Beams With External Concentrated Moments  
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The figure shows a beam of length a plus b with the left end having a pin support at A and the right end is having a roller support at B. The x axis is taken along the length of the beam and the y axis is taken perpendicular to the beam at its left end. A moment M 1 is directed in the counterclockwise direction at a distance a from A.
The figure shows a beam of length a plus b plus c with the left end having a roller support at B and the right end is having a pin support at A. The x axis is taken along the length of the beam and the y axis is taken perpendicular to the beam at its left end. A moment M 1 is directed in the clockwise direction at a distance a from B. A moment M 2 is directed in the clockwise direction at a distance c from A.
The figure shows a beam of length a plus b with a pin support at A and a roller support at B. A is at a distance a from the left end and B is at a distance a plus b from the left end of the beam. The x axis is taken along the length of the beam and the y axis is taken perpendicular to the beam at its left end. A moment M 1 is directed in the counterclockwise direction at the left end of the beam. A uniformly distributed load w 1 is directed vertically downwards between A and B.
The figure shows a beam of length a plus b with the right end marked B. The x axis is taken along the length of the beam and the y axis is taken perpendicular to the beam at its left end. A moment M 1 is directed in the clockwise direction at a distance b from B. A load P 1 is directed vertically downwards at a distance a plus b from B.
The figure shows a beam of length a plus b with the left end marked A. The x axis is taken along the length of the beam and the y axis is taken perpendicular to the beam at its left end. A moment M 1 is directed in the counterclockwise direction at a distance a from A. A load P 1 is directed vertically downwards at a and a load P 2 is directed vertically downwards at a distance a plus b from A.
The figure shows a beam of length a with A at the left end of the beam. The x axis is taken along the length of the beam and the y axis is taken perpendicular to the beam at its left end. A moment M 1 is directed in the clockwise direction at a distance a from A. A uniformly distributed load w 1 is directed vertically downwards from A to a distance a.