What is Structural Analysis?
Structural analysis is the branch of civil engineering that determines how loads travel through a structure — the forces, reactions and stresses in beams, columns and frames. It underpins every safe building, bridge and tower design.
Structural analysis calculates the reactions, internal forces and stresses in a structure under load, using equilibrium equations (ΣF=0, ΣM=0) to keep it safe and stable.
- 1↓Idealize the structureModel beams, columns and joints as lines, pins or fixed supports.
- 2↓Apply loadsAdd dead, live, wind or seismic loads to the model.
- 3↓Find reactionsUse ΣF=0 and ΣM=0 to solve support reactions.
- 4↓Compute internal forcesFind shear, moment and axial force along each member.
- 5Check stresses & deflectionsCompare results against material and code limits.
Try it: interactive calculator
Step-by-step worked examples
A simply supported beam spans 8 m with a 20 kN point load placed 3 m from the left support. Find both reactions.
R₁ = P(L−a)/L = 20×(8−3)/8 = 12.5 kN R₂ = P×a/L = 20×3/8 = 7.5 kN Check: R₁+R₂ = 12.5+7.5 = 20 kN = P ✓
A cantilever beam of length 4 m carries a 10 kN load at its free end. Find the fixed-end reaction and moment.
Vertical reaction: R = P = 10 kN Fixed-end moment: M = P×L = 10×4 = 40 kN·m
A truss joint carries a 15 kN downward load balanced by a diagonal member on a 3-4-5 triangle (3 horizontal, 4 vertical, 5 hypotenuse). Find the member's axial force and horizontal component.
Vertical component must balance the load: F×(4/5) = 15 kN F = 15×5/4 = 18.75 kN Horizontal component = F×(3/5) = 18.75×3/5 = 11.25 kN
Flashcards
Quick quiz
Q1.For a simply supported beam with a single point load, what equations find the reactions?
Q2.A beam is called statically determinate when…
Q3.In R₁ = P(L−a)/L, increasing 'a' (moving the load toward the right support) does what to R₁?
Q4.Which is NOT typically considered a structural load?
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Common mistakes
Assuming a structure has only vertical loads. — Correct: Wind, seismic and lateral loads also act — always check all directions.
Forgetting to check ΣM=0 and only balancing ΣF=0. — Correct: Both force AND moment equilibrium must be satisfied.
Treating every structure as statically determinate. — Correct: Many real structures are indeterminate and need compatibility equations, not just equilibrium.
Ignoring support type (pin vs roller vs fixed). — Correct: Support type sets how many reaction unknowns exist — critical to the solution.
FAQ
What is structural analysis?
It's the engineering process of finding reactions, internal forces and stresses in a structure so it can be designed safely.
What is the formula for beam reactions?
For a simply supported beam with one point load: R₁ = P(L−a)/L and R₂ = Pa/L.
How do you calculate structural analysis problems?
Apply the equilibrium equations ΣF=0 and ΣM=0 to solve unknown reactions and internal forces.
What are examples of structural analysis?
Finding beam reactions, truss member forces, frame bending moments and column axial loads.