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材料力学·结构
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材料力学·结构
12
engines
Beam deflection
Beam deflection
标准工况δ · 弹性曲线 · 可编辑P/w/L/EI
Closed-form elastic curve for standard cases · maximum deflection marked
Influence line
Influence line
单位荷载移动 · 反力/剪力/弯矩响应 · 影响线
How one response changes as a unit load rolls across a simply-supported beam
Moment distribution (Hardy Cross)
Moment distribution (Hardy Cross)
Hardy Cross · 分配系数+传递 · 迭代平衡
Iterative balancing of a continuous beam · fixed-end moments → distribute → carry over
Euler column buckling
Euler column buckling
Pcr=π²EI/(KL)² · 端部系数K · 失稳模态+长细比
Critical load, effective length and the buckled mode shape
Section modulus & bending stress
Section modulus & bending stress
S=I/c · 弯曲应力σ=M/S · 矩形/圆/工字
A, I, extreme-fibre c, S = I/c and σ = M/S for any section
Composite centroid & moment of inertia
Composite centroid & moment of inertia
组合面积形心 · 平行轴定理 · I=Σ(Iᵢ+Aᵢdᵢ²)
Centroid by first moment, I by the parallel-axis theorem
Method of joints · planar truss
Method of joints · planar truss
ΣFx=ΣFy=0逐节点 · 拉/压杆力着色 · 平衡步骤
Solve reactions, then walk joints one at a time (ΣFx=0, ΣFy=0)
Method of sections · direct member force
Method of sections · direct member force
切开桁架 · ΣM/ΣF · 直接求指定杆力
One cut, one equation — solve a member without walking every joint
Castigliano's 2nd theorem · truss deflection
Castigliano's 2nd theorem · truss deflection
δ=∂U/∂P · 应变能法 · ΣNnL/AE
δ = ∂U/∂P = Σ N·(∂N/∂P)·L/(AE) — the deflection at the load point
Torsion of a circular shaft
Torsion of a circular shaft
T/J=τ/r=Gθ/L · 极惯性矩 · 剪应力分布+扭转角
Shear stress grows linearly from the centre; twist follows θ = TL/GJ
Combined axial + bending stress
Combined axial + bending stress
轴力+弯曲 σ=P/A±Mc/I · 中性轴偏移 · 叠加
σ(y) = P/A ± Mc/I — a uniform axial field plus a linear bending field
Thin-walled pressure vessel
Thin-walled pressure vessel
圆筒环向pr/t+轴向pr/2t · 球pr/2t · r/t≥10
Cylinder: σ_hoop = pr/t = 2·σ_long · Sphere: σ = pr/2t