Engineering & Physics CalcyZone Calculator

Simply Supported Beam Deflection Calculator

Calculate maximum deflection and bending moment of a simply supported beam with centre point load or UDL.

Maximum deflection

1.3333 mm

Maximum bending moment

10 kN·m

Span / deflection

L/3000

Step-by-step working

δ = PL³ / (48EI) = 10e3 × 4³ / (48 × 200e9 × 50e-6)
= 1.3333 mm
M = PL/4 = 10 kN·m

Mathematical Formula

Point load at centre: δ = PL³/(48EI), M = PL/4. UDL: δ = 5wL⁴/(384EI), M = wL²/8.

Overview & Explanation

Standard Euler–Bernoulli results for a beam pinned at one end and on a roller at the other.

How It Works

Convert to N, m, Pa, m⁴.
Apply the formula for the load case.
Compare span/deflection with limits such as L/360.

Practical Applications

Preliminary beam sizing.
Checking lintels and shelves.

Example 1: 10 kN at mid-span, 4 m steel, I = 50×10⁶ mm⁴

Typical small steel beam.

Inputs

Load case: Point load P at mid-span (kN) · Load P (kN) or w (kN/m): 10 · Span L (m): 4 · Elastic modulus E (GPa): 200 · Second moment of area I (×10⁶ mm⁴): 50

= entered

Step 1

δ = PL³ / (48EI) = 10e3 × 4³ / (48 × 200e9 × 50e-6)

Step 2

= 1.3333 mm

Step 3

M = PL/4 = 10 kN·m

Maximum deflection

Result

= 1.3333 mm

Example 2: 5 kN/m UDL, 6 m, I = 100×10⁶ mm⁴

Floor joist style.

Inputs

Load case: Uniform load w (kN/m) · Load P (kN) or w (kN/m): 5 · Span L (m): 6 · Elastic modulus E (GPa): 200 · Second moment of area I (×10⁶ mm⁴): 100

= entered