id stringlengths 4 6 | question stringlengths 96 868 | answer stringlengths 4 244 | topic stringclasses 25
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S_Q1 | Force F has a magnitude of 600 lbf acting 60 degrees CCW from the positive x-axis. Determine the scalar components of F in the x and y directions. | Fx = 300 lbf, Fy = 519.6 lbf | force_vectors |
S_Q2 | Force F has a magnitude of 600 lbf acting 60 degrees CCW from the positive x-axis. A new coordinate system is created by rotating the x- and y-axes 65 degrees clockwise. Determine the scalar components of F in the x' and y' directions. | Fx' = -344.1 lbf, Fy' = 491.5 lbf | force_vectors |
S_Q3 | Find the magnitude and direction of force F which has scalar components: Fx = -2 N and Fy = -6 N | 6.325 N, 251.6 degrees | force_vectors |
S_Q4 | Vector R has vector components A and B where A has a magnitude of 4 kN and points 35 degrees CW from the positive x-axis, and B has a magnitude of 6 kN pointing 85 degrees CCW from the positive x-axis. Find the magnitude and direction of force of the resultant R. | 5.3 kN, 44.1 degrees CCW from the positive x-axis | force_vectors |
S_Q5 | Determine the resultant of three forces A, B and C, with scalar components of A (-6.26, 12.5 lbf), B (35.4, -35.4 lbf) and C (-36.8, 27.6 lbf). | 9.06 lbf, 148.3 degrees | force_vectors |
S_Q6 | Three forces act on a particle. Force A is 600 N acting in the negative y direction. Force B acts 15 degrees CCW from the positive y-axis. Force C acts 60 degrees CCW from the positive x-axis. Determine the magnitudes of forces B and C. | B = 424.3 N, C = 219.6 N | force_vectors |
S_Q7 | A small massless ring is located at (0, 0m). A is located at (0, -4m), B is located at (-2, 6m) and C is located at (4, 3m). A force of 400 N is applied to the ring in the direction towards C. The ring is held in equilibrium by two inextensible cables, one connected to point A and one connected to point B. Determine th... | Cable A = 1200 N, Cable B = 1012 N | particle_equilibrium |
S_Q8 | A mass of 10 kg is held in equilibrium by two cables, cable A and cable B. The mass is located at (0, 0m). Point A is located at (-4.25, 3.5m) and point B is located at (4.5, 3.5m). Determine the tension in cable A and cable B. | Cable A = 79.36 N, Cable B = 77.61 N | particle_equilibrium |
S_Q9 | A 2 lb cylinder rests in a trough with smooth frictionless surfaces. The left side of the trough is angled at 35 degrees from the horizontal. The right side of the trough is angled at 60 degrees to the horizontal. Determine the reactions on the cylinder from the left side and the right side of the trough. | Left side = 1.74 lb, right side = 1.15 lb | particle_equilibrium |
S_Q10 | Cable ABC has a length of 8 ft and the cable supports a weight of 100 lbf riding on a frictionless pulley of negligible radius located at B. The cable is supported at A (0, 0 ft) and C (6.5, 2.5 ft). Determine the horizontal distance from A of the pulley and the tension in the cable, required for equilibrium. | Distance = 1.51 ft, tension = 85.8 lbf | particle_equilibrium |
S_Q11 | A 320 mm x 550 mm steel plate 35 mm thick is suspended from a point P located 350 mm above the center of the plate (in the z direction). Three cables support the plate at A, B and D. The four corners of the plate are E located at (0, 0mm), C located at (0, 550mm), B located at (320mm, 550mm) and A located at (320, 0mm)... | Cable A = 97.6 N, cable B = 227.8 N, cable D = 275.4 N | particle_equilibrium |
S_Q12 | A system of cables are suspended by connections at B, E and D. A weight of 75 lbf is located at A and a weight of 55 lbf is located at C. Point B is located at the left end of the system of cables, and cable B to A forms an angle of 10 degrees to the horizontal where A is below and to the right of B. Cable A to C forms... | Cable AB = 171.4 lbf, cable AC = 174.8 lbf, cable CE = 106.7 lbf, cable CD = 132.3 lbf | particle_equilibrium |
S_Q13 | Two cylinders are placed in a 14 ft wide container. The cylinder that sits on the bottom of the container has a radius of 5 ft and weighs 3750 lbf. The second cylinder sits on top of the other cylinder and has a radius of 4.5 ft and weighs 3000 lbf. Assuming smooth contact surfaces determine the magnitude at the contac... | 3406 lbf | particle_equilibrium |
S_Q14 | Point A is located at (-6, -2m), point B is located at (8, -4m) and point C is located at (0, 6m). A force of magnitude 40 kN acts along the line passing through points A and B. Determine to moment of the force about point C, with CCW moments positive. | 350.7 kN.m | moments |
S_Q15 | A 16 in long control rod is connected to the ground at B and extends in a direction 100 degrees CCW from the positive x-axis to its other end at A. A force is applied at the end of the rod at A, in a direction of 45 degrees CW from the line of action of the rod. If the force creates a CW moment of 893.8 lbf.in about po... | 79 lbf | moments |
S_Q16 | An L-shaped bracket ABC is pinned at A (0,0). Point B is located at (-12, 0cm) and point C is located at (-12, 6cm). A cable extends from point B to a support at point D (-15, 11cm). A force of 45 N is applied to the bracket at B, in a direction 50 degrees CW from the positive x-axis. Determine the moment of the force ... | MA = 413.7 N.cm, Cable CD = 57.43 N | moments |
S_Q17 | A rigid bent bar ABCD is pinned at B. The points are located at: A (0,0), B (1, 0ft), C (1, 1ft), D (4, 1ft). A force of 25 lbf is applied at A in a direction of 60 degrees CW from the positive x-axis. A force of 25 lbf is applied at C in a direction of 150 degrees CW from the positive x-axis. A force of 25 lbf is appl... | 128.35 degrees | moments |
S_Q18 | A solid rectangle ABCD has corners A (0, 0m), B (0, 4m), C (10, 4m) and D (10, 0m). Two force couples act on the rectangle. One couple consists of 100 N acting in the negative x-axis direction at A and 100 N acting in the positive x-axis direction at C. The other couple consists of 35 N acting at B in a direction 120 d... | 26.9 N.m | moments |
S_Q19 | An 8 m long cantilever beam has two vertical downwards forces applied, a force of 120 kN applied at the end of the cantilever and a force of 75 kN located at 5.2 m from the end of the cantilever. Determine the single equivalent resultant force and its location from the left end of the beam. | 195 kN located 6 m from the left end | moments |
S_Q20 | An L-bracket has its corner located at C (0, 0 in), its horizontal leg extends 5 in to end A in the positive x direction and its vertical leg extends 4 in to end B in the positive y direction. A vertical downwards force of 150 lbf is applied at C. A force of 160 lbf is applied at A in a direction 60 degrees CCW from th... | 80.8 lbf acting at -8.14 degrees, 1010 lbf.in | moments |
S_Q21 | A force couple systems acting at the origin (0, 0m) consists of a force of 90 N in a direction 20 degrees CCW from the positive x-axis and a couple of 369 N.m CW. Replace the force couple with a single force which has the same effect. Specify the magnitude and direction (CCW from the positive x-axis) of the resultant f... | 90 N at 20 degrees, passing through the x-axis at -12 m | moments |
S_Q22 | The system consists of a rigid linkage. All dimensions are in inches. Point B is a pin support located at the origin, B = (0, 0). From point B, a rigid member extends upward and to the left to point A. Point A is located 24 in to the left of B and 20 in above B, giving A = (−24, 20). A cable connects point A to point C... | 236.7 lbf.in | rigid_body_equilibrium |
S_Q23 | A 75 kg pole is being raised by pulling a cable. Point A is a pin support located on the ground. The member AB is inclined upward from A at an angle of 70 degrees CCW from the positive x-axis. At the end of the pole at point B a cable is attached in order to raise the pole, and the cable extends towards the left creati... | 130.9 N | rigid_body_equilibrium |
S_Q24 | The left end of a 1 m cantilever beam OABC is fixed at point O, which is located at O = (0, 0). Point A lies on the beam 0.2 m to the right of O. Point B lies a further 0.3 m to the right of A. Point C is located 0.5 m to the right of B, at the right end of the beam. An upward vertical force acts at point A. At point C... | MO = 375.7 N.m CCW, Ox = 84.3 N, Oy = -29.3 N | rigid_body_equilibrium |
S_Q25 | A 20 ft long beam ABC supports a frictionless pulley with radius 6 in at point B, located 13 ft from point A at the left end. Point A is a pin support. Point C is the right end of the beam, where the beam is supported by a roller on an inclined surface that makes an angle of 25 degrees with the horizontal. Point D lies... | Reaction C = 62.1 lbf at 115 degrees, Ax = 162.2 lbf, Ay = 30.3 lbf | rigid_body_equilibrium |
S_Q26 | A rigid V-shaped two-member linkage is pinned at A. From point A, one rigid member extends upward and to the left at an angle of 20 degrees above the horizontal, terminating at point B. A vertical downward force acts at point B. From point A, a second rigid member extends upward and to the right at an angle of 30 degre... | B = 507 lbf, C = 476.5 lbf | rigid_body_equilibrium |
S_Q27 | A car is parked on a 15 degree slope, with rear wheels locked by the parking brake. The vehicle dimensions (relative to when it is sitting horizontal) are: the wheelbase (distance between the front and rear wheels) is 2579 mm, the mass is 1291 kg, and the location of the center of gravity is 722 mm behind and 664 mm ab... | Front parallel = 0 N, front perpendicular = 3982 N, rear parallel = 1639 N, rear perpendicular = 2134 N | rigid_body_equilibrium |
S_Q28 | A triangular plate ABC is secured by a pin at A and a roller at C. The interior angles of the triangle at the base are both 65 degrees. At the top point B a force is applied in the direction 60 degrees CCW from edge AB. Determine the reactions at the pin and the roller when the plate is subjected to a 500 lbf load at B... | C = 512.3 lbf, Ax = 286.8 lbf, Ay = 102.7 lbf | rigid_body_equilibrium |
S_Q29 | A truss is pinned at the left side at A, and sits on a roller at the right side at D. The bottom horizontal chord AFED consists of members AF, FE and ED which are all 2 m in length. The top horizontal chord is BC, where B is located 2.6 m above F and C is located 2.6 m above E. The truss has other members AB, BF, BE, E... | D = 4.5 kN upwards | trusses |
S_Q30 | A horizontal beam ABC is loaded with a force of 150 kN at B in the direction 30 degrees CW from the positive x-axis. Distance AB is 0.4 m and distance BC is 1.6 m. Left end A is pinned and right end C rests on a roller. Determine the magnitudes of the resultant reactions at A and C. | A = 143.1 kN, C = 15 kN | trusses |
S_Q31 | A cantilever truss is connected to a wall with pinned joints at E and vertically above E at D. The horizontal bottom chord of the truss extends a distance of X m from E to C, then a further 2X m from C to A. The diagonal top chord extends right and downwards from D to B, then B to A. The angle between EC and internal m... | AB = 800 kN, AC = -693 kN, BC = -823 kN, BD = 1275 kN, CD = 1689 kN, CE = -1949 kN | trusses |
S_Q32 | A triangle truss has horizontal bottom chord members AC and CD, and is pinned at A at the left and sits on a roller at D at the right. A vertical internal member extends vertically upwards from C to B. The angle between members AB and AC is 30 degrees. The angle between members CD and BD is 30 degrees. A vertical downw... | BD = -796 kN, CD = 689 kN, AC = 689 kN, BC = 625 kN, AB = -736 kN | trusses |
S_Q33 | A symmetric triangular truss is pinned at the left side at A. The horizontal bottom chord consists of members extending from A to C, from C to E, from E to G and from G to H. Members AC, CE, EG and GH are all 6 ft long. The truss sits on a roller at H. Joint B is located 5 ft vertically above C. Joint D is located 10 f... | AB = -937 lbf, AC = 720 lbf, BC = 0, BD = -625 lbf, BE = -312 lbf, CE = 720 lbf, DE = 400 lbf, DF = -625 lbf, EF = -312 lbf, EG = 720 lbf, FG = 0, FH = -937.2 lbf, GH = 720 lbf | trusses |
S_Q34 | A cantilever truss connects to a wall with pins at F and G, and F is 6.5 ft vertically above G. The top chord extends horizontally from F to D, from D to B and from B to A. Members FD, DB and BA are each 5 ft long. The diagonal bottom chord extends from G right and upwards towards A, including members GE where joint E ... | DB = 682 lbf, DC = 0, EC = -805 lbf | trusses |
S_Q35 | A triangular Howe truss has overall dimensions of 36 ft wide and 9 ft high. The truss is pinned at A at the left and sits on a roller at G at the right. The horizontal bottom chord consists of members from left to right of AH, HJ, JK, KL, LM, MG and each of these members is 6 ft long. Joint B is located vertically abov... | DE = -484 lbf, KE = 0, KL = 433 lbf | trusses |
S_Q36 | A rectangular Pratt truss has overall dimensions of 16 m wide and 4.5 m high. The top and bottom chords are both horizontal. The truss is pinned at A at the left and sits on a roller at G at the right. The bottom chord consists of members from A to H, from H to J, from J to K and from K to G. Members AH, HJ, JK and KG ... | DE = 12.5 N, JE = 210 N, JK = 273 N | trusses |
S_Q37 | A trussed frame is connected to a wall at A and B. B (0, 0m) is a roller joint. A (0, 6m) is a pin joint. Joint F is located at (6, 6m) and joint C is located at (10, 10m). Truss members include AB, members from A right and upwards towards C and members from B right and upwards towards C. Joint D is at the midpoint bet... | 6120 kg | trusses |
S_Q38 | An A-frame consists of three members. Member AC is pinned at A (0, 0m) and connected to member BC at C (2, 4m) with a pin joint. Member BC is supported by a roller at B (4, 0m). Member DF is 1.5m long and is connected to AC at D (1.5, 3m) and BC at E (2.5, 3m) with pin joints. Member DF cantilevers out from E a distanc... | Ax = 0 N, Ay = 27.5 N, Dx = 82.5 N, Dy = 55 N, Cx = -82.5 N, Cy = -82.5 N | frames |
S_Q39 | A frame consists of two members AB and BC. The left member AB is pinned at A (0, 0m). The right member is pinned at C (8, 2m). The two members are pin connected at B (3, 4m). A vertical downwards force of 250 N is applied at B. Determine the scalar components of the reactions at pins A and C. | Ax = 144.2 N, Ay = 192.3 N, Cx = -144.2 N, Cy = 57.7 N | frames |
S_Q40 | A frame consists of two members AB and BC. The left member AB is pinned at A (0, 0ft). The right member is pinned at C (8, 3ft). The two members are pin connected at B (5, 3ft). A horizontal force of 175 lbf in the positive x direction is applied at the midpoint of AB. Determine the scalar components of the reactions a... | Ax = -118.8 lbf, Ay = -18.8 lbf, Cx = -56.3 lbf, Cy = 18.8 lbf | frames |
S_Q41 | A frame consists of two members AB and BC. The left member AB is pinned at A (0, 0ft). The right member is pinned at C (8, 0ft). The two members are pin connected at B (4, 5ft). A horizontal force of 475 lbf in the negative x direction is applied at the midpoint of AB. A CCW moment of 800 lb.ft is applied at the midpoi... | Ax = 436.3 lbf, Ay = 248.4 lbf, Cx = 38.8 lbf, Cy = -248.4 lbf | frames |
S_Q42 | A frame consists of two members AB and BC. The left member AB is pinned at A (0, 0m). The right member is pinned at C (10, -1m). The two members are pin connected at B (5, 3m). A horizontal force of 75 N in the negative x direction is applied at the midpoint of AB. A CW moment of 100 N.m is applied at the midpoint of B... | Ax = 44.6 N, Ay = 4.29 N, Cx = 30.4 N, Cy = -4.29 N | frames |
S_Q43 | Given the function (y = -1.5.x^2 + 2.x + 2.5), determine the area under the curve from the y-axis to the point where the curve crosses the positive x-axis. The x- and y- coordinates are in inches. | 5.03 in^2 | centroids |
S_Q44 | Use integration with horizontal strips to determine the area of the spandrel bounded by the function (y = h - k.x^0.5) and the lines y = h and x = b, and also find the coordinates of its centroid. Note: b and h are constants. Give your answers for the area and the centroid in terms of b and h. | Area = (b.h / 1.5), centroid x coordinate = (1.5.b / 2.5), centroid y coordinate = (2.5.h / 4) | centroids |
S_Q45 | Determine the coordinates of the centroid of the shaded area bounded by the y-axis, a parabola passing through the origin (0, 0m) and point A, and a straight line passing through points A and B. Point A is located at (9, 3m) and B is located at (0, 9m). | (3.2, 3.7m) | centroids |
S_Q46 | A 16 ft long beam is supported by a pin at A located 1 ft from the left end, and a roller at B located 2 ft from the right end. A downwards vertical uniformly distributed load of 20 lbf/ft is applied between 7 ft from the left end and 4 ft from the right end. The beam weight is negligible. Determine the reactions at A ... | Ax = 0 lbf, Ay = 34.6 lbf, By = 65.4 lbf | beam_reactions |
S_Q47 | A 15 m long beam is supported by a pin at the left end A (0, 0m) and a roller at the right end B (15, 0m). Point C is located at (1, 0m) and D is located at (12, 0m). A downwards vertical distributed load is applied to the beam and varies linearly between 45 kN/m at C to 60 kN/m at D. The beam self weight is 15 kN/m. D... | Ax = 0 kN, Ay = 429.7 kN, B = 372.8 kN | beam_reactions |
S_Q48 | A 20 m long beam is supported by a pin at the left end A (0, 0m) and a roller at the right end B (20, 0m). Point C is located at (6, 0m), D is located at (12, 0m) and E is located at (19, 0m). A downwards vertical distributed load is applied to the beam and varies linearly between 0 kN/m at C to 60 kN/m at D, then rema... | Ax = 0 kN, Ay = 184.5 kN, By = 415.5 kN | beam_reactions |
S_Q49 | An 18 m long beam supports a vertical downwards load that varies uniformly from 50 N/m at the left end to 150 N/m at the right end. The beam is pinned at A (0, 0m) and sits on a roller at B (10, 0m). Determine the internal shear and bending moment at a section passing through point C (6, 0m). | V = -490 N, M = -1640 N.m | beam_internal_forces |
S_Q50 | A beam BC is 4 ft long and is pinned at the right end C (4, 0ft). At the left end B (0, 0ft) the beam is pin connected to member AB. A is located to the left and upwards from B, creating an angle of 25 degrees with the x-axis. Beam BC supports a vertical downwards uniformly distributed load of 15 lbf/ft. Determine the ... | V = 0 lbf, N = 64.3 lbf, M = 30 lbf.ft | beam_internal_forces |
S_Q51 | A 12 m long beam is pinned at the left end A and has a roller at the right end B. Vertical downwards forces are 500 kN at 8 m from A, and 650 kN at 10 m from A. Find the shear and bending moment equations as function of x for the three ranges: 0m < x < 8m, 8m < x < 10m, 10m < x < 12m. | (0m < x < 8m: V = 275 kN, M = 275.x kN.m), (8m < x < 10m: V = -225 kN, M = 275.x - 500.(x - 8)), (10m < x < 12m: V = -875 kN, M = 275.x - 500.(x - 8) - 650.(x - 10)) | beam_internal_forces |
S_Q52 | A 20 m long beam is pinned at the left end A and has a roller at the right end B. Vertical downwards forces are 165 kN at 2 m from A, and 15 kN at 9 m from A. Find the shear and bending moment diagrams, expressed as a series of points at critical locations (x distance from the left end, value). | V (m, kN): (0, 0), (0, 157), (2, 157), (2, -8.3), (9, -8.3), (9, -23.3), (20, -23.3), (20, 0)
M (m, kN.m): (0, 0), (2, 314), (9, 256), (0, 0) | beam_internal_forces |
S_Q53 | A 6 ft long cantilever beam is fixed at the left end A. Vertical downwards forces are 140 lbf at 3 m from A, and 240 lbf at 6 m from A. A CCW moment of 2340 lbf.ft is applied at 4 m from A. Find the shear and bending moment diagrams, expressed as a series of points at critical locations (x distance from the left end, v... | V (ft, lbf): (0, 0), (0, 380), (3, 380), (3, 240), (6, 240), (6, 0)
M (ft, lbf.ft): (0, 0), (0, 480), (3, 1620), (4, 1860), (4, -480), (6, 0) | beam_internal_forces |
S_Q54 | A 20 m long beam is pinned at the left end A and has a roller at the right end B. Vertical downwards uniformly distributed loads are: 200 kN/m from A to 9 m from A, and 180 kN/m from 15 m from A to 20 m from A. Find the shear and bending moment diagrams, expressed as a series of points at critical locations (x distance... | V (m, kN): (0, 0), (0, 1508), (9, -293), (15, -293), (20, -1192), (20, 0)
M (m, kN.m): (0, 0), (7.5, 5681), (9, 5468), (15, 3713), (20, 0) | beam_internal_forces |
S_Q55 | A 20 m long beam is pinned at the left end A and has a roller at the right end B. Vertical downwards loads are 400 kN at 2 m from A and a uniformly distributed load of 300 kN/m from 12 m from A to 17 m from A. Find the shear and bending moment diagrams, expressed as a series of points at critical locations (x distance ... | V (m, kN): (0, 0), (0, 773), (2, 773), (2, 373), (12, 373), (17, -1128), (20, -1128), (20, 0)
M (m, kN.m): (0, 0), (2, 1545), (12, 5270), (13.2, 5501), (17, 3383), (20, 0) | beam_internal_forces |
S_Q56 | A 18 m long beam is pinned at the left end A and has a roller at the right end B. Vertical downwards linearly varying distributed loads are 0 kN/m at A varying linearly to 25 kN/m at 9 m from A, then varying linearly to zero at B. Find the shear and bending moment diagrams, expressed as a series of points at critical l... | V (m, kN): (0, 0), (0, 113), (9, 0), (18, -113), (18, 0)
M (m, kN.m): (0, 0), (9, 675), (18, 0) | beam_internal_forces |
S_Q57 | A 20 m long beam is pinned at the left end A and has a roller at the right end B. The beam is subjected to a vertical downwards symmetric distributed parabolic loading w(x), given by the equation w(x) = -2.x^2 + 40.x kN/m. Find the maximum values of shear and moment and their locations in the beam. | V = 1333 kN at x = 0 m and x = 20 m, M = 8333 kN.m at x = 10 m | beam_internal_forces |
S_Q58 | A 20 ft long beam is pinned at the left end A and has a roller at the right end B. The beam is subjected to a vertical downwards distributed parabolic loading w(x), given by the equation w(x) = - 0.007.x^3 - 0.03.x^2 + 3.x lbf/ft. Find the bending moment function in terms of x. | M = (x^4)/400 + (x^5)/2857 - (x^3)/2 + 124.x | beam_internal_forces |
S_Q59 | A 220 kN horizontal force P is applied to a box with weight 200kN resting on a surface with an incline of 20 degrees from the horizontal. The line of action of P passes through the center of gravity of the box. The box is 4 m wide and 3 m tall, and the static and kinetic coefficients of friction between the box and the... | 138.3 kN | friction |
S_Q60 | A block weighs 500 N and is resting on an incline of 30 degrees from the horizontal. The coefficient of friction between the block and the inclined surface is 0.4 . A force P is applied to the box. The line of action of P passes through the center of gravity of the box and is inclined 65 degrees from the horizontal. De... | Maximum = 404 N, minimum = 130 N | friction |
S_Q61 | A block with mass 10 kg rests on a horizontal surface. A block with mass 35 kg rests on top of the 10 kg block, and is restrained from moving horizontally. The coefficient of friction between all surfaces is 0.2. A horizontal force P is applied to the 10 kg block with a line of action through its center of gravity. Det... | 157 N | friction |
S_Q62 | A 2D object is defined by 5 vertices in the x-y space with straight lines between them. The vertices are: (-1, 0cm), (-7, 0cm), (0, 7cm), (1, 7cm), (1, 6cm). Calculate the moment of inertia and radius of gyration with respect to the x-axis. | Ix = 278.4 cm^4, kx = 3.3 cm | moments_of_inertia |
S_Q63 | A square has vertices in the x-y space of (0, 6in), (-4, 6in), (-4, 10in) and (0, 10in). Calculate the moments of inertia of the object about both the x- and y-axes. | Ix = 1045 in^4, Iy = 85.3 in^4 | moments_of_inertia |
S_Q64 | A 2D object is defined by 6 vertices in the x-y space with straight lines between them. The vertices are: (0,0ft), (0, 9ft), (1, 9ft), (1, 3ft), (4, 3ft), (4, 0ft). Calculate the moments of inertia of the object about both the x- and y-axes. | Ix = 270 ft^4, Iy = 66 ft^4 | moments_of_inertia |
S_Q65 | A circle has a diameter of 8 in and is positioned in the x-y space such that its centre is located at (5, 4in). Determine the moment of inertia and radius of gyration about the y-axis. | Iy = 1458 in^4, ky = 5.4 in | moments_of_inertia |
S_Q66 | A rectangle has vertices in the x-y space of (0, 0cm), (0, 8cm), (10, 8cm), (10, 0cm). Inside this rectangle is a rectangular void with vertices of (1, 6cm), (1, 7cm), (9, 7cm), (9, 6cm). Determine the moment of inertia of the composite shape about the horizontal neutral axis of the composite shape. | 370.4 cm^4 | moments_of_inertia |
S_Q67 | A 2D object is defined by 8 vertices in the x-y space with straight lines between them. The vertices are: (0, 2ft), (7, 2ft), (7, 8ft), (8, 8ft), (8, -8ft), (7, -8ft), (7, -2ft), (0, -2ft). Calculate the moment of inertia of the object about the vertical neutral axis of the object. | 278.6 ft^4 | moments_of_inertia |
S_Q68 | Two steel channel sections are placed back to back to each other with a distance of 120 mm separating them. They are placed upright such that their large dimension (depth) is in line with the vertical y-axis. A built up beam is constructed by welding two plates to these channels, symmetrically placed, one on the top an... | Ix = 728800000 mm^4, kx = 154.6 mm, Iy = 217600000 mm^4, ky = 84.5 mm | moments_of_inertia |
M_Q1 | A pedestal has a triangular cross section. If it is subjected to a compressive force P of 500 lb, specify the x and y coordinates for the location of point P(x, y), where the load must be applied on the cross section, so that the average normal stress is uniform. Compute the stress. Vertices of the triangular cross sec... | x = 4in, y = 4in, stress = 9.26psi | stress |
M_Q2 | A metal rod specimen failed in a tension test at an angle of 52 degrees (to the longitudinal axis) when the axial load was 19.80 kip. If the diameter of the specimen is 0.5 in., determine the average normal and average shear stress acting on the area of the inclined failure plane. Also, what is the average normal stres... | Average normal stress on cross section: 100.9 ksi, Average normal stress on inclined failure plane: 62.7 ksi, Average shear stress on inclined failure plane: 48.9 ksi | stress |
M_Q3 | Rods AB and BC have diameters of 4 mm and 6 mm, respectively. The geometry: Point A: Pin support on left, Point B: Ring connection where both rods meet, Point C: Pin support on right, Rod AB: Horizontal, connects A to B, Rod BC: Inclined at theta = 60 degrees above horizontal, connects B to C. If a vertical downwards l... | AB = 368MPa, BC = 327MPa | stress |
M_Q4 | The bars of the truss each have a cross-sectional area of 1.25 in squared. Geometry: Joint A: (0 ft, 0 ft), Joint B: (4 ft, 3 ft), Joint C: (8 ft, 3 ft), Joint E: (4 ft, 0 ft), Joint D: (8 ft, 0 ft), Joint C: Pinned to wall, Joint D: Pinned to wall. Members: AB, AE, ED, EB, BC, BD. Force P = 8 kip acting downward at jo... | AB=10.7ksi T, AE=8.53ksi C, ED=8.53ksi C, EB=4.8ksi T, BC=23.5ksi T, BD=18.7ksi C | stress |
M_Q5 | A beam and hanger assembly is used to support a distributed loading of w = 0.8 kip/ft. Beam: Pinned to the wall at C (0, 0ft) and extends horizontal for 6ft. Hanger rod AB: Pinned to the wall at B (0, 3ft) and connected to the beam with a bolt at A (4, 0ft). Uniformly distributed load w = 0.8 kip/ft acting downward ove... | Bolt: shear stress=23.9ksi, FOS=1.05. Rod: stress=30.6ksi, FOS=1.24 | stress |
M_Q6 | A rod BC is made of steel having an allowable tensile stress of 155 MPa and supports the left end of beam AB. Joint A: (4.5, 0 m) right end, pinned support, Joint B: (0, 0 m) left end, connection point on beam for rod BC, Joint C: Above point B, upper connection of rod to support. Distributed downwards load increases f... | 11.1 mm | stress |
M_Q7 | A thin strip of rubber has an unstretched length of 15 in. If it is stretched around a pipe having an outer diameter of 5 in., determine the average normal strain in the strip. | 0.0472 in/in | strain |
M_Q8 | A bar CA has length L m and is supported at its right end A by a wire AB. At the left end the bar is attached to a wall by a pin at C. The wire is attached to the wall at B which is L m vertically above C. When the wire AB is unstretched it makes an angle of theta = 45 degrees below the horizontal at B. If a load is ap... | 0.0343 m/m | strain |
M_Q9 | Two wires are connected together at A with a ring. Wire CA: Connects C to A, length = 300 mm, oriented at 30 degrees above horizontal (measured from horizontal at A). Wire BA: Connects B to A, length = 300 mm, oriented at 30 degrees below horizontal (measured from horizontal at A). B and C are connections to a wall and... | Strain in both wires = 0.0058 mm/mm | strain |
M_Q10 | A right-angled triangular plate ABC has vertices: A (0, 0mm), B (0, 800mm), C (800, 0mm). Edge BC is fixed, and its apex A is given a displacement of 5 mm in the direction perpendicular to edge BC. Determine the shear strain at A. | 0.0088 rad | strain |
M_Q11 | A rectangular plastic block is glued at its top and bottom to rigid plates. Point A: Bottom-left corner (0, 0). Point D: Bottom-right corner. Point B: Top-left corner (0, 2in). Point C: Top-right corner. A horizontal force P is applied to the top plate in the positive x direction, and causes the material to deform so t... | A = 0, B = 0.199 rad | strain |
M_Q12 | The stress - strain diagram for an elastic fibre has coordinates: (0 in/in, 0 psi), (2 in/in, 11 psi), (2.25 in/in, 55 psi). Determine the modulus of elasticity and estimate the modulus of toughness and modulus of resilience. | modulus of elasticity = 5.5psi, modulus of toughness = 19.25psi, modulus of resilience = 11 psi | mechanical_properties |
M_Q13 | The stress-strain (s-e) diagram for a bone is described by the equation e = 0.45(10^-6)s + 0.36(10^-12)s^3, where s is in kPa. Determine the modulus of toughness and the amount of elongation of a 200 mm long region just before it fractures if failure occurs at e = 0.12 mm/mm. | 613MPa, 24mm | mechanical_properties |
M_Q14 | A specimen is originally 1 ft long, has a diameter of 0.5 in., and is subjected to a force of 500 lb. When the force is increased to 1800 lb, the specimen elongates 0.9 in. Determine the modulus of elasticity for the material if it remains elastic. | 88.3ksi | mechanical_properties |
M_Q15 | A bar BC has length 10 ft and is supported at its right end B by a wire AB with diameter 0.2 in made of A-36 steel. At the left end the bar is attached to a wall by a pin at C. The wire is attached to the wall at A which is vertically above C. Wire AB makes an angle of 30 degrees above the horizontal at B. A downwards ... | 0.246kip/ft | mechanical_properties |
M_Q16 | An aluminum block has a rectangular cross section and is subjected to an axial compressive force of 8 kip. If the 1.5 in. side changed its length to 1.500132 in., determine Poisson's ratio and the new length of the 2 in. side. The modulus of elasticity is 10(10^3) ksi. | Poissons ratio = 0.33, side length = 2.00018 in | mechanical_properties |
M_Q17 | An 8 mm diameter brass rod has a modulus of elasticity of 100 GPa. If it is 3 m long and subjected to an axial load of 2 kN, determine its elongation. What is its elongation under the same load if its diameter is 6 mm? | For 8mm diameter = 1.19mm, for 6mm diameter = 2.12m | mechanical_properties |
M_Q18 | An assembly consists of a steel rod CB of length 3 m and an aluminum rod BA of length 2 m, each having a diameter of 12 mm. The rod is fixed at C and free at A and is subjected to axial loadings at A and at B: 6 kN acting at B in the negative x-direction, 18 kN acting at end A in the positive x-direction. Determine the... | 6.14mm | axial_load |
M_Q19 | A truss is made of three A-36 steel members AB, BC and CA, each having a cross-sectional area of 400 mm squared. Joint A: (0 m, 0 m), Joint C: (1.4 m, 0 m), Joint B: (0.8 m, 0.8 m). Joint A is pinned and joint C is a roller. Forces: Force P acting downward at joint B, force 5 kN acting horizontally to the right at join... | 21.7kN | axial_load |
M_Q20 | A linkage is made of three pin-connected A-36 steel members DA, CA and AB, each having a cross-sectional area of 0.730 in squared. Joint D: (0 ft, 0 ft), Joint C: (6 ft, 0 ft), Joint A: (3 ft, -4 ft), Joint B: (3 ft, -10 ft). Joints C and D are pinned. A vertical force of P = 50 kip is applied to the end B of member AB... | 0.281in | axial_load |
M_Q21 | A 500 mm long steel pipe is filled with concrete and subjected to a compressive force of 80 kN. The steel pipe outer diameter is 80 mm and inner diameter is 70 mm. Modulus of elasticity (steel) is 200 GPa, Modulus of elasticity (concrete) is 24 GPa. Determine the stress in the concrete and the steel due to this loading... | steel stress = 48.8MPa, concrete stress = 5.85MPa | axial_load |
M_Q22 | A 10 mm diameter steel bolt is surrounded by a bronze sleeve. The outer diameter of this sleeve is 20 mm, and its inner diameter is 10 mm. The assembly is subjected to a compressive load P. The yield stress for the steel is 640 MPa and the bronze is 520 MPa. Modulus of elasticity (steel) is 200 GPa, Modulus of elastici... | 126kN | axial_load |
M_Q23 | A tapered member is fixed connected at its ends A and B and is subjected to a downwards load P. The member is 2 in thick and 60 in long. The height tapers linearly from 6 in at A to 3 in at B. Determine the distance from A of the load position and its greatest magnitude, if the allowable normal stress for the material ... | 28.9in, 60.4kip | axial_load |
M_Q24 | A post is made from 6061-T6 aluminum and has a diameter of 50 mm and length 0.5 m. It is fixed supported at A and B and at its center C there is a coiled spring with stiffness 200 MN/m attached to a rigid collar. If the spring is originally uncompressed, determine the compression of the spring when a load of P = 50 kN ... | 0.039mm | axial_load |
M_Q25 | A thermo gate consists of two 6061-T6 aluminum plates that have a width of 15 mm and are fixed supported at their ends. One plate is 600 mm length, the other is 400 mm length, and both plates have thickness 10 mm. If the gap between them is 1.5 mm when the temperature is 25 degrees C, determine the temperature required... | 87.5 degrees C | axial_load |
M_Q26 | A member is to be made from a steel plate that is 0.25 in thick. If a 1 in hole is drilled through its center, determine the approximate width of the plate so that it can support an axial force of 3350 lb. The allowable stress is 22 ksi. | 2.49in | axial_load |
M_Q27 | A 0.25 in diameter steel rivet having a temperature of 1500 degrees F is secured between two plates such that at this temperature it is 2 in long and exerts a clamping force of 250 lb between the plates. Determine the approximate clamping force between the plates when the rivet cools to 70 degrees F. Assume that the he... | 16.5kip | axial_load |
M_Q28 | A copper pipe has outer diameter 40 mm and inner diameter 37 mm. It is fixed at a wall at A and the axis is the longitudinal axis, positive away from the wall. Three torques are applied, sequentially moving away from the wall: -30 Nm, 20 Nm then -80 Nm. Determine the maximum shear stress in the pipe. | 26.7MPa | torsion |
M_Q29 | A steel tube having an outer diameter of 2.5 in. is used to transmit 350 hp when turning at 27 rev/min. Determine the inner diameter of the tube if the allowable shear stress is 10 ksi. | 2.48in | torsion |
M_Q30 | Two steel 20 mm diameter steel shafts are connected using a brass coupling. If the yield point for the steel is 100 MPa and for the brass is 250 MPa, determine the required outer diameter of the coupling so that the steel and brass begin to yield at the same time when the assembly is subjected to a torque T. Assume tha... | 21.9mm | torsion |
M_Q31 | The drive shaft of an automobile is made of a steel having an allowable shear stress of 8 ksi. If the outer diameter of the shaft is 2.5 in. and the engine delivers 200 hp to the shaft when it is turning at 1140 rev/min, determine the minimum required thickness of the shaft's wall. | 0.174in | torsion |
M_Q32 | A 0.75 in. diameter shaft for an electric motor develops 0.5 hp and runs at 1740 rev/min. Determine the torque produced and compute the maximum shear stress in the shaft. The shaft is 6 in long and supported by ball bearings at its ends. | 1.51lbft, 219psi | torsion |
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