Beams must be sufficiently strong to carry the applied bending moments and shear forces.
A primary concern of engineering design is to ensure that a chosen beam is strong enough to carry the load imposed on it safely. This simple concept is far from simple to quantify.
The beam has to carry both the bending moment and the shear force.
The bending moment and shear force capacities are related to the physical properties of the cross-section and material strength.
The bending moment capacity is expressed simply as:
- moment capacity = allowable bending stress x section modulus
and the shear force capacity as:
- shear capacity = allowable shear stress x shear area
The shear area for any section is calculated from the area of the vertical part of the cross-section.
Note the maximum allowable stress is the stress of yield point and is called the yield stress.
- moment capacity / actual bending moment = adequate factor of safety
- shear capacity / actual shear force = adequate factor of safety
everywhere along the beam then the beam is strong enough.