How do I draw shear force and bending moment diagrams for a beam with UDL?
- Expert answer
- Undergraduate
- Asked
The question
My structural mechanics assignment asks me to draw shear force and bending moment diagrams for a simply supported beam with a UDL.
I need reactions, maximum moment and the diagram shapes.
Short answer
For a simply supported beam with a uniformly distributed load, replace the UDL by its equivalent point load for reactions, draw shear as a straight line, and draw bending moment as a parabola with maximum moment where shear is zero.
Full expert answer
Structural engineering tutor
MEng Civil Engineering, CEng
A uniformly distributed load, or UDL, spreads load along a length of beam. In beam diagram assignments, the important idea is that the UDL creates a linearly changing shear force and a parabolic bending moment curve.
What the question is asking
The question is asking you to calculate support reactions, then show how shear and bending moment vary along the beam. You need equations, diagram shapes and a maximum moment value.
Key concepts to cover
- Equivalent point load of UDL
- Support reactions
- Shear force sign convention
- Bending moment equation
- Maximum moment where shear equals zero
- Diagram shape
- Units: kN and kNm
Mini example
A 6 m simply supported beam carries a UDL of 4 kN/m across the whole span. Total load is:
textW = wL = 4 x 6 = 24 kNBecause the load is symmetrical:
textRA = RB = 12 kNShear starts at +12 kN and decreases linearly to -12 kN. At midspan, shear is zero.
Maximum bending moment at midspan:
textMmax = wL^2 / 8 = 4 x 6^2 / 8 = 18 kNmSample questions and short answers
1. Where does the equivalent point load act?
For a full-span UDL, it acts at the centre of the loaded length.
2. What shape is the shear force diagram?
For a UDL, shear changes linearly, so the shear force diagram is a straight sloping line.
3. What shape is the bending moment diagram?
For a UDL, bending moment is parabolic.
4. Where is maximum bending moment?
At the point where shear force is zero. For a symmetrical full-span UDL, this is midspan.
Common student mistakes
- Forgetting to convert UDL to total load for reactions
- Putting the equivalent load at the wrong position
- Drawing bending moment as a triangle for a UDL
- Missing units
- Not using a sign convention
Related questions
- How do I find the reactions of a simply supported beam with a point load?
- How do I analyse stress, strain and factor of safety in a machine component?
- How do I apply Bernoulli's equation to a tank or nozzle problem?
Academic use note
Use this as a method guide. For partial UDLs or combined loads, split the beam into regions and write equations for each region.
Sources and further reading
This answer explains a method for you to apply to your own work. Copying it into a submission would count as plagiarism, and it is indexed by similarity checkers.
All questions