Represent the real load model
Use the form only when one simple span, one point force and a full-span uniform load reasonably represent the arrangement. Set an unused load to zero.
BEAMS & SECTIONS / TOOL 12
Simply Supported Beam Analysis Calculator
Use this to examine elastic deflection and beam actions for one simple span with one downward point force and a full-span uniform load.
Before you start: required inputs
- Determine the distance between the two ideal support lines and the position of the point force from the left support.
- Obtain E and the second moment of area about the actual bending axis. Convert the complete distributed load, including self-weight, to kN/m.
Calculation diagram
A PRACTICAL WALKTHROUGH
How to use this calculator
Match stiffness and units
Use span and point position in m, force in kN, uniform load in kN/m, E in MPa and I in mm⁴.
Read actions and deflection separately
Review maximum deflection, maximum moment, support reactions and shear. The line plot shows downward deflection along the beam, not a moment diagram.
6 m beam with a central 20 kN point force
THE INPUTS
Span 6 m; point force 20 kN at 3 m; uniform load 2 kN/m; E = 200,000 MPa; I = 200,000,000 mm⁴.
THE RESULT
Maximum downward elastic deflection is 3.09375 mm at midspan. Maximum sagging moment is 39 kN·m; each support reaction is 16 kN.
What does the result mean?
01
Deflection describes movement of the ideal elastic beam; no allowable-deflection limit is assigned.
02
Moment and shear are unfactored internal actions. Reactions are the forces transferred to the supports in this model.
03
An eccentric point load can place maximum deflection away from the point load and away from midspan. The reported locations identify where the calculated maxima occur.
Watch for this
Entering kg as a kN point force, using Iy for bending about x, or assuming the program adds beam self-weight automatically.
Formula & model conditions +
RA = P × (L − a) / L + w × L / 2; RB = P × a / L + w × L / 2
M(x) = RA × x − w × x² / 2 − P × max(x − a, 0)
Elastic point-load and uniform-load deflections are superimposed; maximum deflection is located from zero slope.
- A straight, prismatic, linearly elastic Euler–Bernoulli beam has ideal simple supports at both ends.
- The point load and the full-span uniform load act downward in one bending plane. Input the distributed self-weight explicitly.
- Small deflection, constant E and I, no shear deformation and no connection flexibility are assumed.
- Results are unfactored actions and elastic deflection. Strength, stability, fatigue and allowable deflection are not checked.
Common questions
Does this work for a continuous runway beam?
No. A continuous beam has different support and bending behaviour. This tool assumes a single ideal simply supported span.
Does a small calculated deflection mean the beam is adequate?
Not by itself. Strength, stability, fatigue, connections, local effects and the relevant deflection criterion must be checked separately.