Laboratory Work Sheet_Shear and Moment

1) To determine the bending moment and shear force on the beam.

Shear Stress in Beams: When a beam is subjected to nonuniform bending, both bending moments, M, and shear forces, V, act on the cross section. The normal stresses, σ x , associated with the bending moments are obtained from the flexure formula. We will now consider the distribution of shear stresses, τ, associated with the shear force, V. Let us begin by examining a beam of rectangular cross section. We can reasonably assume that the shear stresses τ act parallel to the shear force V. Let us also assume that the distribution of shear stresses is uniform across the width of the beam. Shear stresses on one side of an element are accompanied by shear stresses of equal magnitude acting on perpendicular faces of an element. Thus, there will be horizontal shear stresses between horizontal layers (fibers) of the beam, as well as, transverse shear stresses on the vertical cross section. At any point within the beam these complementary shear stresses are equal in magnitude. The existence of horizontal shear stresses in a beam can be demonstrated as follows. A single bar of depth 2h is much stiffer that two separate bars each of depth h.

1993

The shear capacity of the concrete beams having stirrups is assumed as the sum of individual contributions of both the concrete and shear reinforcement. Different international building codes have suggested empirical relations for both of these contributions. In this research seventy beams with five values of longitudinal reinforcement and seven values of shear span to depth (a/d) ratios were tested in two sets of thirty five beams each, without and with shear reinforcement to study the contribution of the stirrups in resisting the shear. The beams were tested under the concentrated load at the mid span. The test results were analyzed for the contribution of stirrups, the effect of longitudinal steel and shear span to depth a/d ratios. It has been shown by the results that the assumption of summing the individual contribution of steel and concrete for the shear strength of reinforced beams is not proved.

7-4. If the T-beam is subjected to a vertical shear of determine the maximum shear stress in the beam. Also, compute the shear-stress jump at the flangeweb junction AB. Sketch the variation of the shear-stress intensity over the entire cross section. V = 12 kip, B B V ϭ 12 kip 6 in. 3 in. 4 in. 4 in. 4 in. A 07 Solutions 46060 5/26/10 2:04 PM Page 475 •7-5. If the T-beam is subjected to a vertical shear of determine the vertical shear force resisted by the flange. V = 12 kip, 476

2021

Figure shows a simple beam, one of the widely used statically determinate beams loaded with a central point load W.