Using the Moment-Area Method to Calculate Slope and Deflection of Beams

Explanation:

The Moment-Area method is used to calculate the slope and deflection of beams subjected to various loads.

Cantilever beam with concentrated load:

To calculate the slope and deflection, we need to determine the area of the moment diagram caused by the concentrated load. Using the Moment-Area method, the slope can be found by dividing the area of the moment diagram by the Young's modulus and the cross-sectional moment of inertia. The deflection can be found by integrating the equation for the slope.

Cantilever beam with UDL:

The slope and deflection for a beam with a uniformly distributed load can be determined using the Moment-Area method in a similar manner as described for the concentrated load case. The only difference is that the moment diagram will have a triangular shape. Calculate the area of the triangular moment diagram and use it to find the slope and deflection.

Simply supported beam with UDL:

The slope and deflection for a simply supported beam with a uniformly distributed load can also be calculated using the Moment-Area method. In this case, the moment diagram will be a parabolic shape. Find the area of the parabolic moment diagram and use it to determine the slope and deflection.

Simply supported beam with central concentrated load:

Calculate the area of the moment diagram caused by the central concentrated load and use it to find the slope and deflection of the simply supported beam using the Moment-Area method.