We are asked to determine the components of reaction at hinges A and B if hinge B resists only forces in the x and y directions and A resists forces in the x, y, z directions.
To find Ay by taking moment along x-axis under equilibrium condition use the following relation.
$$\ A_y(a) + B_y(a+b+c) - W(d) $$Substitute the known values in the above expression.
$$\ A_y(18 cm) - B_y(18 cm + 24 cm +24 cm) - (100 N)(18 cm) = 0 $$$$\ A_y = \frac{undefined N\cdot cm - B_y(0 cm)}{18 cm} $$Find By by adding all the forces along y-axis using the following relation.
$$\ A_y + B_y = 0 $$Substitute the known values in the above expression.
$$\ (\frac{undefined N\cdot cm - B_y(0 cm)}{18 cm}) + B_y = 0 $$$$\ undefined N\cdot cm - B_y(0 cm) + B_y(18 cm) = 0 $$$$\ B_y = \frac{undefined N\cdot cm}{-18 cm} $$$$\ B_y = undefined N $$To find Ay use the following relation.
$$\ A_y + B_y = 0 $$Substitute the known values in the above expression.
$$\ A_y + undefined N = 0 $$$$\ A_y = -undefined N$$Find Az by adding all the forces along z-axis using the following relation.
$$\ A_z - W = 0 $$Substitute the known values in the above expression.
$$\ A_z - 100N = 0 $$$$\ A_z = 100N $$To find Ax by taking moment along y-axis under equilibrium condition use the following relation.
$$\ A_x(a) + B_x(a + b + c) = 0 $$Substitute the known values in the above expression.
$$\ A_x18 cm - B_x(18 cm +24 cm +24 cm) = 0 $$$$\ A_x = \frac{-B_x(0 cm)}{18 cm} $$Find Bx by adding all the forces along x-axis using the following relation.
$$\ A_x + B_x = 0 $$Substitute the known values in the above expression.
$$\ \frac{-B_x(0 cm)}{18 cm} + B_x = 0 $$$$\ B_x = 0 $$Find reaction Ax using the following relation.
$$\ A_x + B_x = 0 $$Substitute the known values in the above expression.
$$\ A_x + 0 = 0 $$$$\ A_x = 0 $$