1. Beams and Deflections Zach Gutzmer, EIT
Civil and Environmental Engineering
South Dakota State University

2. What is a Beam?
Beam elements are subjected to loads along the member’s axis AND loads transverse to the member’s axis.

3. What is a Beam? Beams develop internal forces to carry loads
Vc = internal shear force
Nc = internal normal force
Mc = internal bending moment
These internal forces typically vary along the beam’s length. We can show this variation with diagrams.

4. Bending Moment Diagrams and the Elastic Curve

5. Supports
Supports support beams and provide proper constraints so the beam will stay in equilibrium.
The THREE most common supports are:
Pin
Roller
Fixed

6. Deflection of Beams
The elastic curve is derived from the ‘elastic beam theory’
The elastic curve can be used to determine the displacement at any point on the beam
For common loadings and beam configurations, the equations for the elastic curve and deflections have been tabulated.

7. Deflection of Beams
Handout:

8. Deflection of Beams The deflection is directly proportional to:
The load, P
Beam length, L
The deflection is indirectly proportional to:
Modulus of Elasticity, E
Moment of Inertia, I

9. There is no I in Beam
The moment of inertia, I, is a cross sectional property based on geometry
This property gives a good indication on a section’s bending capacity
Some cross sections have different moments of inertia depending on how the shape is oriented.
Higher I = strong axis
Lower I = weak axis

10. There is no I in Beam
2” x 4” Example