Structural Design 04 - Bending Moments & Shear Forces

 Today we will discuss about bending moments and shear forces. These parameters are the reinforcement amount governing factors in the design process most of the time. There are few others such as Torsion etc. We can discuss about them in future. 

According to the type of the beam and the nature or support conditions and loading patterns, few formulas are available for finding the values of BM and SFs. If we have several loading patterns we can go for the theorem of super-positioning. Let's discuss few common types  that can be useful in basic structural designs. We focus mainly about beams here. Here we go.

(a). SIMPLY SUPPORTED BEAM - 

This means the support allows the beam for the rotation. that means no any restriction for rotation of the beam. For this support and beam should not be monotonically casted.

In simply support, support can be a Rock, R/R Masonry wall, Another beam, Brick wall or concrete wall.

When we idealize the situation we can find the values of bending moment and shear force using below equations. When we have only a UDL (Uniformly Distributed Load) on the beam and if the value is "n kN/m" and if the length of the two simply supports is "l", the value of Bending Moment at the middle bottom of the beams will be, (nl^2/)8 as shown. Shear force at a support would be (nl)/2. Shear force is coming from equating the loads in Up-Down direction and the BM values come from by taking the area of that shear force diagram.

We can show you several types of BM and SF diagrams according to few different common situation below. 

(b). Simply support beam with a point load at the middle

(c). Simply support beam with a UDL and a point load at the middle

(d). Two end fixed beam with a UDL

(e). Two end fixed beam with a pint load at the middle

(f). Cantilever beam (One end free beam) with a UDL

(g). Propped cantilever beam with a UDL

Beam Reactions, Bending Moments and Deflections values and equations can be directly taken from the Appendix 3 of the book of "Design of Structural Elements" by W.M.C.McKenzie. He is a teaching Fellow of Napier University of Edinburgh. I will mention those in below for your kind references. (All rights should belongs to the original author of the book)