import math import gradio import pandas as pd # ---------------- Settings ---------------- TITLE = "Simply-Supported I-Beam" DESC = "Point load @ midspan or uniform load (UDL). SI units. Euler–Bernoulli." # ---------------- Deterministic backend ---------------- def _compute(load_type, L_m, E_GPa, Ix_m4, mode, Sx_m3, depth_m, P_kN, w_kNpm, sigma_allow_MPa, defl_ratio): # --- Validation --- if L_m <= 0: raise ValueError("Span L must be > 0.") if E_GPa <= 0: raise ValueError("E must be > 0.") if Ix_m4 <= 0: raise ValueError("Ix must be > 0.") has_Sx = (mode == "I have Sx") if has_Sx and Sx_m3 <= 0: raise ValueError("Sx must be > 0.") if (not has_Sx) and depth_m <= 0: raise ValueError("Depth must be > 0 when Sx not provided.") if load_type == "Point @ midspan" and P_kN <= 0: raise ValueError("P must be > 0 for point load.") if load_type == "Uniform (UDL)" and w_kNpm <= 0: raise ValueError("w must be > 0 for UDL.") # --- Units --- E = E_GPa * 1e9 P = P_kN * 1e3 w = w_kNpm * 1e3 # --- Section properties --- if has_Sx: Sx = Sx_m3 c = Ix_m4 / Sx h = 2 * c else: h = depth_m c = h / 2 Sx = Ix_m4 / c # --- Beam formulas --- if load_type == "Point @ midspan": Mmax = P * L_m / 4.0 dmax = P * (L_m**3) / (48.0 * E * Ix_m4) else: Mmax = w * (L_m**2) / 8.0 dmax = 5.0 * w * (L_m**4) / (384.0 * E * Ix_m4) sigma = Mmax / Sx # --- Checks --- stress_ok, SF = None, None if sigma_allow_MPa and sigma_allow_MPa > 0: sigma_MPa = sigma / 1e6 SF = sigma_allow_MPa / max(sigma_MPa, 1e-12) stress_ok = sigma_MPa <= sigma_allow_MPa defl_ok, defl_lim = None, None if defl_ratio and defl_ratio > 0: defl_lim = (L_m * 1e3) / defl_ratio defl_ok = (dmax * 1e3) <= defl_lim # --- Context text --- text = [] text.append(f"### 🔍 Contextual Explanation") text.append(f"**Beam Type:** Simply supported ({load_type.lower()}) with span **L = {L_m:.2f} m**.") text.append(f"**Material:** E = {E_GPa:.1f} GPa, **Section:** Ix = {Ix_m4:.2e} m⁴, Sx = {Sx:.2e} m³, depth = {h:.3f} m.") text.append(f"\n#### Results Overview") text.append(f"- Maximum bending moment **Mmax = {Mmax/1e3:.2f} kN·m**.") text.append(f"- Maximum deflection **δmax = {dmax*1e3:.3f} mm**, ratio **δ/L = {dmax/L_m:.5f}**.") text.append(f"- Bending stress **σmax = {sigma/1e6:.2f} MPa**.") if sigma_allow_MPa > 0: if stress_ok: text.append(f"✅ Stress **({sigma/1e6:.2f} MPa)** ≤ allowable **({sigma_allow_MPa:.2f} MPa)**.") else: text.append(f"⚠️ Stress **({sigma/1e6:.2f} MPa)** exceeds allowable **({sigma_allow_MPa:.2f} MPa)**.") if defl_ratio > 0: if defl_ok: text.append(f"✅ Deflection **({dmax*1e3:.3f} mm)** ≤ limit (L/{defl_ratio:.0f} = {defl_lim:.2f} mm).") else: text.append(f"⚠️ Deflection **({dmax*1e3:.3f} mm)** exceeds limit (L/{defl_ratio:.0f} = {defl_lim:.2f} mm).") text.append("\n#### Engineering Meaning") text.append("The bending moment represents internal torque; deflection is beam sag. " "Safe design ensures both remain below limits to prevent failure or deformation.") context_text = "\n".join(text) # --- Return two outputs --- data = { "inputs": { "load_type": load_type, "L_m": L_m, "E_GPa": E_GPa, "Ix_m4": Ix_m4, "Sx_m3": Sx, "depth_m": h, "P_kN": P_kN if load_type.startswith("Point") else 0.0, "w_kN_per_m": w_kNpm if load_type.startswith("Uniform") else 0.0, "sigma_allow_MPa": sigma_allow_MPa or None, "deflection_ratio": defl_ratio or None, }, "solution": { "M_max_kN_m": Mmax / 1e3, "sigma_max_MPa": sigma / 1e6, "delta_max_mm": dmax * 1e3, "delta_over_L": dmax / L_m, }, "checks": { "stress_ok": stress_ok, "SF_stress": SF, "deflection_ok": defl_ok, "deflection_limit_mm": defl_lim, "deflection_ratio": defl_ratio or None, }, } return data, context_text # ---------------- Gradio UI ---------------- with gradio.Blocks() as demo: gradio.Markdown(f"# {TITLE}") gradio.Markdown(DESC) with gradio.Row(): load_type = gradio.Radio(choices=["Point @ midspan", "Uniform (UDL)"], value="Point @ midspan", label="Load case") L_m = gradio.Number(value=3.0, label="Span L [m]", precision=4) E_GPa = gradio.Number(value=200.0, label="Young's modulus E [GPa]", precision=3) Ix_m4 = gradio.Number(value=8.0e-6, label="Second moment Ix [m^4]", precision=10) with gradio.Row(): mode = gradio.Radio(choices=["I have Sx", "I have depth (h) only"], value="I have Sx", label="Section input") Sx_m3 = gradio.Number(value=4.0e-4, label="Section modulus Sx [m^3]", precision=8, visible=True) depth_m = gradio.Number(value=0.30, label="Depth h [m]", precision=4, visible=False) def _toggle(v): return gradio.update(visible=(v=="I have Sx")), gradio.update(visible=(v!="I have Sx")) mode.change(_toggle, inputs=mode, outputs=[Sx_m3, depth_m]) with gradio.Row(): P_kN = gradio.Number(value=20.0, label="Point load P [kN]", precision=3) w_kNpm = gradio.Number(value=5.0, label="UDL w [kN/m]", precision=4) with gradio.Row(): sigma_allow = gradio.Number(value=250.0, label="Allowable stress [MPa] (0=skip)", precision=3) defl_ratio = gradio.Number(value=360, label="Deflection limit L/ratio (0=skip)", precision=0) # --- Two output sections --- with gradio.Tab("Numerical Results"): out = gradio.JSON(label="Results") with gradio.Tab("Understanding the Results"): context_out = gradio.Markdown() inputs = [load_type, L_m, E_GPa, Ix_m4, mode, Sx_m3, depth_m, P_kN, w_kNpm, sigma_allow, defl_ratio] for comp in inputs: comp.change(fn=_compute, inputs=inputs, outputs=[out, context_out]) gradio.Examples( examples=[ ["Point @ midspan", 3.0, 200.0, 8.0e-6, "I have Sx", 4.0e-4, 0.30, 20.0, 0.0, 250.0, 360], ["Uniform (UDL)", 4.5, 200.0, 1.2e-5, "I have Sx", 6.0e-4, 0.35, 0.0, 8.0, 200.0, 360], ["Uniform (UDL)", 2.5, 70.0, 3.5e-6, "I have depth (h) only", 0.0, 0.22, 0.0, 6.0, 160.0, 240], ], inputs=inputs, label="Examples", cache_examples=False, ) demo.launch()