 9.5.2, EC 2)\nDiameter of bars. EC 2 recommends that the\nminimum diameter of longitudinal bars in columns\nis 12 mm.\n\n[TABLES]\n[[{\"0\": \"\", \"1\": \"Design of columns\"}, {\"0\": \"Table 8.17Exponent a for rectangular\", \"1\": \"Reinforcement percentages. The area of longi-\"}, {\"0\": \"cross-sections\", \"1\": \"lie  within  thetudinal  reinforcement,  As,  should\"}, {\"0\": \"\", \"1\": \"following limits:\"}, {\"0\": \"0.10.71.0NEd/NRd\", \"1\": \"0 10.N\"}, {\"0\": \"a =1.01.52.0\", \"1\": \"Edgreater of  and 0.002 Ac < As < 0.04Acfyd\"}, {\"0\": \"\", \"1\": \"where\"}, {\"0\": \"ais the exponent; a = 2 for circular cross\", \"1\": \"design yield strength of the reinforcementfyd\"}, {\"0\": \"sections and for rectangular sections is\", \"1\": \"design axial compression forceNEd\"}, {\"0\": \"\", \"1\": \"cross-section of the concreteAc\"}, {\"0\": \"obtained from Table 8.17 in which NRdis the design axial resistance of section\", \"1\": \"Note that the upper limit should be increased to\"}, {\"0\": \"= Ac fcd + As fyd where Ac is the gross area\", \"1\": \"0.08Ac at laps.\"}, {\"0\": \"of the concrete section and As is the areaof longitudinal steel\", \"1\": \"8.11.7.2 Transverse reinforcement (links)\"}, {\"0\": \"For  rectangular  sections,  use  of  this  equation\", \"1\": \"(Cl. 9.5.3, EC 2)\"}, {\"0\": \"assumes  that  the  ratio  of  the  relative  first  order\", \"1\": \"Size  and  spacing  of  links. The  diameter  of  the\"}, {\"0\": \"eccentricities, namely ey/h and ez/b, satisfies the fol-lowing relationship\", \"1\": \"links should not be less than 6 mm or one quarter\"}, {\"0\": \"\", \"1\": \"of the maximum diameter of the longitudinal bar,\"}, {\"0\": \"(8.65)0.2 ≤ (ey/h) ÷ (ez/b) ≤ 5\", \"1\": \"whichever is the greater.\"}, {\"0\": \"Unlike  BS  8110,  the  design  procedure  in  EC  2\", \"1\": \"The spacing of links along the column should not\"}, {\"0\": \"is iterative and involves estimating an area of longi-\", \"1\": \"exceed the least of the following three dimensions:\"}, {\"0\": \"tudinal  steel  which  is  then  checked  using  expres-\", \"1\": \"(i)20 times the minimum diameter of the longi-\"}, {\"0\": \"sion 8.64. To cut down the number of iterations it\", \"1\": \"tudinal bars\"}, {\"0\": \"would  be  sensible  to  use  the  approach  currently\", \"1\": \"(ii)the lesser lateral dimension of the column\"}, {\"0\": \"recommended in BS 8110 (section 3.13.5.2(ii)) to\", \"1\": \"(iii) 400 mm\"}, {\"0\": \"obtain  an  initial  estimate  of  the  required  area  of\", \"1\": \"Arrangement of links. With regard to the\"}, {\"0\": \"longitudinal steel, which can be verified using equa-\", \"1\": \"arrangement of links around the longitudinal\"}, {\"0\": \"tion 8.64, as shown in example 8.17.\", \"1\": \"reinforcement, EC 2 recommends that:\"}, {\"0\": \"8.11.7 REINFORCEMENT DETAILS FOR\", \"1\": \"(a)every longitudinal bar placed in a corner should\"}, {\"0\": \"COLUMNS\", \"1\": \"be supported by a link passing around the bar\"}, {\"0\": \"8.11.7.1 Longitudinal reinforcement\", \"1\": \"and\"}, {\"0\": \"(Cl. 9.5.2, EC 2)\", \"1\": \"(b) no  bar  within  a  compression  zone  should  be\"}, {\"0\": \"\", \"1\": \"further than 150 mm from a restrained bar.\"}, {\"0\": \"Diameter  of  bars. EC  2  recommends  that  the\", \"1\": \"\"}, {\"0\": \"minimum diameter of longitudinal bars in columns\", \"1\": \"\"}, {\"0\": \"is 12 mm.\", \"1\": \"\"}], [], []]", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0386.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 387, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\nEurocodes 2: Design of concrete structures\n366\nExample 8.13 Column supporting an axial load and uni-axial bending\n(EC 2)\nAn internal column in a multi-storey building is subjected to an ultimate axial load (NEd) of 1600 kN and bending\nmoment (M) of 60 kNm including effect of imperfections. Design the column cross-section assuming fck = 30 N mm−2,\nfyk = 500 N mm−2 and ∆cdev = 5 mm.\nCROSS-SECTION\nSince the design bending moment is relatively small, use equation 8.59 to size the column:\nnu = 1 + ω = 1 + Asfyd/A cfcd\nClause 9.5.2 of EC 2 stipulates that the percentage of longitudinal reinforcement, As, should generally lie within the\nfollowing limits:\ngreater of \n    \n0 10\n.\nN\nf\nEd\nyd\n and 0.002Ac < As < 0.04Ac\nAssuming that the percentage of reinforcement is equal to, say, 2 per cent gives\nAsc = 0.02Ac\nSubstituting this into the above equation gives\n    \n1 6\n10\n0 85\n30 1 5\n1\n0 02\n500 1 15\n0 85\n30 1 5\n6\n.   \n( .\n  \n/ . )    .\n(\n/ .\n)\n( .\n  \n/ . )\n×\n×\n=\n+\n×\nA\nA\nA\nc\nc\nc\nHence, Ac = 62267 mm2.\nFor a square column b = h = √62267 = 250 mm.\nTherefore a 300 mm square column is suitable.\nLONGITUDINAL STEEL\nDesign moment, MEd\nMinimum eccentricity, e0 = \n    \nh\n30\n300\n30\n10\n20\n  \n  \n \n  \n \n=\n=\n≥\nmm\nmm\nMinimum design moment = e0NEd = 20 × 10−3 × 1.6 × 103 = 32 kNm < M\nHence MEd = M = 60 kNm assuming λ < λlim\nDesign chart\nMinimum cover to links for exposure class XC1, cmin,dur = 15 mm (Table 8.9)\nAssuming diameter of longitudinal bars (Φ) = 25 mm, minimum cover to main steel for bond, cmin,b = 25 mm and the\nnominal cover, cnom = cmin,b + ∆cdev = 25 + 5 = 30 mm\nAssuming diameter of links, (Φ′) = 8 mm,\n⇒ minimum cover to links = cnom − Φ′ − ∆cdev = 30 − 8 − 5 = 17 mm > cmin,dur = 15 mm\nOK\nTherefore, d2 = 30 + 25/2 = 42.5 mm\n    \nd\nh\n2\n42 5\n300\n0 142\n  \n.   .\n=\n=\nRound up to 0.15 and use chart no. 1 (Fig. 8.32).\nLongitudinal steel area\n    \nN\nbhf\nEd\nck\n  \n.   \n  \n  \n  .\n=\n×\n×\n×\n=\n1 6\n10\n300\n300\n30\n0 593\n6\n    \nM\nbh f\nEd\nck\n2\n6\n2\n60\n10\n300\n300\n30\n0 074\n  \n  \n  \n  \n  .\n=\n×\n×\n×\n=\n\n[TABLES]\n[[{\"0\": \"Eurocodes 2: Design of concrete structures\"}, {\"0\": \"Example 8.13 Column supporting an axial load and uni-axial bending\"}, {\"0\": \"(EC 2)\"}, {\"0\": \"An  internal  column  in  a  multi-storey  building  is  subjected  to  an  ultimate  axial  load  (NEd)  of  1600  kN  and  bending\"}, {\"0\": \"moment (M) of 60 kNm including effect of imperfections. Design the column cross-section assuming fck = 30 N mm−2,\"}, {\"0\": \"fyk = 500 N mm−2 and ∆cdev = 5 mm.\"}, {\"0\": \"CROSS-SECTION\"}, {\"0\": \"Since the design bending moment is relatively small, use equation 8.59 to size the column:\"}, {\"0\": \"nu = 1 + ω = 1 + A sfyd/A cfcd\"}, {\"0\": \"Clause 9.5.2 of EC 2 stipulates that the percentage of longitudinal reinforcement, A s, should generally lie within thefollowing limits:\"}, {\"0\": \"0 10.NEdgreater of  and 0.002A c < A s < 0.04A c\"}, {\"0\": \"fyd\"}, {\"0\": \"Assuming that the percentage of reinforcement is equal to, say, 2 per cent gives\"}, {\"0\": \"A sc = 0.02A c\"}, {\"0\": \"Substituting this into the above equation gives\"}, {\"0\": \"× ×61 6  100 02A(500 1 15)c=+\"}, {\"0\": \"1  ×A(0 85  30 1 5)A(0 85  30 1 5)cc\"}, {\"0\": \"Hence, A c = 62267 mm2.For a square column b = h = √62267 = 250 mm.\"}, {\"0\": \"Therefore a 300 mm square column is suitable.\"}, {\"0\": \"LONGITUDINAL STEEL\"}, {\"0\": \"Design moment, MEd300\"}, {\"0\": \"h 3==≥    10 mm  20 mmMinimum eccentricity, e 0 =\"}, {\"0\": \"030\"}, {\"0\": \"Minimum design moment = e 0N Ed = 20 × 10−3 × 1.6 × 103 = 32 kNm < M\"}, {\"0\": \"Hence MEd = M = 60 kNm assuming λ < λlim\"}, {\"0\": \"Design chart\"}, {\"0\": \"Minimum cover to links for exposure class XC1, cmin,dur = 15 mm (Table 8.9)\"}, {\"0\": \"Assuming diameter of longitudinal bars (Φ) = 25 mm, minimum cover to main steel for bond, cmin,b = 25 mm and the\"}, {\"0\": \"nominal cover, cnom = cmin,b + ∆cdev = 25 + 5 = 30 mm\"}, {\"0\": \"Assuming diameter of links, (Φ′) = 8 mm,\"}, {\"0\": \"OK⇒ minimum cover to links = cnom − Φ′ − ∆cdev = 30 − 8 − 5 = 17 mm > cmin,dur = 15 mm\"}, {\"0\": \"Therefore, d2 = 30 + 25/2 = 42.5 mm\"}, {\"0\": \"d h42 52==    0 142\"}, {\"0\": \"300\"}, {\"0\": \"Round up to 0.15 and use chart no. 1 (Fig. 8.32).\"}, {\"0\": \"Longitudinal steel area\"}, {\"0\": \"6×N1 6  10Ed==\"}, {\"0\": \"0 593××bhf300  300  30ck\"}, {\"0\": \"6×M60  10Ed==\"}, {\"0\": \"0 0742××bh f300  300  30ck\"}, {\"0\": \"366\"}], [], []]\n\n[FORMULAS]\ncnom = cmin", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0387.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 388, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\n367\n(a)\n(b)\n1402 kN\n1412 kN\nBeam A\nBeam B\nExample 8.13 continued\n    \nA f\nbhf\nA\ns yk\nck\ns\n  \n  \n  \n  \n  .\n=\n×\n×\n×\n≈\n500\n300\n300\n30\n0 28\n(Fig. 8.32)\n⇒ As = 1512 mm2\nProvide 4H25 (1960 mm2)\n%Asc/Ac = 1960/(300 × 300) = 2.2% (acceptable)\nLINKS\nDiameter of links is the greater of:\n(i)\n6 mm\n(ii)\n1/4Φ = 1/4 × 25 = 6.25 mm\nSpacing of links should not exceed the lesser of:\n(i)\n20Φ = 20 × 25 = 500 mm\n(ii) least dimension of column = 300 mm\n(iii) 400 mm\nTherefore, provide H8 links at 300 mm centres.\nDesign of columns\nH8 – 300\n4H32\nExample 8.14 Classification of a column (EC 2)\nDetermine if column GH shown in Fig. 8.34a should be designed for first or second order effects assuming that it\nresists the design loads and moments in (b). Assume the structure is non-sway and fck = 25 Nmm−2.\nFig. 8.34\n\n[TABLES]\n[[{\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"4H32\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\"}], [{\"0\": \"Beam A\", \"1\": \"Beam B\"}, {\"0\": \"\", \"1\": \"(a)\"}], [], []]", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0388.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 389, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\nEurocodes 2: Design of concrete structures\n368\nExample 8.14 continued\nSLENDERNESS RATIO OF COLUMN GH\nEffective height\nkbeam A = 2(EI/L)A = \n    \n2\n275\n550\n12\n5\n10\n3\n3\nE\n  \n    \n×\n×\n×\n\n\n\n = 1.525 × 106 E\nkbeam B = 2(EI/L)B = \n    \n2\n275\n550\n12\n7\n10\n3\n3\nE\n  \n    \n×\n×\n×\n\n\n\n = 1.089 × 106 E\nkcolumn GH = (EI/L)GH = \n    \nE\n275\n275\n12\n3 5\n10\n3\n3\n  \n  .   \n×\n×\n×\n\n\n\n = 1.362 × 105 E\n    \nk\nk\nk\nk\nE\nE\nE\nG\ncolumn GH\nbeamA\nbeamB\n  \n  \n  \n.\n  \n.\n  \n  .\n  \n  .\n  .\n=\n+\n=\n×\n×\n+\n×\n=\n≥\n1 362\n10\n1 525\n10\n1 089\n10\n0 052\n0 1\n5\n6\n6\nkH = 0.1 (since column is assumed to be fully fixed at the base)\n    \nl\nl\nk\nk\nk\nk\no  .\n  .\n  \n  .\n  \n=\n+\n+\n\n\n\n\n+\n+\n\n\n\n\n0 5\n1\n0 45\n1\n0 45\n1\n1\n2\n2\n    \nl\nl\no  .   \n  \n.\n.\n  .\n  \n.\n.\n  .\n  .\n  \n=\n×\n+\n+\n\n\n\n\n+\n+\n\n\n\n=\n=\n0 5\n3500\n1\n0 1\n0 45\n0 1 1\n0 1\n0 45\n0 1\n0 59\n2068 mm\n(Note that using Table 3.21 of BS 8110, β = 0.75 ⇒ lo = β.lcol = 0.75 × (3500 − 550) = 2212.5 mm)\nRadius of gyration\nRadius of gyration, i, is given by\n    i\nI A\n  (\n)\n=\n/\n    =\n=\n=\n=\n [(\n/\n)/(\n)]  /\n  \n/\n  \n.  \nbh\nbh\nh\n3 12\n12\n275\n12\n79 4 mm\nSlenderness ratio\nSlenderness ratio, λ, is given by\n    \nλ  \n  \n.   \n=\n=\n=\nl\ni\no\n2067\n79 4\n26\nCRITICAL SLENDERNESS RATIO, λlim\nA = 0.7\nB = 1.1\nC = 1.7 − rm = 1.7 − (M01/M02) = 1.7 − (−29.4/58.8) = 2.2\nn = NEd/Acfcd = 1402 × 103/275 × 275 × (0.85/1.5) × 25 = 1.31\n    λlim  \n/\n  \n  .   .   . /\n.\n  \n.\n=\n=\n×\n×\n×\n=\n20\n20\n0 7\n1 1\n2 2\n1 31\n29 6\nABC\nn\nSince λ < λlim only first order effects need to be considered.\n\n[TABLES]\n[[{\"0\": \"\", \"1\": \"Eurocodes 2: Design of concrete structures\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"Example 8.14 continued\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"SLENDERNESS RATIO OF COLUMN GH\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"Effective height\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"275\", \"8\": \"×\", \"9\": \"3 550\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"kbeam A = 2(EI/L)A =\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \" 2E\", \"7\": \"×12\", \"8\": \"5\", \"9\": \"3×  10\", \"10\": \" \", \"11\": \"= 1.525 × 106 E\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"275\", \"8\": \"×\", \"9\": \"3 550\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"kbeam B = 2(EI/L)B =\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \" 2E\", \"7\": \"×12\", \"8\": \"7\", \"9\": \"3× 10\", \"10\": \" \", \"11\": \"= 1.089 × 106 E\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"275\", \"8\": \"×\", \"9\": \"3275\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"kcolumn GH = (EI/L)GH =\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \" E12\", \"7\": \"×\", \"8\": \"3 5\", \"9\": \"3×  10\", \"10\": \" \", \"11\": \"= 1.362 × 105 E\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"=\", \"2\": \"\", \"3\": \"k\", \"4\": \"column GH\", \"5\": \"\", \"6\": \"\", \"7\": \"=\", \"8\": \"\", \"9\": \"\", \"10\": \"1 362\", \"11\": \"\", \"12\": \"×\", \"13\": \"5 10E\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"=\", \"18\": \"≥\", \"19\": \"\"}, {\"0\": \"k\", \"1\": \"G\", \"2\": \"k\", \"3\": \"beamA\", \"4\": \"+\", \"5\": \"k\", \"6\": \"beamB\", \"7\": \"\", \"8\": \"1 525\", \"9\": \"×\", \"10\": \"610\", \"11\": \"E\", \"12\": \"+\", \"13\": \"1 089\", \"14\": \"×\", \"15\": \"10\", \"16\": \"6\", \"17\": \"E\", \"18\": \"0 052\", \"19\": \"0 1\"}, {\"0\": \"\", \"1\": \"kH = 0.1 (since column is assumed to be fully fixed at the base)\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"=l o\", \"1\": \"0 5l\", \"2\": \" \", \"3\": \"+1\", \"4\": \"\", \"5\": \"k\", \"6\": \"1\", \"7\": \"  1\", \"8\": \"+\", \"9\": \"k2\", \"10\": \"\", \"11\": \" \", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"0 45\", \"5\": \"\", \"6\": \"+k 1\", \"7\": \"\", \"8\": \"\", \"9\": \"+0 45\", \"10\": \"k\", \"11\": \"2\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"=l o\", \"1\": \"0 5\", \"2\": \"×\", \"3\": \"3500\", \"4\": \" \", \"5\": \"1\", \"6\": \"+\", \"7\": \"0 1\", \"8\": \"\", \"9\": \"  1\", \"10\": \"+\", \"11\": \"\", \"12\": \"\", \"13\": \"0 1\", \"14\": \" \", \"15\": \"=\", \"16\": \"0 59\", \"17\": \"l\", \"18\": \"=2068 mm\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"+0 45\", \"8\": \"0 1\", \"9\": \"\", \"10\": \"\", \"11\": \"0 45\", \"12\": \"\", \"13\": \"+0 1\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"(Note that using Table 3.21 of BS 8110, β = 0.75 ⇒ lo = β.lcol = 0.75 × (3500 − 550) = 2212.5 mm)\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"Radius of gyration\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"Radius of gyration, i, is given by\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"i\", \"3\": \"=\", \"4\": \"(I A\", \"5\": \")\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"=\", \"4\": \"[(bh\", \"5\": \"\", \"6\": \"3 12\", \"7\": \")/(bh\", \"8\": \"=)]\", \"9\": \"h/\", \"10\": \"12\", \"11\": \"=\", \"12\": \"275\", \"13\": \"/12\", \"14\": \"=\", \"15\": \"\", \"16\": \"79 4 mm\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"Slenderness ratio\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"Slenderness ratio, λ, is given by\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"=λ\", \"8\": \"iol\", \"9\": \"=\", \"10\": \"2067\", \"11\": \"\", \"12\": \"=\", \"13\": \"26\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"79 4\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"CRITICAL SLENDERNESS RATIO, λ\", \"2\": \"\", \"3\": \"\", \"4\": \"lim\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"A = 0.7\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"B = 1.1\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"C = 1.7 − rm = 1.7 − (M01/M02) = 1.7 − (−29.4/58.8) = 2.2\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"n = NEd/A cfcd = 1402 × 103/275 × 275 × (0.85/1.5) × 25 = 1.31\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"λ\", \"1\": \"lim\", \"2\": \"=\", \"3\": \"20\", \"4\": \"ABC\", \"5\": \"/\", \"6\": \"=n\", \"7\": \"20\", \"8\": \"×\", \"9\": \"×0 7\", \"10\": \"1 1\", \"11\": \"×\", \"12\": \"2 2\", \"13\": \"/\", \"14\": \"1 31\", \"15\": \"=\", \"16\": \"\", \"17\": \"29 6\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"Since λ < λ\", \"1\": \"lim only first order effects need to be considered.\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"368\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}, {\"0\": \"9780415467193_C08368\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\", \"14\": \"\", \"15\": \"\", \"16\": \"9/3/09, 3:06 PM\", \"17\": \"\", \"18\": \"\", \"19\": \"\"}], [], []]\n\n[FORMULAS]\nβ = 0; lo = β; rm = 1; 25 = 1", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0389.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 390, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\n369\n696 kN\n716 kN\n(a)\n(b)\nBeam A\nBeam B\n55 kNm\n27.5 kNm\nExample 8.15 Classification of a column (EC 2)\nDetermine if column PQ should be designed for second order effects assuming it resists the design loads and moment\nshown in Fig. 8.35b. Further assume the structure is non-sway and fck = 25 Nmm−2.\nFig. 8.35\nDesign of columns\nSLENDERNESS RATIO OF COLUMN PQ\nEffective height\nkbeam A = 2(EI/L)A = \n    \n2\n275\n550\n12\n5\n10\n3\n3\nE\n  \n    \n×\n×\n×\n\n\n\n = 1.525 × 106 E\nkbeam B = 2(EI/L)B = \n    \n2\n275\n550\n12\n7\n10\n3\n3\nE\n  \n    \n×\n×\n×\n\n\n\n = 1.089 × 106 E\nkcolumn PQ = (EI/L)PQ = \n    \nE\n275\n275\n12\n7\n10\n3\n3\n  \n    \n×\n×\n×\n\n\n\n = 6.8085 × 104 E\n    \nk\nk\nk\nk\nE\nE\nE\nP\ncolumn PQ\nbeamA\nbeamB\n  \n  \n  \n.\n  \n.\n  \n  .\n  \n  .\n  .\n=\n+\n=\n×\n×\n+\n×\n=\n≥\n6 8085\n10\n1 525\n10\n1 089\n10\n0 026\n0 1\n4\n6\n6\nkQ = 0.1 (since column is assumed to be fully fixed at the base)\n    \nl\nl\nk\nk\nk\nk\no  .\n  .\n  \n  .\n  \n=\n+\n+\n\n\n\n\n+\n+\n\n\n\n\n0 5\n1\n0 45\n1\n0 45\n1\n1\n2\n2\n    \nl\nl\no  .   \n  \n.\n.\n  .\n  \n.\n.\n  .\n  .\n  \n=\n×\n+\n+\n\n\n\n\n+\n+\n\n\n\n=\n=\n0 5\n7000\n1\n0 1\n0 45\n0 1 1\n0 1\n0 45\n0 1\n0 59\n4136 mm\n(Alternatively, using the coefficients in Table 3.21 of BS 8110, lo = β.lcol = 0.75 × (7000 − 550) = 4837.5 mm)\nRadius of gyration\nRadius of gyration, i, is given by\n    i\nI A\n  (\n)\n=\n/\n    =\n=\n=\n=\n [(\n)]  /\n  \n/\n  \n.  \nbh\nbh\nh\n3 12\n12\n275\n12\n79 4\n/\n)/(\nmm\n\n[TABLES]\n[[{\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"Design of columns\"}, {\"0\": \"\", \"1\": \"Example 8.15 Classification of a column (EC 2)\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"Determine if column PQ should be designed for second order effects assuming it resists the design loads and moment\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"shown in Fig. 8.35b. Further assume the structure is non-sway and fck = 25 Nmm−2.\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"696 kN\", \"12\": \"\", \"13\": \"55 kNm\"}, {\"0\": \"Beam A\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"Beam B\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"27.5 kNm\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"716 kN\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"(a)\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"(b)\", \"13\": \"\"}, {\"0\": \"Fig. 8.35\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"SLENDERNESS RATIO OF COLUMN PQ\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"Effective height\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"×275\", \"5\": \"\", \"6\": \"550\", \"7\": \"3\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"k beam A = 2(EI/L)A =\", \"2\": \"\", \"3\": \"2E\", \"4\": \" ×12  5\", \"5\": \"×\", \"6\": \"10\", \"7\": \" 3\", \"8\": \"= 1.525 × 106 E\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"×275\", \"5\": \"\", \"6\": \"550\", \"7\": \"3\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"k beam B = 2(EI/L)B =\", \"2\": \"\", \"3\": \"2E\", \"4\": \" ×12  7\", \"5\": \"×\", \"6\": \"10\", \"7\": \" 3\", \"8\": \"= 1.089 × 106 E\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"×  275\", \"5\": \"275\", \"6\": \"3\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"kcolumn PQ = (EI/L)PQ =\", \"2\": \"\", \"3\": \" E\", \"4\": \"××   127\", \"5\": \"10\", \"6\": \"3\", \"7\": \" \", \"8\": \"= 6.8085 × 104 E\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"=\", \"1\": \"k\", \"2\": \"column PQ\", \"3\": \"\", \"4\": \"=\", \"5\": \"\", \"6\": \"\", \"7\": \"6 8085\", \"8\": \"\", \"9\": \"×  10\", \"10\": \"4E\", \"11\": \"\", \"12\": \"=\", \"13\": \"≥\"}, {\"0\": \"k  Pk\", \"1\": \"beamA\", \"2\": \"\", \"3\": \"beamB\", \"4\": \"\", \"5\": \"1 525\", \"6\": \"×\", \"7\": \"10\", \"8\": \"6E\", \"9\": \"+\", \"10\": \"×1 089\", \"11\": \"6 10E\", \"12\": \"0 026\", \"13\": \"0 1\"}, {\"0\": \"\", \"1\": \"kQ = 0.1 (since column is assumed to be fully fixed at the base)\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \" =l 0 5lo\", \"1\": \"+1\", \"2\": \"\", \"3\": \"k1\", \"4\": \"  +1\", \"5\": \"\", \"6\": \"k\", \"7\": \"2\", \"8\": \" \", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"0 45\", \"3\": \"+\", \"4\": \"k1\", \"5\": \"0 45\", \"6\": \"\", \"7\": \"+  k\", \"8\": \"2\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"=×l   0 5o\", \"1\": \"7000\", \"2\": \" \", \"3\": \"+  1\", \"4\": \"0 1\", \"5\": \" \", \"6\": \" \", \"7\": \"+  1\", \"8\": \"\", \"9\": \"0 1\", \"10\": \" \", \"11\": \"=  0 59\", \"12\": \"=4136 mml\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"+  0 45\", \"5\": \"0 1\", \"6\": \"\", \"7\": \"\", \"8\": \"0 45\", \"9\": \"+\", \"10\": \"0 1\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"(Alternatively, using the coefficients in Table 3.21 of BS 8110, lo = β.lcol = 0.75 × (7000 − 550) = 4837.5 mm)\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"Radius of gyration\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"Radius of gyration, i, is given by\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"i\", \"1\": \"=\", \"2\": \"(I A\", \"3\": \")\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"=\", \"2\": \"[(\", \"3\": \"bh3 12\", \"4\": \"=)/(bh)]\", \"5\": \"h\", \"6\": \"/\", \"7\": \"12\", \"8\": \"=\", \"9\": \"275/\", \"10\": \"12\", \"11\": \"= 79 4\", \"12\": \"mm\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"369\"}, {\"0\": \"9780415467193_C08369\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"9/3/09, 3:06 PM\", \"13\": \"\"}], [], []]\n\n[FORMULAS]\nlo = β", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0390.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 391, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\nEurocodes 2: Design of concrete structures\n370\nExample 8.15 continued\nSlenderness ratio\nSlenderness ratio, λ, is given by\n    \nλ  \n  \n.   \n=\n=\n=\nl\ni\no\n4136\n79 4\n52\nCritical slenderness ratio, λlim\nA = 0.7\nB = 1.1\nC = 1.7 − rm = 1.7 − (M01/M02) = 1.7 − (−27.5/55) = 2.2\nn = NEd/Acfcd = 696 × 103/275 × 275 × 0.567 × 25 = 0.6493\n    λlim  \n/\n  \n  .   .   . /\n.\n  \n=\n=\n×\n×\n×\n=\n20\n20\n0 7\n1 1\n2 2\n0 6493\n42\nABC\nn\nSince λ > λlim column will need to be designed for second order moments.\nExample 8.16 Column design (i) λ < λlim; (ii) λ > λlim (EC 2)\nDesign the columns in Examples 8.14 and 8.15. Assume the effective creep coefficient, ϕef, is 0.87 and ∆cdev = 5 mm.\nCOLUMN GH\nLongitudinal steel\nDesign moment, MEd\n      \nei\ni\n  \n  \n  \n  \n= \n\n\n= \n\n\n× \n\n\n=\nθ B0\n2\n1\n200\n2068\n2\n5.2 mm\nMinimum eccentricity, \n    \ne\nmm\nmm\n0  \n  \n  .  \n  \n \n=\n=\n=\n≥\nh\n30\n275\n30\n9 2\n20\nMinimum design moment = e0NEd = 20 × 10−3 × 1402 = 28 kNm\nFirst order end moment, M02 = M + ei.NEd = 58.8 + 5.2 × 10−3 × 1402 = 66.1 kNm\nHence design moment, MEd = 66.1 kNm\nLongitudinal steel area\nAssume:\ndiameter of longitudinal steel, Φ = 32 mm\ndiameter of links, Φ′ = 8 mm\nminimum cover for durability, cmin,dur = 25 mm > cmin,b = Φ − Φ′(= 32 − 8 = 24 mm)\n⇒ nominal cover to reinforcement, cnom = c + ∆cdev = 25 + 5 = 30\nTherefore, d2 = Φ/2 + Φ′ + cnom = 32/2 + 8 + 30 = 54 mm\n    \nd\nh\n2\n54\n275\n0 196\n  \n  .\n=\n=\nUse graph with d2/h = 0.20 (Fig. 8.32a)\n    \nN\nbhf\nEd\nck\n  \n.\n  \n  \n  \n  .\n=\n×\n×\n×\n=\n1 402\n10\n275\n275\n25\n0 742\n6\n\n[TABLES]\n[[{\"0\": \"Eurocodes 2: Design of concrete structures\", \"1\": \"\"}, {\"0\": \"Example 8.15 continued\", \"1\": \"\"}, {\"0\": \"Slenderness ratio\", \"1\": \"\"}, {\"0\": \"Slenderness ratio, λ, is given by\", \"1\": \"\"}, {\"0\": \"io4136l===52λ\", \"1\": \"\"}, {\"0\": \"79 4\", \"1\": \"\"}, {\"0\": \"Critical slenderness ratio,  λλλλλlim\", \"1\": \"\"}, {\"0\": \"A = 0.7\", \"1\": \"\"}, {\"0\": \"B = 1.1\", \"1\": \"\"}, {\"0\": \"C = 1.7 − rm = 1.7 − (M01/M02) = 1.7 − (−27.5/55) = 2.2\", \"1\": \"\"}, {\"0\": \"n = NEd/A cfcd = 696 × 103/275 × 275 × 0.567 × 25 = 0.6493\", \"1\": \"\"}, {\"0\": \"λ==×××= 20ABC/n  20  0 7  1 1  2 2/0 6493  42lim\", \"1\": \"\"}, {\"0\": \"Since λ > λlim column will need to be designed for second order moments.\", \"1\": \"\"}, {\"0\": \"Example 8.16 Column design (i) λ < λlim; (ii) λ > λ\", \"1\": \"lim (EC 2)\"}, {\"0\": \"Design the columns in Examples 8.14 and 8.15. Assume the effective creep coefficient, ϕ\", \"1\": \"ef, is 0.87 and ∆cdev = 5 mm.\"}, {\"0\": \"COLUMN GH\", \"1\": \"\"}, {\"0\": \"Longitudinal steel\", \"1\": \"\"}, {\"0\": \"Design moment, MEd\", \"1\": \"\"}, {\"0\": \"      12068==×θ B 0=5.2 mm        eii\", \"1\": \"\"}, {\"0\": \"22002\", \"1\": \"\"}, {\"0\": \"h 3275===≥Minimum eccentricity, e     9 2 mm  20 mm0\", \"1\": \"\"}, {\"0\": \"030\", \"1\": \"\"}, {\"0\": \"Minimum design moment = e0NEd = 20 × 10−3 × 1402 = 28 kNm\", \"1\": \"\"}, {\"0\": \"First order end moment, M02 = M + ei.NEd = 58.8 + 5.2 × 10−3 × 1402 = 66.1 kNm\", \"1\": \"\"}, {\"0\": \"Hence design moment, MEd = 66.1 kNm\", \"1\": \"\"}, {\"0\": \"Longitudinal steel area\", \"1\": \"\"}, {\"0\": \"Assume:\", \"1\": \"\"}, {\"0\": \"diameter of longitudinal steel, Φ = 32 mm\", \"1\": \"\"}, {\"0\": \"diameter of links, Φ′ = 8 mm\", \"1\": \"\"}, {\"0\": \"minimum cover for durability, cmin,dur = 25 mm > cmin,b = Φ − Φ′(= 32 − 8 = 24 mm)\", \"1\": \"\"}, {\"0\": \"⇒ nominal cover to reinforcement, cnom = c + ∆cdev = 25 + 5 = 30\", \"1\": \"\"}, {\"0\": \"Therefore, d2 = Φ/2 + Φ′ + cnom = 32/2 + 8 + 30 = 54 mm\", \"1\": \"\"}, {\"0\": \"d h542==    0 196\", \"1\": \"\"}, {\"0\": \"275\", \"1\": \"\"}, {\"0\": \"Use graph with d2/h = 0.20 (Fig. 8.32a)\", \"1\": \"\"}, {\"0\": \"6×N1 402  10Ed==\", \"1\": \"\"}, {\"0\": \"0 742××bhf275  275  25ck\", \"1\": \"\"}, {\"0\": \"370\", \"1\": \"\"}], [], []]\n\n[FORMULAS]\nrm = 1; 25 = 0; M02 = M + ei; 1402 = 66; MEd = 66", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0391.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 392, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\n371\n    \nM\nbh f\nEd\nck\n2\n6\n2\n66 1\n10\n275\n275\n25\n0 127\n  \n.   \n  \n  \n  .\n=\n×\n×\n×\n=\n    \nA f\nbhf\nA\ns yk\nck\ns\n  \n  \n  \n  \n  .\n=\n×\n×\n×\n≈\n500\n275\n275\n25\n0 7\n(Fig. 8.32)\n⇒ As = 2647 mm2\nProvide 4H32 (3220 mm2)\nLinks\nDiameter of links is the greater of:\n(i)\n6 mm\n(ii)\n1/4Φ = 1/4 × 32 = 8 mm\nSpacing of links should not exceed the lesser of:\n(i)\n20Φ = 20 × 32 = 640 mm\n(ii) least dimension of column = 275 mm\n(iii) 400 mm\nTherefore, provide H8 at 275 mm centres.\nExample 8.16 continued\nCOLUMN PQ\nFirst order end moments, M01, M02\n      \nei\ni\n  \n  \n  \n  \n= \n\n\n= \n\n\n× \n\n\n=\nθ B0\n2\n1\n200\n4136\n2\n10.34 mm\nei.NEd = 10.34 × 10−3 × 696 = 7.2 kNm\nM01 = MQ + ei.NEd = −27.5 + 7.2 = −20.3 kNm\nM02 = MP + ei.NEd = 55 + 7.2 = 62.2 kNm\nEquivalent first order moment, M0Ed\nM0Ed = M0e = (0.6M02 + 0.4M01) ≥ 0.4M02 = 0.4 × 62.2 = 24.9 kNm\n= (0.6 × 62.2 + 0.4 × −20.3) = 29.2 kNm\nNominal second order moment, M2\nAssume\ndiameter of longitudinal steel (Φ) = 20 mm\ndiameter of links (Φ′) = 8 mm\nDesign of columns\nH8 – 275\n2H32\n2H32\nLongitudinal\nbars 4H32\n\n[TABLES]\n[[{\"0\": \"\", \"1\": \"\"}, {\"0\": \"\", \"1\": \"\"}], [], []]\n\n[FORMULAS]\n696 = 7; 7.2 = −20; .2 = 62; 62.2 = 24", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0392.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 393, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\nEurocodes 2: Design of concrete structures\n372\nExample 8.16 continued\nminimum cover for durability, cmin,dur = 30 mm > cmin,b (= Φ − Φ′ = 20 − 8 = 16 mm)\n⇒ nominal cover to reinforcement, cnom = c + ∆cdev = 30 + 5 = 35\nThus\nd = h − ((Φ/2 + Φ′ + cnom)\n= 275 − (20/2 + 8 + 35) = 222 mm\n    \n1\n0 45\n500 1 15 200\n10\n0 45\n222\n2 176\n10\n3\n5\nr\nd\no\nyd\n.\n  \n  (\n/ .\n)/\n  \n.\n  \n  .\n  \n=\n=\n×\n×\n=\n×\n−\nε\nβ = 0.35 + fck/200 − λ/150 = 0.35 + 25/200 − 52/150 = 0.1283\nKϕ = 1 + βϕef = 1 + 0.1283 × 0.87 = 1.111 ≥ 1.0\nAssume Kr = 0.8\n    \n1\n1\n0 8\n1 111\n2 176\n10\n1 934\n10\n5\n5\nr\nK K\nr\n  \n  .   .\n  .\n  \n  .\n  \n=\n\n\n\n=\n×\n×\n×\n=\n×\n−\n−\nr\no\nϕ\n      \ne\nr\n2\n2\n5\n2\n1\n10\n1 934\n10\n4136 10\n  \n/\n  .\n  \n  \n/\n  \n= \n\n\n\n=\n×\n×\n=\n−\nB0\n33.1 mm\nM2 = NEd.e2 = 696 × 33.1 × 10−3 = 23 kNm\nDesign moment, MEd\nMEd = maximum of {M0Ed + M2; M02; M01 + 0.5M2}\nMEd = maximum of {29.2 + 23 = 52.2 kNm; 62.2 kNm; −20.3 + 0.5 × −23 = 31.8 kNm}\nLongitudinal steel area\nd2 = Φ/2 + Φ′ + cnom = 20/2 + 8 + 35 = 53 mm\n    \nd\nh\n2\n53\n275\n0 193\n  \n  .\n=\n=\nUse graph with d2/h = 0.2 (Fig. 8.32)\n    \nN\nbhf\nEd\nck\n  \n  \n  \n  \n  .\n=\n×\n×\n×\n=\n696\n10\n275\n275\n25\n0 368\n3\n    \nM\nbh f\nEd\nck\n2\n6\n2\n62 2\n10\n275\n275\n25\n0 12\n  \n.   \n  \n  \n  .\n=\n×\n×\n×\n=\n    \nA f\nbhf\nA\ns yk\nck\ns\n  \n  \n  \n  \n  .\n=\n×\n×\n×\n=\n500\n275\n275\n25\n0 3\n⇒ As = 1134 mm2\nProvide 4H20 (1260 mm2)\nCheck assumed value of Kr\nnu = 1 + Asfyd/Acfcd = 1 + 1260 × (0.87 × 500)/(275 × 275 × 0.567 × 25) = 1.51\nn = NEd/Acfcd = 696 × 103/(275 × 275 × (0.85/1.5) × 25) = 0.65\n\n[TABLES]\n[[{\"0\": \"\", \"1\": \"Eurocodes 2: Design of concrete structures\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"Example 8.16 continued\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"minimum cover for durability, cmin,dur = 30 mm > cmin,b (= Φ − Φ′ = 20 − 8 = 16 mm)\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"⇒ nominal cover to reinforcement, cnom = c + ∆cdev = 30 + 5 = 35Thus\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"d = h − ((Φ/2 + Φ′ + cnom)\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"= 275 − (20/2 + 8 + 35) = 222 mm\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"1=\", \"1\": \"ε\", \"2\": \"yd\", \"3\": \"=\", \"4\": \"(\", \"5\": \"500 1 15 200\", \"6\": \"\", \"7\": \"3×  10=\", \"8\": \"\", \"9\": \"×\", \"10\": \"−5\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"ro\", \"1\": \"0 45\", \"2\": \"d\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"0 45\", \"7\": \"× 222\", \"8\": \"2 176\", \"9\": \"10\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"β = 0.35 + fck/200 − λ/150 = 0.35 + 25/200 − 52/150 = 0.1283\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"Kϕ = 1 + βϕ\", \"2\": \"\", \"3\": \"\", \"4\": \"ef = 1 + 0.1283 × 0.87 = 1.111 ≥ 1.0\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"Assume K r = 0.8\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"1\", \"1\": \"=\", \"2\": \"K K\", \"3\": \" ϕ\", \"4\": \"1\", \"5\": \" =\", \"6\": \"0 8\", \"7\": \"××1 111\", \"8\": \"2 176\", \"9\": \"−5×=10\", \"10\": \"1 934\", \"11\": \"×\", \"12\": \"10\", \"13\": \"−5\"}, {\"0\": \"r\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"ro\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"e2\", \"1\": \"=\", \"2\": \"  1\", \"3\": \"B0\", \"4\": \"/10\", \"5\": \"=\", \"6\": \"1 934\", \"7\": \"−5××  10\", \"8\": \"4136\", \"9\": \"2=/10\", \"10\": \"33.1 mm\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"r\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"M2 = NEd.e2 = 696 × 33.1 × 10−3 = 23 kNm\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"Design moment, MEd\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"MEd = maximum of {M0Ed + M2; M02; M01 + 0.5M2}\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"MEd = maximum of {29.2 + 23 = 52.2 kNm; 62.2 kNm; −20.3 + 0.5 × −23 = 31.8 kNm}\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"Longitudinal steel area\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"d2 = Φ/2 + Φ′ + cnom = 20/2 + 8 + 35 = 53 mm\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"d h2\", \"3\": \"=\", \"4\": \"53\", \"5\": \"=\", \"6\": \"0 193\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"275\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"Use graph with d2/h = 0.2 (Fig. 8.32)\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"NEd\", \"6\": \"=\", \"7\": \"3×696  10\", \"8\": \"\", \"9\": \"=\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"bhfck\", \"6\": \"\", \"7\": \"××275  275\", \"8\": \"25\", \"9\": \"0 368\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"MEd\", \"6\": \"=\", \"7\": \"6×62 2  10\", \"8\": \"\", \"9\": \"=\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"bh fck\", \"6\": \"\", \"7\": \"2××275  275\", \"8\": \"25\", \"9\": \"0 12\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"A fyk\", \"6\": \"=\", \"7\": \"×A  500s\", \"8\": \"\", \"9\": \"= 0 3\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"bhfck\", \"6\": \"\", \"7\": \"××275  275\", \"8\": \"25\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"⇒ A s = 1134 mm2\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"Provide 4H20 (1260 mm2)\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"Check assumed value of Kr\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"nu = 1 + A sfyd/A cfcd = 1 + 1260 × (0.87 × 500)/(275 × 275 × 0.567 × 25) = 1.51\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"\", \"1\": \"n = NEd/A cfcd = 696 × 103/(275 × 275 × (0.85/1.5) × 25) = 0.65\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}, {\"0\": \"372\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\", \"8\": \"\", \"9\": \"\", \"10\": \"\", \"11\": \"\", \"12\": \"\", \"13\": \"\"}], [], []]\n\n[FORMULAS]\nλ/150 = 0; 52/150 = 0; 0.87 = 1; 23 = 52; 23 = 31", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0393.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 394, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\n373\nH6 – 275\n4H20\n    \nK\nn\nn\nn\nn\nr\nu\nu\nbal\n  \n  \n  \n  .\n  .\n.\n  .\n  .\n=\n−\n−\n=\n−\n−\n=\n1 51\n0 65\n1 51\n0 4\n0 775\nTherefore assumed value is acceptable.\nLinks\nDiameter of links is the greater of:\n(i) 6 mm\n(ii)\n1/4Φ = 1/4 × 20 = 5 mm\nSpacing of links should not exceed the lesser of:\n(i)\n20Φ = 20 × 20 = 400 mm\n(ii) least dimension of column = 275 mm\n(iii) 400 mm\nTherefore, provide H6 links at 275 mm centres.\nExample 8.16 continued\nRELATIVE ECCENTRICITIES\nThe column is subject to an axial load, NEd = 1250 kN, a moment about the major axis (y-y), MEdy = 35 kNm and a\nmoment about the minor axis (z-z), MEdz = 25 kNm\n    \ne\nM\nN\ny\nEdy\nEd\nmm\n  \n  \n  \n  \n  \n \n=\n=\n×\n×\n=\n35\n10\n1250\n10\n28\n6\n3\n    \ne\nM\nN\nz\nEdz\nEd\nmm\n  \n  \n  \n  \n  \n \n=\n=\n×\n×\n=\n25\n10\n1250\n10\n20\n6\n3\n(ey/h) ÷ (ez/b) = (28/275) ÷ (20/275) = 1.4 > 0.2\nTherefore check column for bi-axial bending\nDesign of columns\nExample 8.17 Column subjected to combined axial load and biaxial\nbending (EC 2)\nCheck the column in Example 3.22(b) using the procedure in EC 2.\n2H25\nH8-275\n2H25\n275 × 275\n\n[TABLES]\n[[{\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"4H20\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"\", \"3\": \"\"}], [{\"0\": \"\", \"1\": \"\"}, {\"0\": \"\", \"1\": \"\"}, {\"0\": \"\", \"1\": \"\"}, {\"0\": \"\", \"1\": \"\"}], [], []]", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0394.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 395, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\nEurocodes 2: Design of concrete structures\n374\nExample 8.17 continued\nDESIGN ULTIMATE MOMENT OF RESISTANCE, MRd\nd2 = 35 + 8 + 25/2 = 55.5 mm and d2/h = 55.5/275 = 0.2\n    \nA f\nbhf\ns yk\nck\n  \n  \n  \n  \n  .\n=\n×\n×\n×\n=\n1960\n500\n275\n275\n25\n0 518\n    \nN\nbhf\nEd\nck\n  \n  \n  \n  \n  .\n=\n×\n×\n×\n=\n1250\n10\n275\n275\n25\n0 66\n3\n    \nM\nbh f\nRd\nck\n2\n0 105\n  .\n≈\n(Fig. 8.32)\n⇒ MRd = 54.6 kNm\nEXPONENT, a\nNRd = Acfcd + Asfyd\n= [2752 × (0.85 × 25/1.5) + 1960 × (500/1.15)] × 10−3\n= 1071.35 + 852.17 = 1923.5 kN\n    \nN\nN\nEd\nRd\n  \n.   .\n=\n=\n1250\n1923 5\n0 65\nFrom Table 8.17, a ≈ 1.46\nRESISTANCE CHECK\n    \nM\nM\nM\nM\nEdz\nRdz\na\nEdy\nRdy\na\n1.46\n1.46\n\n\n\n+ \n\n\n≤\n=\n×\n×\n\n\n\n\n+\n×\n×\n\n\n\n\n=\n+\n=\n<\n  \n    \n  \n.   \n  \n  \n.   \n  .\n  .\n  .\n  \n1\n25\n10\n54 6\n10\n35\n10\n54 6\n10\n0 32\n0 52\n0 84\n1\n6\n6\n6\n6\n\n[TABLES]\n[[{\"0\": \"Eurocodes 2: Design of concrete structures\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\"}, {\"0\": \"Example 8.17 continued\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\"}, {\"0\": \"DESIGN ULTIMATE MOMENT OF RESISTANCE, MRd\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"d2 = 35 + 8 + 25/2 = 55.5 mm and d2/h = 55.5/275 = 0.2\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\"}, {\"0\": \"\", \"1\": \"A fyk\", \"2\": \"\", \"3\": \"=\", \"4\": \"×1960  500\", \"5\": \"=\", \"6\": \"0 518\", \"7\": \"\"}, {\"0\": \"\", \"1\": \"bhfck\", \"2\": \"\", \"3\": \"\", \"4\": \"××275  275  25\", \"5\": \"\", \"6\": \"\", \"7\": \"\"}, {\"0\": \"\", \"1\": \"NEd\", \"2\": \"\", \"3\": \"=\", \"4\": \"3×1250  10\", \"5\": \"=\", \"6\": \"\", \"7\": \"\"}, {\"0\": \"\", \"1\": \"bhfck\", \"2\": \"\", \"3\": \"\", \"4\": \"××275  275  25\", \"5\": \"\", \"6\": \"0 66\", \"7\": \"\"}, {\"0\": \"\", \"1\": \"MRd\", \"2\": \"\", \"3\": \"≈\", \"4\": \"0 105\", \"5\": \"(Fig. 8.32)\", \"6\": \"\", \"7\": \"\"}, {\"0\": \"\", \"1\": \"bh fck\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"⇒ MRd = 54.6 kNm\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\"}, {\"0\": \"EXPONENT, a\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"NRd = A cfcd + A sfyd\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"= [2752 × (0.85 × 25/1.5) + 1960 × (500/1.15)] × 10−3\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\"}, {\"0\": \"\", \"1\": \"\", \"2\": \"= 1071.35 + 852.17 = 1923.5 kN\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\"}, {\"0\": \"\", \"1\": \"N NEd\", \"2\": \"=\", \"3\": \"\", \"4\": \"1250=  0 65\", \"5\": \"\", \"6\": \"\", \"7\": \"\"}, {\"0\": \"\", \"1\": \"Rd\", \"2\": \"\", \"3\": \"1923 5\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\"}, {\"0\": \"From Table 8.17, a ≈ 1.46\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\"}, {\"0\": \"RESISTANCE CHECK\", \"1\": \"\", \"2\": \"\", \"3\": \"\", \"4\": \"\", \"5\": \"\", \"6\": \"\", \"7\": \"\"}, {\"0\": \"a\", \"1\": \"\", \"2\": \"a\", \"3\": \"\", \"4\": \"\", \"5\": \"1.46\", \"6\": \"\", \"7\": \"1.46\"}], [], []]\n\n[FORMULAS]\n.5/275 = 0; MRd = 54; 3\n= 1071; 852.17 = 1923", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0395.png"}
{"pdf_file": "Design of Structural Elements_ Concrete, Steelwork, Masonry and Timber Designs to British Standards and Eurocodes, 3rd Edition   ( PDFDrive ).pdf", "page_num": 396, "prompt": "Analyze this page with diagrams, tables, formulas, calculations, and explanations.", "response": "[NATIVE TEXT]\n375\nChapter 9\nEurocode 3: Design\nof steel structures\nThis chapter describes the contents of selected sub-parts\nof Part 1 of Eurocode 3, the new European standard\nfor the design of buildings in steel, which is expected to\nreplace BS 5950 by about 2010. The chapter highlights\nthe principal differences between Eurocode 3 and BS\n5950 and illustrates the new design procedures by means\nof a number of worked examples on beams, columns\nand connections. To help comparison but primarily to\nease understanding of the Eurocode, the material has\nhere been presented in a similar order to that in Chap-\nter 4 of this book on BS 5950.\n9.1 Introduction\nEurocode 3 applies to the design of buildings and\ncivil engineering works in steel. It is based on limit\nstate principles and comes in several parts as shown\nin Table 9.1.\nPart 1, which is the subject of this discussion,\ngives the basic rules for design of buildings in steel.\nIt is largely similar in scope to BS 5950: Part 1,\nwhich it will replace by about 2010. Originally\nplanned as a three sub-part document, the norm-\native version was eventually published in twelve\nsub-parts as indicated in Table 9.2. This step was\ntaken in order to avoid repetition of design guidance\nand provide a concise set of standards for design of\nsteel buildings. But this also means that engineers\nTable 9.1 Overall scope of Eurocode 3\nPart\nSubject\n1\nGeneral rules and rules for buildings\n2\nSteel bridges\n3\nTowers, masts and chimneys\n4\nSilos, tanks and pipelines\n5\nPiling\n6\nCrane supporting structures\nTable 9.2 Scope of Part 1 of Eurocode 3\nPart\nSubject\n1.1\nGeneral rules and rules for buildings\n1.2\nStructural fire design\n1.3\nCold formed thin gauge members and sheeting\n1.4\nStainless steels\n1.5\nPlated structural elements\n1.6\nStrength and stability of shell structures\n1.7\nStrength and stability of planar plated structures\ntransversely loaded\n1.8\nDesign of joints\n1.9\nFatigue strength of steel structures\n1.10\nSelection of steel for fracture toughness and\nthrough thickness properties\n1.11\nDesign of structures with tension components\nmade of steel\n1.12\nSupplementary rules for high strength steel\nwill now have to refer to a number of standards\nin order to design even the simplest of elements.\nIn the case of beams, for example, the designer\nwill have to refer to Part 1.1, hereafter referred to\nas EC 3, for guidance on bending and shear, Part\n1.5, hereafter referred to as EC 3–5, for web and\nstiffener design and Part 1.8, hereafter referred to\nas EC 3–8, for connection design. In addition, but\nlike the other material-specific codes, i.e. EC 2–EC\n6 and EC 9, the designer will have to refer to EN\n1990 and Eurocode 1 to determine the design\nvalues of actions and combination of actions, includ-\ning values of the partial factors for actions.\nEC 3 was published in draft form in November\n1990 and then as a voluntary standard, DD ENV\n1993–1–1, in September 1992. It was finally\nissued as a Euronorm, EN 1993–1–1, but with a\nmuch reduced content, in 2004. EC 3 deals with\nthe following subjects:\n\n[TABLES]\n[[{\"0\": \"This chapter describes the contents of selected sub-parts\", \"1\": \"Table 9.2 Scope of Part 1 of Eurocode 3\"}, {\"0\": \"of  Part  1  of  Eurocode  3,  the  new  European  standard\", \"1\": \"\"}, {\"0\": \"for the design of buildings in steel, which is expected to\", \"1\": \"PartSubject\"}, {\"0\": \"replace BS 5950 by about 2010. The chapter highlights\", \"1\": \"\"}, {\"0\": \"the  principal  differences  between  Eurocode  3  and  BS\", \"1\": \"1.1General rules and rules for buildings\"}, {\"0\": \"5950 and illustrates the new design procedures by means\", \"1\": \"1.2Structural fire design\"}, {\"0\": \"of  a  number  of  worked  examples  on  beams,  columns\", \"1\": \"1.3Cold formed thin gauge members and sheeting\"}, {\"0\": \"and  connections.  To  help  comparison  but  primarily  to\", \"1\": \"1.4Stainless steels\"}, {\"0\": \"ease  understanding  of  the  Eurocode,  the  material  has\", \"1\": \"1.5Plated structural elements\"}, {\"0\": \"here been presented in a similar order to that in Chap-\", \"1\": \"1.6Strength and stability of shell structures\"}, {\"0\": \"ter 4 of this book on BS 5950.\", \"1\": \"1.7Strength and stability of planar plated structures\"}, {\"0\": \"\", \"1\": \"transversely loaded\"}, {\"0\": \"\", \"1\": \"1.8Design of joints\"}, {\"0\": \"9.1 Introduction\", \"1\": \"1.9Fatigue strength of steel structures\"}, {\"0\": \"Eurocode 3 applies to the design of buildings and\", \"1\": \"1.10Selection of steel for fracture toughness and\"}, {\"0\": \"civil engineering works in steel. It is based on limit\", \"1\": \"through thickness properties\"}, {\"0\": \"state principles and comes in several parts as shown\", \"1\": \"1.11Design of structures with tension components\"}, {\"0\": \"in Table 9.1.\", \"1\": \"made of steel\"}, {\"0\": \"Part  1,  which  is  the  subject  of  this  discussion,\", \"1\": \"1.12Supplementary rules for high strength steel\"}, {\"0\": \"gives the basic rules for design of buildings in steel.\", \"1\": \"\"}, {\"0\": \"It  is  largely  similar  in  scope  to  BS  5950:  Part  1,\", \"1\": \"\"}, {\"0\": \"which it  will  replace  by  about  2010.  Originally\", \"1\": \"will  now  have  to  refer  to  a  number  of  standards\"}, {\"0\": \"planned  as  a  three  sub-part  document,  the  norm-\", \"1\": \"in  order  to  design  even  the  simplest  of  elements.\"}, {\"0\": \"ative  version  was  eventually  published  in  twelve\", \"1\": \"In  the  case  of  beams,  for  example,  the  designer\"}, {\"0\": \"sub-parts  as  indicated  in  Table  9.2.  This  step  was\", \"1\": \"will have to refer to Part 1.1, hereafter referred to\"}, {\"0\": \"taken in order to avoid repetition of design guidance\", \"1\": \"as EC 3, for guidance on bending and shear, Part\"}, {\"0\": \"and provide a concise set of standards for design of\", \"1\": \"1.5,  hereafter  referred  to  as  EC 3–5,  for  web  and\"}, {\"0\": \"steel buildings. But this also means that engineers\", \"1\": \"stiffener  design  and  Part  1.8,  hereafter  referred  to\"}, {\"0\": \"\", \"1\": \"as EC 3–8, for connection design. In addition, but\"}, {\"0\": \"Table 9.1 Overall scope of Eurocode 3\", \"1\": \"like the other material-specific codes, i.e. EC 2–EC\"}, {\"0\": \"\", \"1\": \"6 and EC 9, the designer will have to refer to EN\"}, {\"0\": \"PartSubject\", \"1\": \"1990  and  Eurocode  1  to  determine  the  design\"}, {\"0\": \"\", \"1\": \"values of actions and combination of actions, includ-\"}, {\"0\": \"1General rules and rules for buildings\", \"1\": \"ing values of the partial factors for actions.\"}, {\"0\": \"2Steel bridges\", \"1\": \"EC 3 was published in draft form in November\"}, {\"0\": \"3Towers, masts and chimneys\", \"1\": \"1990 and then as a voluntary standard, DD ENV\"}, {\"0\": \"4Silos, tanks and pipelines\", \"1\": \"1993–1–1, in  September  1992. It  was  finally\"}, {\"0\": \"5Piling\", \"1\": \"issued  as  a  Euronorm,  EN  1993–1–1,  but  with  a\"}, {\"0\": \"6Crane supporting structures\", \"1\": \"much  reduced  content,  in  2004.  EC  3  deals  with\"}, {\"0\": \"\", \"1\": \"the following subjects:\"}], [], []]", "page_type": "mixed", "image": "Design of Structural Elements_ Concr_a6902759_p0396.png"}