Element Stiffness For Beam Elements

Question 1

Beam theory assumptions

Answer 1

• Small deformations (first order theory)
• Linearly elastic homogenous material (Hooks’s law apply)
• Shear deformation is neglected
• Stress normal to the longitudinal axis neglected

Question 2

The solution to the strong form satisfies

Answer 2

• Pointwise equilibrium for 0<= x =< L

* Kinematical and mechanical BC’s exactly

Question 3

Principle of viritual displacement is expressed by

Answer 3

Internal virtual work = external virtual work(distributed load+nodal forces)

Question 4

Explain w = Nv

Answer 4

w = deflection 
N = shape function
v = nodal displacement

Question 5

What is Nq and q

Answer 5

Nq = generalized displacement patters
q = generalized coordinates

Question 6

What is the B matrix

Answer 6

Strain displacement mateix

Question 7

What are the steps to calculate the B matrix?

Answer 7

Fill in

Question 8

What is the difference in the equation for k for bar and beam?

Answer 8

For bar it is EA, for beam it is EI

Question 9

Steps to find k

Answer 9

w = Nq•q
Bq = d^2Nq / dx^2
kq = EI (integral 0-L) Bq^T Bq dx

k = (A^-1)^T kq (A^-1)