Continuous Beam — Two Equal Spans — Uniform Load on One Span

1

Geometry and load

Both spans ℓ; UDL on the left span only (R₁→R₂)

Span ℓ

m

Distributed load w

kN/m

2

R₁, R₂, R₃, V₁, V₂, V₃, M_max, M₁

R₁ = V₁= 716wℓ = —kN

R₂= 58wℓ = —kN

R₃ = V₃= −116wℓ = —kN

V₂just left of R₂= 916wℓ = —kN

M_maxat x = 7ℓ/16= 49512wℓ² = —kN·m

M₁at R₂= 116wℓ² = —kN·m

3

σ_max = M_krit / S

Section modulus S

cm³

Allow. bending F_b

MPa

σ_max= —MPa

M_krit = max(M_max, M₁)

—σ / F_b

4

V_x and M_x at the given x (closed form)

Distance x

m

0ℓ (R₂)2ℓ (R₃)

V_x=—kN

M_x=—kN·m