Beam Deflection Check
Beam Deflection Check
Simply supported beam under uniformly distributed load (UDL) — deflection and stress check.
Inputs
Beam span
L:=6m=19.69 ft
Uniformly distributed load
w:=10kN/m=10000 kg/s^2
Young's modulus — structural steel
E:=200GPa=29007.55 ksi
Section width
b:=150mm=5.91 in
Section depth
d:=300mm=11.81 in
Yield strength — S275 steel
f_y:=275MPa=39.89 ksi
Deflection limit denominator (span/360)
L_limit:=360=360
Section Properties
Cross-sectional area
A_sec:=b·d=0.48 ft^2
I:=(b·d^3)/(12)=3.38e-04 m^4
Second moment of area about major axis
y_max:=(d)/(2)=5.91 in
Distance from neutral axis to extreme fibre
Z_el:=(I)/(y_max)=0.08 ft^3
Elastic section modulus
Calculations
R:=(w·L)/(2)=6744.27 lbf
Support reaction (UDL, symmetric)
M_max:=(w·L^2)/(8)=33190.3 lbf*ft
Maximum bending moment at midspan
Maximum shear force at support
V_max:=R=6744.27 lbf
delta_max:=(5·w·L^4)/(384·E·I)=0.1 in
Maximum midspan deflection (UDL)
delta_allow:=(L)/(L_limit)=0.66 in
Allowable deflection limit (span / 360)
sigma_max:=(M_max)/(Z_el)=2.9 ksi
Maximum bending stress at extreme fibre
tau_max:=(3·V_max)/(2·A_sec)=145.04 psi
Maximum shear stress (rectangular section)
Results
- Deflection unity check: δ_max / δ_allow — must be ≤ 1.0
- Bending stress unity check: σ_max / f_y — must be ≤ 1.0
delta_max=0.1 in
Midspan deflection
Allowable deflection
delta_allow=0.66 in
UC_deflection:=(delta_max)/(delta_allow)=0.15
Deflection unity check (≤ 1.0 = PASS)
Peak bending stress
sigma_max=2.9 ksi
UC_bending:=(sigma_max)/(f_y)=0.07
Bending stress unity check (≤ 1.0 = PASS)
Peak shear stress
tau_max=145.04 psi
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