1
Q
Beam theory assumptions
A
- Small deformations (first order theory)
- Linearly elastic homogenous material (Hooks’s law apply)
- Shear deformation is neglected
- Stress normal to the longitudinal axis neglected
2
Q
The solution to the strong form satisfies
A
- Pointwise equilibrium for 0<= x =< L
* Kinematical and mechanical BC’s exactly
3
Q
Principle of viritual displacement is expressed by
A
Internal virtual work = external virtual work(distributed load+nodal forces)
4
Q
Explain w = Nv
A
w = deflection N = shape function v = nodal displacement
5
Q
What is Nq and q
A
Nq = generalized displacement patters q = generalized coordinates
6
Q
What is the B matrix
A
Strain displacement mateix
7
Q
What are the steps to calculate the B matrix?
A
Fill in
8
Q
What is the difference in the equation for k for bar and beam?
A
For bar it is EA, for beam it is EI
9
Q
Steps to find k
A
w = Nq•q Bq = d^2Nq / dx^2 kq = EI (integral 0-L) Bq^T Bq dx
k = (A^-1)^T kq (A^-1)
