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4 stepsTo determine the reactions at supports A and B, we will use the equations of static equilibrium. Support A is a pin support, so it has both horizontal () and vertical () reaction components. Support B is a roller support, so it has only a vertical reaction component ().
Convert the uniformly distributed load (UDL) into an equivalent point load.
The UDL is over a length of .
The equivalent point load is:This equivalent load acts at the centroid of the UDL, which is from support A.
Apply the equilibrium equation for the sum of horizontal forces.
Assume forces acting to the right are positive.
The negative sign indicates that acts to the left.
Apply the equilibrium equation for the sum of moments about point A.
Assume counter-clockwise moments are positive. The horizontal force of passes through point A's horizontal line of action, so it creates no moment about A.
Apply the equilibrium equation for the sum of vertical forces.
Assume upward forces are positive.
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