When a beam is designed on the basis of strength the bending and shear stress should not be greater than the allowable stresses. To determine if the beam is can support the load(s) the following analysis can be used.
Section Modulus: a ratio of the moment of inertia and distance (between the neutral axis and a point)
Srequired = Mmax / σallowable
Where...
- S is the section modulus
- M is the max moment, determinded from the moment diagram
- σ is the allowable bending stress
When the section modulus is calculated, look in tables for S values that are greater than the calculated Srequired (The AISC Manual has a list of data)
There are several structural shapes for beam designs such as: wide-flange, channels (C-shapes), angles, etc. They are designated in the form of: (Letter) (number) x (number) For example a wide-flange beam would be: W24 x 55. The numbers tell you the size and strength of the beam's cross section. The first number, following the letter, is the depth of the cross section. The last number indicates the weight per unit length.
Once you have several design beams chosen, usually the one with the smallest cross section is picked because it will be made of less material making it lighter, which is the more economical choice.
Check to see if the shear stress is within the allowable limits.
allowable ≥ VQ / ItFor a wide-flange beam you can use:
= Vmax / Aweb Where...
- Vmax is the maximum shear stress
- Aweb is the area of the cross section (web). Product of the beam's depth and the thickness of the web.
allowable than that beam design will be able to support the loadings.The reason why a wide-flange beam is efficient at resisting moments is because when I (moment of inertia) is increased, Srequired will increase. To have a larger I, the majority of the material will be located as far away from the neutral axis.
Beams can also be "built-up" involving 2 or more parts that are joined together. For more info on built up beams and shear flow click here.
For more topics on Mechanics of Materials click here
