Beams With Triangular Loading  
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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 linearly increasing load q 1 is directed vertically downwards from A to a distance a.
The figure shows a beam of length a with B at the right 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 linearly increasing load q 1 is directed vertically downwards at a distance a from B.
The figure shows a beam of length a plus b with A having a pin support at the left end of the beam and B having a roller support at the right 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 linearly increasing load q 1 is directed vertically downwards to a distance a to A. A linearly decreasing load q 2 is directed vertically downwards from a distance a from A to B.
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 linearly decreasing load q 1 is directed vertically downwards from A to a distance a.
The figure shows a beam of length a with B at the right 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 linearly decreasing load q 1 is directed vertically downwards from a distance a to B.
The figure shows a beam of length a plus b with A having a pin support at the left end of the beam and B having a roller support at the right 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 linearly decreasing load q 1 is directed vertically downwards from A to a distance a. A linearly increasing load q 2 is directed vertically downwards from a distance a from A to B.