Continuous Beam — Two Equal Spans — Uniformly Distributed Load (Both Spans)

1

Geometry and Load

Span ℓ for each; UDL w on both spans

Span ℓ

m

Distributed load w

kN/m

2

R₁=R₃, R₂, V₁=V₃=Vmax, M₁, M₂

R₁=R₃= 38wℓ = —kN

R₂= 108wℓ = —kN

V_max= 58wℓ = —kN

M₁at R₂= 18wℓ² = —kN·m

M₂at x = 3ℓ/8= 9128wℓ² = —kN·m

Δ_maxx=0.4215ℓ= wℓ⁴185EI = —mm

3

Compute Δ_max from EI

Flexural rigidity EI

kN·m²

Δ_max= —mm

Δ = wℓ⁴ / (185EI) — at 0.4215ℓ from R₁ and R₃

4

σ_max = M_cr / S

Section modulus S

cm³

Allow. bending F_b

MPa

σ_max=—MPa

M_cr = max(M₁, M₂) = M₁ = wℓ²/8

—σ / F_b

5

V_x and M_x at a given x

Distance x

m

0ℓ2ℓ

V_x=—kN

M_x=—kN·m