By J. S. C. Browne, N. Hiller and G. E. Walker (Auth.)
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Diagrams. m. (lbf ft) First of all we make a sketch of the beam, Fig. 13a. The reaction at the roller VB will be vertical, and is determined by taking moments about the pin. hence %VB = 4 0 x 1 0 x 5 + 500x6 cos 30°, VR = 575 lbf SHEARING FORCE AND BENDING MOMENT 61 The vertical component of the reaction at the pin, VA is determined by taking moments about the roller. SVA = 40x10x3 + 500x2 cos 30° hence VA = 258 lbf It is worth checking at this stage, that the sum of VA and VB, which is 833 lbf, is equal to the total vertical loading 500 cos 30°+400 = 833 lbf.
23 EQUILIBRIUM OF STRUCTURES 39 E are in a horizontal plane and the plane of the jib and the tie bisects the angle DAE, which is a right angle. Determine the forces in the stays and in the post. ) 18. Three members AD, BD and CD are connected together at D and are attached to a vertical wall at A, B and C. This framework forms a FIG. 24 bracket which supports a vertical load of 4 tonf and a horizontal load of 2 tonf as shown in Fig. 24. Assuming that all the connections are pinjoints, determine the magnitude and sense of the force in each member of the framework.
The heights of A, B9 C and P above the floor can also be measured, being the z co-ordinates of these points. Before the x and y co-ordinates of the points can be measured, it will be necessary to arbitrarily rule two straight lines, intersecting at right angles, on the floor to act as the x and y axes. Imagine now that the x, y and z co-ordinates of A, B, C and P have been measured in inches and that they are A (3, 5, 36), B (6, 36, 44), C (40, 19, 54) and P(20, 20, 18). The component of the force in a cord parallel to any axis is the tension in the cord multiplied by the cosine of the angle between the cord and any line parallel to the axis under consideration which intersects the cord.