Module 15
Virtual work and energy methods
Strain energy, the principle of virtual work, and the unit-load method — one technique that finds the deflection of almost anything.
What this module covers
- Calculate strain energy stored in axial members and in bending
- State the principle of virtual work and explain what makes a virtual system valid
- Use the unit-load method to find the deflection of a pin-jointed truss
- Use the unit-load method to find beam deflections and rotations
- Apply Maxwell's reciprocal theorem and know why it is useful
Lessons
Where the ½ in ½Pδ comes from, and what the structure does with the energy.
Start lesson →One idea that finds the deflection of any pin-jointed structure.
Start lesson →The same idea with an integral instead of a sum — plus a result that saves real work.
Start lesson →The other two ways a member stores the work you do on it.
Start lesson →Differentiate the strain energy, and the deflection falls out.
Start lesson →
Module checkpoint
Check what you have taken in
4 questions
Question 1
Why does the factor of ½ appear in U = ½Pδ?
Question 2
A bar 2.00 m long, area 1200 mm², E = 205 000 N/mm², carries a gradually applied 50.0 kN load. What is the strain energy stored, in joules?
Question 3
In the unit-load method, what must the virtual (unit-load) system satisfy?
Question 4
A pin-jointed member has N = 60 kN, n = 1.5, L = 4000 mm, A = 800 mm² and E = 205 000 N/mm². What is this member's contribution to the joint deflection, in mm?