Continuous Beam — Two Equal Spans — Concentrated Load at Center of One Span

1

Geometry and load

Both spans ℓ; P at the center of the left span only

Span ℓ

m

Concentrated load P

kN

2

R₁, R₂, R₃, V₁, V₂, V₃, M_max, M₁

R₁ = V₁= 1332P = —kN

R₂= 1116P = —kN

R₃ = V₃= −332P = —kN

V₂just left of R₂= 1932P = —kN

M_maxat x = ℓ/2= 1364Pℓ = —kN·m

M₁at R₂= 332Pℓ = —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

Distance x

m

0ℓ2ℓ

V_x=—kN

M_x=—kN·m