Subject : Structural Analysis 1

Topic : Deflection in Beams

Difficulty : Medium

Macaulay's method:

1. It is a simple method based on the double integration concept. In this method, bending moment at any section is expressed in the systematic order.
2. The section x is to be taken in the last portion of the beam. In this method, bending moment due to each force or UDL is separated by compartment lines.
3. Slope is obtained by integrating bending moment and then deflection is obtained by integrating of slope equation.

Moment Area Method:

1. Moment area method is used to determine the slope and deflection at a particular point in determinate and indeterminate structure.
2. Theorems of moment are method suggested by Mohr and thus, these theorems are called Mohr theorem.

First theorem:

Statement: "The difference of deflection angles at two points B and A on the deflected curve of a beam is equal to the area under the bending moment diagram between two points A and B divided by EI."

Second theorem:

Statement: "If A and B are two points one the deflected shape of a beam, the vertical distance of point B from the tangent drawn to the elastic curve at point A is equal to moment of area of BMD between point A and B about the vertical line from point B divided by EI."