Question

Determine the reaction forces at supports on a horizontal beam by using the equations of equilibrium for a static application. As shown, beam ABC is supported by the roller at A and pin at C. The geometry of the beam is given by and . The applied forces are and . Force is applied at an angle with the horizontal. Neglect the weight of the beam.

a) Determine the vertical reaction at A.
b) Determine the horizontal component of the pin reaction at C.
c) Determine the vertical component of the pin reaction at C.

Answer 1

The reactions at the supports of a static horizontal beam can be determined by applying the conditions of equilibrium and resolving forces into their components to create a system of equations.

Step-by-step explanation:

Understanding the equilibrium of a horizontal beam involves applying the conditions for equilibrium, namely the sum of forces in both x and y directions should be zero, and the sum of torques should also be zero.

The reactions at the supports can be found by considering the vertical reaction at support A (Ay), the horizontal reaction at support C (Cx), and the vertical reaction at support C (Cy). By analyzing the beam with applied forces and using free-body diagrams, one can set up systems of equations that reflect these equilibrium conditions.

To determine the vertical reaction at point A, one must sum the vertical forces and set them equal to zero. Similarly, for the horizontal reaction at point C, the horizontal forces are summed, while the vertical reaction at point C involves considering the forces in the vertical direction and the torques around a chosen pivot point. Careful consideration of the angles at which the forces are applied is crucial when resolving them into their horizontal and vertical components.