● System Active

BEAMCALC STRESS & DEFLECTION CALCULATOR

Beam Configuration

Load Type

Max Deflection

—

↓ DEFL

Max Reaction

—

⇧ REACT

Max Moment

—

kN·m

↻ MOMENT

Bending Stress

—

MPa

σ STRESS

Computing...

Second Mom. Area

—

mm⁴

Section Modulus

—

mm³

EI Stiffness

—

kN·m²

Beam Diagram

Beam

Shear Force

Bending Moment

Deflection

Beam Geometry

Span Length 4000 mm

500625012000

Load Position (a) 2000 mm

0L/2L

Point Load 10.0 kN

0.1250500

Material

Elastic Modulus (E) 200 GPa

1 GPa200400

Yield Strength (σ_y) 250 MPa

1010002000

Cross-Section

Formula Reference

Beam Stress & Deflection Calculator: Structural Engineering Guide

Beam analysis is at the core of structural engineering. Calculating bending stress, shear force diagrams and maximum deflection for simply supported, cantilever and fixed beams is essential for bridge design, building frames and machine structures. This calculator delivers results per IS 800 and Eurocode standards.

📋 How to Use This Calculator

Select beam type, Simply Supported, Cantilever or Fixed-Fixed.
Enter beam length (m), cross-section type and dimensions.
Select loading type, UDL (Uniform Distributed Load), Point Load or Moment.
Enter load magnitude, view the Bending Moment Diagram, Shear Force Diagram and maximum deflection.

📐 Formula & Working Principle

Simply Supported + UDL: Max BM = wL²/8, Max Deflection = 5wL⁴/(384EI). Cantilever + UDL: Max BM = wL²/2, Max Deflection = wL⁴/(8EI). Bending Stress σ = M×y/I.

💡 Worked Example

Simply supported steel beam, L=6 m, UDL=10 kN/m. Max BM = 10×6²/8 = 45 kN·m. ISMB 200 section: I=2235 cm⁴. Bending stress = 45×10⁶×100/(2235×10⁴) = 201 MPa (Fe250: fy=250 MPa, safe).

❓ Frequently Asked Questions (FAQ)

Q: What is the deflection limit?

Per IS 456, deflection limits are L/250 for slabs and L/300 for beams. Live load deflection should not exceed L/360.

Q: Why are I-section beams used?

The I-shape places material far from the neutral axis, providing greater bending stiffness for the same weight. The weight-to-strength ratio is excellent.

Q: Which is better: fixed beam or simply supported beam?

A fixed beam has a max BM of wL²/12 (vs wL²/8 for simply supported), 33% lower. However, fixed beams are more expensive and complex to construct.

Q: When does shear failure occur?

Maximum shear stress occurs at beam ends. If calculated shear stress exceeds allowable shear stress → provide web stiffeners or a higher section.

Q: When are composite beams used?

Steel beam + concrete slab in composite action, both deflection and depth are reduced. Common in multi-storey buildings and bridges.