Title: Beam Element Stiffness Equation Sect' 10'3
1Beam Element Stiffness Equation (Sect. 10.3)
- Bernoulli-Euler Beam Theory
- Plane cross-section remains plane after the
deformation (slender beams). - Linear, elastic material behavior.
- We limit our discussion to
- Shear and bending loads only (axial load will be
considered later). - Straight, prismatic beams only (No coordinate
transformation is considered).
2Stiffness Matrix for a Beam Element
3Stiffness Matrix for a Beam Element
Consider a point on the beam cross-section The
position vector of this point with respect to the
beam axis is
The vector displacement consists of pure
translation as well as rigid body rotation
4Stiffness Matrix for a Beam Element (cont.)
y
z
Beam cross-section
5Stiffness Matrix for a Beam Element (cont.)
6Summary
Useful Relationships for a Beam Element
7Distributed Load Definition for the Beam Element
2
1
2
1
L
8Distributed Load Definition for the Beam Element
(Cont.)
2
1
2
1
L
9Distributed Load Definition for the Beam Element
(Cont.)
P
2
a
1
2
1
L