Question

For determining the deflection 'y' of a loaded beam at a distance 'x' by Macaulay's method, which one or more of the following is/are used?
1. The basic differential equation for deflection $El\frac{d^{2}y}{d{x}^2}=-M;$ where El is the flexural rigidity of the beam, M is the bending moment.
2. Successive integration of the differential equation given in 1.
3. Known positions of zero deflection in the beam.
Select the correct answer using the codes given below:

• A. 1 only
• B. 1 and 2
• C. 3 only
• D. 1, 2 and 3

Answer 1

The correct option is D 1, 2 and 3

To find out the deflection using Macaulay's method, basic differential equation $EI=\frac{d^{2}y}{d{x}^2}=-M$ is integrated successively and known boundary conditions such as zero slope etc. are used to find out constant of integration.