Engin Exam · Free practical tool

Simply supported beam calculator

Check equilibrium, internal forces and elastic deflection for two standard exam load cases. Read the reaction and bending results before interpreting the displacement curve.

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The method

Central P: R=P/2, Mmax=PL/4, δmax=PL³/(48EI). Uniform w: R=wL/2, Mmax=wL²/8, δmax=5wL⁴/(384EI).

Before using the result

  • Simply supported prismatic Euler–Bernoulli beam; linear elasticity and small deflection. No shear deformation, self-weight unless included in load, or strength/code check.

Worked examples

These original training examples illustrate the method for Structural Engineering (SE) Examination. Use the matching “Load example” button above to explore a variation; example values are not equipment settings or prescribed criteria.

1. Worked example

Check equilibrium, internal forces and elastic deflection for two standard exam load cases. Read the reaction and bending results before interpreting the displacement curve.

Simply supported span
4 m
Load case
Central point load
Central point load
10 kN
Elastic modulus
200,000 MPa
Second moment of area
8,000,000 mm⁴
  1. Load case: Central point load; L = 4 m; EI = 1600000 N·m².
  2. Support reactions = 5000 N each.
  3. Maximum deflection = 0.008333333333333333 m at midspan.
  • Left reaction: 5,000 N
  • Right reaction: 5,000 N
  • Maximum moment: 10,000 N·m
  • Maximum downward deflection: 0.008333333 m

2. Comparison example

Compare a different supplied condition using the same method. For Engin Exam, the important check is that the input meaning, units and method assumptions still match the problem.

Simply supported span
5 m
Load case
Central point load
Central point load
10 kN
Elastic modulus
200,000 MPa
Second moment of area
8,000,000 mm⁴
  1. Load case: Central point load; L = 5 m; EI = 1600000 N·m².
  2. Support reactions = 5000 N each.
  3. Maximum deflection = 0.016276041666666668 m at midspan.
  • Left reaction: 5,000 N
  • Right reaction: 5,000 N
  • Maximum moment: 12,500 N·m
  • Maximum downward deflection: 0.01627604 m

Check your understanding

1. Which relationship is used?

Central P: R=P/2, Mmax=PL/4, δmax=PL³/(48EI). Uniform w: R=wL/2, Mmax=wL²/8, δmax=5wL⁴/(384EI).

2. Which assumption should you check first?

Simply supported prismatic Euler–Bernoulli beam; linear elasticity and small deflection. No shear deformation, self-weight unless included in load, or strength/code check.

3. How should you verify a different unit system?

Convert every input to the displayed calculation units first. Equivalent physical inputs must give equivalent results; a unit label alone does not convert a number.

Continue with the matching exam topic

This tool connects to Structural Engineering (SE) Examination free practice. Work through a question independently, then use the calculation steps to identify where your method differs. The tool stays free whether or not you choose paid preparation.