Structural analysis / exercises
Deflection and general stress analysis
Modules 13 to 15: deflection, complex stress and strain, and energy methods. Several of these can be done more than one way — if two routes agree, you have a real check.
Teaching basis and review status
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesPractice
A simply supported beam spans 8.00 m under a UDL of 15.0 kN/m, with E = 205 000 N/mm² and I = 4.00 × 10⁸ mm⁴. What is the maximum deflection, in mm? (15 kN/m = 15 N/mm.)
Practice
At a point σx = 120 N/mm², σy = 30 N/mm² and τxy = 50 N/mm². What is the major principal stress, in N/mm²?
Practice
For that same stress state, what is the von Mises equivalent stress, in N/mm²?
Practice
A cantilever of span 2.50 m carries a 20.0 kN tip load, with E = 205 000 N/mm² and I = 9.00 × 10⁷ mm⁴. Using Castigliano or the unit-load method, what is the tip deflection, in mm?
Check yourself
In the unit-load method, what must the virtual system satisfy, and what must the real system satisfy?
Practice
At a point εx = 300 µ, εy = 100 µ and γxy = 160 µ. What is the major principal strain, in microstrain?