Beam Fixed at Both Ends — Uniformly Distributed Load

1

Geometry and Load

Fixed at both ends — Distributed load w over the full length

Length ℓ

m

Distributed load w

kN/m

2

R, Mmax, M₁, zero-moment locations

R = Vat the supports = wℓ2 = —kN

M_maksat the ends = wℓ²12 = —kN·m

M₁at midspan = wℓ²24 = —kN·m

x₀M=0 point = 0.2113 ℓ = —m

3

Δ_max = wℓ⁴ / 384EI (at midspan, closed form)

Elastic modulus E

MPa

Moment of inertia I

cm⁴

Δ_maksat midspan = wℓ⁴384EI = —mm

Deflected Shape Diagram

4

σ_max = M_maks / S

Section modulus S

cm³

Allowable bending F_b

MPa

σ_max = —MPa

Critical moment = M_maks = wℓ²/12 (fixed-end moment)

—σ / F_b

5

V_x, M_x, Δ_x at a given x

Distance x

m

0ℓ/2ℓ

V_x=—kN

M_x=—kN·m

Δ_x=—mm