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import math |
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import numpy as np |
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import matplotlib.pyplot as plt |
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import gradio as gr |
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import pandas as pd |
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plt.rcParams.update({"figure.dpi": 120}) |
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def reactions_simply_supported(L, point_loads, udls): |
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Wp = sum(P for (_x, P) in point_loads) |
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Wu = sum(w * (x2 - x1) for (x1, x2, w) in udls) |
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Wtot = Wp + Wu |
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Mp = sum(P * x for (x, P) in point_loads) |
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Mu = sum((w * (x2 - x1)) * ((x1 + x2) / 2.0) for (x1, x2, w) in udls) |
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RB = (Mp + Mu) / L |
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RA = Wtot - RB |
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return RA, RB |
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def vm_diagrams(L, point_loads, udls, n=1001): |
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RA, RB = reactions_simply_supported(L, point_loads, udls) |
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x = np.linspace(0.0, L, n) |
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V = np.zeros_like(x, dtype=float) |
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M = np.zeros_like(x, dtype=float) |
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def udl_active_length(xi, x1, x2): |
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if xi <= x1: |
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return 0.0 |
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elif xi >= x2: |
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return (x2 - x1) |
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else: |
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return (xi - x1) |
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for i, xi in enumerate(x): |
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v = RA |
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for (xp, P) in point_loads: |
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if xp <= xi + 1e-12: |
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v -= P |
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for (x1, x2, w) in udls: |
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a = udl_active_length(xi, x1, x2) |
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v -= w * max(0.0, a) |
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V[i] = v |
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m = RA * xi |
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for (xp, P) in point_loads: |
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a = max(0.0, xi - xp) |
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m -= P * a |
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for (x1, x2, w) in udls: |
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a = udl_active_length(xi, x1, x2) |
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if a > 0: |
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centroid = x1 + a / 2.0 |
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m -= w * a * (xi - centroid) |
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M[i] = m |
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return x, V, M, (RA, RB) |
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def draw_beam_sketch(L, point_loads, udls, RA, RB): |
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fig, ax = plt.subplots(figsize=(7, 1.8)) |
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ax.set_xlim(-0.02*L, 1.02*L) |
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ax.set_ylim(-1.2, 1.2) |
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ax.plot([0, L], [0, 0], lw=4, color="black") |
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triA = plt.Polygon([[0,0],[ -0.05*L, -0.5],[ 0.05*L, -0.5]], color="gray") |
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triB = plt.Polygon([[L,0],[ L-0.05*L, -0.5],[ L+0.05*L, -0.5]], color="gray") |
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ax.add_patch(triA); ax.add_patch(triB) |
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ax.annotate("", xy=(0,0.6), xytext=(0,0.05), |
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arrowprops=dict(arrowstyle="->", lw=2)) |
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ax.text(0, 0.7, f"R_A={RA:.1f} N", ha="center", va="bottom", fontsize=9) |
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ax.annotate("", xy=(L,0.6), xytext=(L,0.05), |
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arrowprops=dict(arrowstyle="->", lw=2)) |
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ax.text(L, 0.7, f"R_B={RB:.1f} N", ha="center", va="bottom", fontsize=9) |
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for (xp, P) in point_loads: |
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ax.annotate("", xy=(xp,-0.7), xytext=(xp,0.05), |
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arrowprops=dict(arrowstyle="->", lw=2)) |
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ax.text(xp, -0.8, f"P={P:.0f} N", ha="center", va="top", fontsize=9) |
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for (x1, x2, w) in udls: |
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ax.plot([x1, x2], [0.25, 0.25], lw=6, color="tab:blue") |
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n_ar = max(2, int((x2-x1)/(L/10)) ) |
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xs = np.linspace(x1, x2, n_ar) |
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for xk in xs: |
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ax.annotate("", xy=(xk,0.05), xytext=(xk,0.4), |
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arrowprops=dict(arrowstyle="->", lw=1.5)) |
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ax.text((x1+x2)/2, 0.45, f"w={w:.0f} N/m", ha="center", va="bottom", fontsize=9, color="tab:blue") |
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ax.axis("off") |
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ax.set_title("Beam & Loads (simply supported)") |
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fig.tight_layout() |
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return fig |
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def plot_line(x, y, title, ylbl): |
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fig, ax = plt.subplots(figsize=(7, 2.5)) |
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ax.axhline(0, color="k", lw=1) |
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ax.plot(x, y, lw=2) |
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ax.set_xlabel("x [m]") |
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ax.set_ylabel(ylbl) |
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ax.set_title(title) |
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ax.grid(True, alpha=0.3) |
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fig.tight_layout() |
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return fig |
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EX_POINT = pd.DataFrame( |
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[[2.0, 8000], |
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[5.0, 6000]], |
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columns=["x (m)", "P (N, down +)"] |
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) |
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EX_UDL = pd.DataFrame( |
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[[1.0, 3.0, 1500], |
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[6.0, 8.5, 1000]], |
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columns=["x1 (m)", "x2 (m)", "w (N/m, down +)"] |
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) |
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HELP_MD = """ |
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**How to use** |
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1) Set **span L** and enter loads: |
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- **Point loads:** `(x, P)`; `P>0` is downward. |
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- **UDLs:** `(x1, x2, w)`; `w>0` is downward, active on `[x1,x2]`. |
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2) Use **Add** (limited to 2 rows per type), **Delete rows**, **Clear**, or **Reset examples**. |
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3) Click **Compute** to see reactions, the beam sketch, **V(x)** and **M(x)**, and equilibrium checks. |
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**Sign convention** |
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- Upward reactions positive. Downward loads positive inputs. |
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- Shear: positive upward on left face; Moment: sagging positive. |
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""" |
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def _parse_row_list(s, n_rows): |
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if not s: |
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return [] |
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idxs = [] |
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for tok in str(s).replace(" ", "").split(","): |
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if not tok: |
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continue |
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try: |
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k = int(tok) |
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if 1 <= k <= n_rows: |
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idxs.append(k-1) |
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except ValueError: |
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pass |
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return sorted(set(idxs), reverse=True) |
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def delete_point_rows(df_points, rows_to_delete, confirm): |
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if not confirm: |
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return df_points, "Deletion NOT performed (check 'Confirm delete')." |
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if df_points is None or len(df_points) == 0: |
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return pd.DataFrame(columns=["x (m)","P (N, down +)"]), "No point rows to delete." |
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idxs = _parse_row_list(rows_to_delete, len(df_points)) |
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if not idxs: |
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return df_points, "No valid point row indices provided." |
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df = df_points.copy() |
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for i in idxs: |
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df = df.drop(df.index[i]) |
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df = df.reset_index(drop=True) |
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return df, f"Deleted point rows: {', '.join(str(i+1) for i in idxs)}." |
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def delete_udl_rows(df_udl, rows_to_delete, confirm): |
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if not confirm: |
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return df_udl, "Deletion NOT performed (check 'Confirm delete')." |
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if df_udl is None or len(df_udl) == 0: |
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return pd.DataFrame(columns=["x1 (m)","x2 (m)","w (N/m, down +)"]), "No UDL rows to delete." |
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idxs = _parse_row_list(rows_to_delete, len(df_udl)) |
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if not idxs: |
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return df_udl, "No valid UDL row indices provided." |
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df = df_udl.copy() |
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for i in idxs: |
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df = df.drop(df.index[i]) |
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df = df.reset_index(drop=True) |
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return df, f"Deleted UDL rows: {', '.join(str(i+1) for i in idxs)}." |
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def clear_points(): |
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return pd.DataFrame(columns=["x (m)","P (N, down +)"]), "Cleared all point loads." |
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def clear_udls(): |
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return pd.DataFrame(columns=["x1 (m)","x2 (m)","w (N/m, down +)"]), "Cleared all UDLs." |
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def reset_examples_points(): |
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return EX_POINT.copy(), "Restored example point loads." |
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def reset_examples_udls(): |
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return EX_UDL.copy(), "Restored example UDLs." |
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MAX_POINTS = 2 |
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MAX_UDLS = 2 |
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def add_point_row(df_points, x, P): |
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df = df_points.copy() if df_points is not None else pd.DataFrame(columns=["x (m)","P (N, down +)"]) |
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if len(df) >= MAX_POINTS: |
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return df, f"Limit reached: max {MAX_POINTS} point loads." |
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try: |
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x = float(x); P = float(P) |
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except Exception: |
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return df, "Provide numeric x and P." |
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if P < 0: |
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return df, "Use P ≥ 0 (downward +)." |
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df = pd.concat([df, pd.DataFrame([[x, P]], columns=df.columns)], ignore_index=True) |
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return df, f"Added point load #{len(df)}." |
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def add_udl_row(df_udl, x1, x2, w): |
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df = df_udl.copy() if df_udl is not None else pd.DataFrame(columns=["x1 (m)","x2 (m)","w (N/m, down +)"]) |
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if len(df) >= MAX_UDLS: |
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return df, f"Limit reached: max {MAX_UDLS} UDLs." |
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try: |
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x1 = float(x1); x2 = float(x2); w = float(w) |
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except Exception: |
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return df, "Provide numeric x1, x2, w." |
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if not (x1 < x2): |
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return df, "Require x1 < x2." |
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if w < 0: |
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return df, "Use w ≥ 0 (downward +)." |
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df = pd.concat([df, pd.DataFrame([[x1, x2, w]], columns=df.columns)], ignore_index=True) |
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return df, f"Added UDL #{len(df)}." |
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def run_once(L, df_points, df_udl, npts): |
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try: |
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L = float(L) |
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n = int(npts) |
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if L <= 0: |
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raise ValueError("Beam length L must be > 0.") |
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if n < 201: |
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n = 201 |
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point_loads = [] |
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if df_points is not None and len(df_points) > 0: |
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for _, row in df_points.iterrows(): |
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x = float(row[0]); P = float(row[1]) |
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if 0 <= x <= L and P >= 0: |
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point_loads.append((x, P)) |
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udls = [] |
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if df_udl is not None and len(df_udl) > 0: |
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for _, row in df_udl.iterrows(): |
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x1 = float(row[0]); x2 = float(row[1]); w = float(row[2]) |
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if 0 <= x1 < x2 <= L and w >= 0: |
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udls.append((x1, x2, w)) |
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x, V, M, (RA, RB) = vm_diagrams(L, point_loads, udls, n=n) |
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fig_beam = draw_beam_sketch(L, point_loads, udls, RA, RB) |
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fig_V = plot_line(x, V, "Shear Force Diagram V(x)", "V [N]") |
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fig_M = plot_line(x, M, "Bending Moment Diagram M(x)", "M [N·m]") |
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total_down = sum(P for _, P in point_loads) + sum(w*(x2-x1) for (x1,x2,w) in udls) |
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eq_sumF = RA + RB - total_down |
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Mp = sum(P * x for (x, P) in point_loads) |
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Mu = sum(w*(x2-x1)*( (x1+x2)/2 ) for (x1,x2,w) in udls) |
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eq_MA = RB*L - (Mp + Mu) |
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df = pd.DataFrame([{ |
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"RA [N]": round(RA, 3), |
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"RB [N]": round(RB, 3), |
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"ΣF (should ≈ 0) [N]": round(eq_sumF, 6), |
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"ΣM_A (should ≈ 0) [N·m]": round(eq_MA, 6), |
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"max|V| [N]": round(float(np.max(np.abs(V))), 3), |
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"max|M| [N·m]": round(float(np.max(np.abs(M))), 3), |
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}]) |
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return df, fig_beam, fig_V, fig_M, "" |
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except Exception as e: |
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return pd.DataFrame(), None, None, None, f"Input error:\n{e}" |
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with gr.Blocks(title="Shear & Moment Diagrams — Simply Supported Beam") as demo: |
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gr.Markdown("# Shear & Bending Moment Diagram Generator") |
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gr.Markdown(HELP_MD) |
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with gr.Row(): |
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with gr.Column(): |
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L = gr.Number(value=10.0, label="Span L [m]") |
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npts = gr.Slider(minimum=201, maximum=5001, step=100, value=1201, label="Resolution (points)") |
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with gr.Column(): |
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gr.Markdown("### Point loads (downward +) — max 2") |
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df_points = gr.Dataframe( |
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value=EX_POINT, headers=["x (m)","P (N, down +)"], |
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datatype=["number","number"], row_count=(1, "dynamic") |
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) |
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with gr.Row(): |
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x_new = gr.Number(value=1.0, label="x (m)") |
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P_new = gr.Number(value=5000.0, label="P (N, down +)") |
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btn_add_pt = gr.Button("Add point load", variant="primary") |
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with gr.Row(): |
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del_pts_rows = gr.Textbox(label="Delete point rows (e.g., 1,2)") |
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confirm_pts = gr.Checkbox(value=False, label="Confirm delete") |
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with gr.Row(): |
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btn_del_pts = gr.Button("Delete selected point rows", variant="secondary") |
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btn_clr_pts = gr.Button("Clear ALL point loads", variant="stop") |
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btn_rst_pts = gr.Button("Reset example points", variant="primary") |
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with gr.Column(): |
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gr.Markdown("### Uniform distributed loads (downward +) — max 2") |
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df_udl = gr.Dataframe( |
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value=EX_UDL, headers=["x1 (m)","x2 (m)","w (N/m, down +)"], |
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datatype=["number","number","number"], row_count=(1, "dynamic") |
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) |
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with gr.Row(): |
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x1_new = gr.Number(value=2.0, label="x1 (m)") |
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x2_new = gr.Number(value=4.0, label="x2 (m)") |
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w_new = gr.Number(value=1000.0, label="w (N/m)") |
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btn_add_udl = gr.Button("Add UDL", variant="primary") |
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with gr.Row(): |
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del_udl_rows = gr.Textbox(label="Delete UDL rows (e.g., 1)") |
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confirm_udl = gr.Checkbox(value=False, label="Confirm delete") |
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with gr.Row(): |
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btn_del_udl = gr.Button("Delete selected UDL rows", variant="secondary") |
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btn_clr_udl = gr.Button("Clear ALL UDLs", variant="stop") |
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btn_rst_udl = gr.Button("Reset example UDLs", variant="primary") |
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go_btn = gr.Button("Compute", variant="primary") |
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gr.Markdown("### Reactions & Checks") |
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out_tbl = gr.Dataframe(interactive=False) |
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gr.Markdown("### Beam sketch") |
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out_beam = gr.Plot() |
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with gr.Row(): |
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out_V = gr.Plot() |
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out_M = gr.Plot() |
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status = gr.Textbox(label="Status / Errors", interactive=False) |
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def _add_point(df, x, P): |
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new_df, msg = add_point_row(df, x, P) |
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return new_df, msg |
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btn_add_pt.click(_add_point, inputs=[df_points, x_new, P_new], outputs=[df_points, status]) |
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def _add_udl(df, x1, x2, w): |
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new_df, msg = add_udl_row(df, x1, x2, w) |
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return new_df, msg |
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btn_add_udl.click(_add_udl, inputs=[df_udl, x1_new, x2_new, w_new], outputs=[df_udl, status]) |
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def _delete_pts(df, rows_txt, confirm): |
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new_df, msg = delete_point_rows(df, rows_txt, confirm) |
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return new_df, msg |
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btn_del_pts.click(_delete_pts, inputs=[df_points, del_pts_rows, confirm_pts], |
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outputs=[df_points, status]) |
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def _clear_pts(): |
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return clear_points() |
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btn_clr_pts.click(_clear_pts, inputs=None, outputs=[df_points, status]) |
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def _reset_pts(): |
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return reset_examples_points() |
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btn_rst_pts.click(_reset_pts, inputs=None, outputs=[df_points, status]) |
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def _delete_udl(df, rows_txt, confirm): |
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new_df, msg = delete_udl_rows(df, rows_txt, confirm) |
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return new_df, msg |
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btn_del_udl.click(_delete_udl, inputs=[df_udl, del_udl_rows, confirm_udl], |
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outputs=[df_udl, status]) |
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def _clear_udl(): |
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return clear_udls() |
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btn_clr_udl.click(_clear_udl, inputs=None, outputs=[df_udl, status]) |
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def _reset_udl(): |
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return reset_examples_udls() |
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btn_rst_udl.click(_reset_udl, inputs=None, outputs=[df_udl, status]) |
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go_btn.click( |
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fn=run_once, |
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inputs=[L, df_points, df_udl, npts], |
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outputs=[out_tbl, out_beam, out_V, out_M, status] |
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) |
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if __name__ == "__main__": |
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demo.launch(debug=False) |
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