Documented elementary cases
Beam deflection & reactions
Inputs
Only the diagrammed elementary cases are available.
Downward magnitude at the diagrammed load point.
Distance between the fixed point or supports.
Assumes a homogeneous, linear-elastic member.
Use the bending-axis second moment of area.
Results
Fixed-end reaction
1
Maximum bending moment
1.2
Maximum elastic deflectionδ
2.4
δmax = PL³ / 3EI; Mmax = PL
A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.
Nearby: Axial response · Elastic stability · Solid-shaft torsion · Baseline L10 life
Method
Formula, when it applies, and when it does not
Set a bounded support and load arrangement, then inspect response quantities with an explicit diagram.
δmax = PL³ / 3EI; Mmax = PL
When
- Straight prismatic beam
- Small deflection
- Documented boundary case
Don’t
- This response uses a narrow, linear-elastic straight-beam model. Check that support conditions, small-deflection behavior, load position, and bending axis match the diagram.
Roark's Formulas for Stress and Strain — beam reactions and deflection cases