Beams and Deflections

Zach Gutzmer, EIT

Civil and Environmental Engineering

South Dakota State University

What is a Beam?

• Beam elements are subjected to loads along the member’s axis AND loads transverse to the member’s axis.

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.

Bending Moment Diagrams and the Elastic Curve

Supports• Supports support beams and provide proper constraints so the beam will stay in equilibrium.

• The THREE most common supports are:– Pin

– Roller

– Fixed

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.

Deflection of Beams

Handout:

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

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

There is no I in Beam

2” x 4” Example