Beam Overhanging Both Supports — Unequal Overhangs

1

Geometry and Load

Left overhang a, span b, right overhang c; distributed load w (total length ℓ = a+b+c)

Left overhang a

m

Span b

m

Right overhang c

m

Distributed load w

kN/m

R₁: left support (x = a); R₂: right support (x = a+b). ℓ = 7.5 m

2

Show calculation details

R₁, R₂, M₁, M₂, M₃, V₁…V₄

R₁ = wℓ(ℓ−2c)2b = — = —kN

R₂ = wℓ(ℓ−2a)2b = — = —kN

M₁at x = a = −wa²/2 = —kN·m

M₂at x = a+b = −wc²/2 = —kN·m

M₃max. positive = R₁(R₁/2w − a) = —kN·m

V₁=wa =—kN V₂=R₁−V₁ =—kN

V₄=wc =—kN V₃=R₂−V₄ =—kN

3

Deflection calculation

Define E and I for δ_max

Elastic modulus E

MPa

Moment of inertia I

cm⁴

δ_maxin the span, numerical = —mm

Deflected Shape Diagram

4

Stress check

Compare σ_max against the allowable stress

Section modulus S

cm³

Allowable bending F_b

MPa

σ_max = M_kritS = — = —MPa

M_krit = max(|M₁|, |M₂|, M₃)

—σ / F_b

5

Point analysis

V_x, M_x, δ_x at a given point x

Distance x

m

0 (left end) a (R₁) a+b (R₂) ℓ

V_x=—kN

M_x=—kN·m

δ_x=—mm