Max Deflection Calculator for Simply Supported Beam

Beam Deflection Inputs

Load case

Beam span

Length unit

Elastic modulus, E

E unit

Moment of inertia, I

I unit

Point load 1

Point load 1 position from left

Point load 2

Point load 2 position from left

Point load unit

Uniform load over full span

Uniform load unit

Deflection limit denominator

Example: enter 360 for L/360.

Numerical stations

Example Data Table

Case	Span	E	I	Load	Expected Use
Center point load	6 m	200 GPa	80,000,000 mm^4	12 kN at midspan	Beam with concentrated equipment load
Uniform load	5 m	11 GPa	120,000,000 mm^4	4 kN/m	Floor joist or timber beam check
Combined load	7.5 m	200 GPa	180,000,000 mm^4	8 kN plus 3 kN/m	Steel beam preliminary sizing

Formula Used

The calculator uses elastic small-deflection beam theory. It converts all entered values to a consistent base system before solving.

General curvature relation: E I d²y/dx² = M(x)
Center point load: δmax = P L³ / 48 E I
Full-span uniform load: δmax = 5 w L⁴ / 384 E I
Allowable deflection: δallow = L / limit denominator
Left reaction: RA = total load - RB
Right reaction: RB = moment of loads about left support / L

For off-center and combined loading, the page builds the bending moment diagram numerically. It integrates curvature twice and applies y(0) = 0 and y(L) = 0.

How to Use This Calculator

Select the load case that best matches the beam.
Enter span, elastic modulus, and moment of inertia.
Enter point loads, positions, and uniform load as needed.
Choose the correct units for each input group.
Enter the deflection limit denominator, such as 240, 360, or 480.
Press the calculate button.
Review maximum deflection, location, reactions, moment, and status.
Download CSV or PDF after a successful calculation.

Beam Deflection Guide

Why Beam Deflection Matters

A simply supported beam can look strong and still feel weak in service. Strength checks prevent breaking. Deflection checks control sag, cracks, ponding, vibration, door binding, ceiling damage, and poor appearance. This calculator focuses on service behavior. It estimates the largest vertical displacement along the clear span. It also reports reactions, bending moment, stiffness demand, and the selected span limit. These values help designers compare sections before ordering timber, steel, or concrete members.

Advanced Inputs

The tool accepts a center point load, an off center point load, a second point load, a full span uniform load, or a combined case. You may enter common engineering units. The script converts them to a consistent base system before calculation. Elastic modulus represents material stiffness. Moment of inertia represents section stiffness. A long span, low modulus, small inertia, or heavy load increases deflection quickly. Because span is raised to high powers, small length changes can create large movement changes.

Reading the Results

The maximum deflection is the key output. The location shows where the worst sag occurs. The allowable deflection equals span divided by the selected limit value, such as L over 360. A pass result means the calculated sag is within that selected serviceability limit. A fail result means the beam may need more depth, a stronger material, closer supports, reduced load, or a different layout. Reaction values help with bearing checks and connection planning. Maximum moment helps compare the same load case with flexural strength design.

Practical Use

For early estimating, adjust one input at a time. Increase inertia first, then compare material modulus carefully. This method shows which change gives the best deflection improvement without changing every project variable at once.

Good Construction Practice

Use verified loads from drawings, codes, or a qualified professional. Include dead load, live load, finishes, partitions, equipment, and any temporary construction load. Use actual section properties from manufacturer tables. Do not mix gross and cracked inertia without understanding the design method. For critical members, continuous beams, cantilevers, notches, holes, lateral bracing, vibration, creep, moisture, and connection slip may control performance. Treat this calculator as a planning aid. Final construction decisions should follow the applicable building code and a competent structural review.

FAQs

1. What is maximum beam deflection?

Maximum beam deflection is the largest vertical displacement along the span. It usually appears near midspan for symmetric loading, but it may shift when point loads are off center.

2. What does simply supported beam mean?

A simply supported beam rests on two supports. One support usually acts like a pin. The other acts like a roller. The ends can rotate, but vertical movement is restrained.

3. Which deflection limit should I use?

Common limits include L/240, L/360, and L/480. The correct value depends on material, finish sensitivity, occupancy, local code, and project requirements.

4. Why does moment of inertia matter?

Moment of inertia measures section stiffness. A larger inertia greatly reduces deflection. Beam depth often improves inertia more effectively than added width.

5. Can this calculator size steel beams?

It can support preliminary serviceability checks. Final steel design must also check strength, shear, bearing, buckling, bracing, connections, and code requirements.

6. Does this include beam self weight?

You can include self weight by adding it to the uniform load. Use the member weight per length plus other dead and live loads.

7. Why is my beam failing deflection?

The span may be long, the load may be high, or the section may be too flexible. Increasing inertia, reducing span, or changing material can help.

8. Is this suitable for final construction approval?

No. This is a planning calculator. Final decisions should follow applicable codes and should be reviewed by a qualified structural professional.