Beam Fixed at Both Ends — Concentrated Load at Center

1

Geometry and Load

Fixed at both ends — concentrated load P at midspan

Length ℓ

m

Concentrated load P

kN

2

R, V, M_maks, zero-moment locations

R = Vat the supports = P2 = —kN

M_maksend + midspan = Pℓ8 = —kN·m

x₀M = 0 point = ℓ/4 = —m

3

Δ_max = Pℓ³ / 192EI (at midspan, closed form)

Elastic modulus E

MPa

Moment of inertia I

cm⁴

Δ_maksat midspan = Pℓ³192EI = —mm

Deflected Shape Diagram

4

σ_max = M_maks / S

Section modulus S

cm³

Allowable bending F_b

MPa

σ_max = —MPa

—σ / F_b

5

V_x, M_x, Δ_x (closed form for x < ℓ/2)

Distance x

m

0ℓ/2ℓ

V_x=—kN

M_x=—kN·m

Δ_x=—mm