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

What is the Moment-Area method and how is it used to calculate the slope and deflection of beams? The Moment-Area method is used to calculate the slope and deflection of beams subjected to different loads. It involves determining the area of the moment diagram caused by the load and using it to find the slope and deflection. Four specific cases are considered: cantilever beam with concentrated load, cantilever beam with uniformly distributed load, simply supported beam with uniformly distributed load, and simply supported beam with central concentrated load.

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.

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