Beam Element Stiffness Equation Sect' 10'3

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Beam 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).

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Stiffness Matrix for a Beam Element
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Stiffness 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
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Stiffness Matrix for a Beam Element (cont.)
y
z
Beam cross-section
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Stiffness Matrix for a Beam Element (cont.)
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Summary
Useful Relationships for a Beam Element
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Distributed Load Definition for the Beam Element
2
1
2
1
L
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Distributed Load Definition for the Beam Element
(Cont.)

• Linearly varying load

2
1
2
1
L
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Distributed Load Definition for the Beam Element
(Cont.)

• Concentrated load

P
2
a
1
2
1
L