![]() Hence, welded cover plates are often used for parts of prismatic beams where the moment is large-for instance, in a bridge girder. ![]() For a structural member, fabrication and design constraints make it impractical to produce a beam of constant stress. Ultimately, the shear stress at those beam locations where the moment is small controls the design.Įxamples of beams with uniform strength include leaf springs and certain cast machine elements. Tapered beams designed in this way are called beams of constant strength. Where M presents the bending moment on an arbitrary section. To reduce the stress concentration at the juncture of the web and the flange, the sharp corners should be rounded. Fortunately, this defect of the shearing stress formula does not lead to serious error since, as pointed out previously, the web carries almost all the shear force. This contradiction cannot be resolved by the elementary theory instead, the theory of elasticity must be applied to obtain the correct solution. (c) is fictitious, because the inner planes of the flanges must be free of shearing stress, as they are load-free boundaries of the beam. This result is indicated by the dotted lines in Fig. As a consequence, the approximate average value of shear stress in the beam may be found by dividing P by the web cross section, with the web height assumed to be equal to the beam′s overall height: τ avg = p/2. 5.11b.Ĭomments Clearly, for a thin flange, the shear stress is very small as compared with the shear stress in the web. This is the parabolic equation for the variation of stress in the flange, shown by the dashed lines in Fig. Maximum Shearing Stress for Some Typical Beam Cross-Sectional Forms For instance, in the case of a cross section having nonparallel sides, such as a triangular section, the maximum value of Q/b (and thus τ xy) occurs at midheight, h/2, while the neutral axis is located at a distance h/3 from the base. Nevertheless, the maximum shear stress does not always occur at the neutral axis. Observe that shear stress can always be expressed as a constant times the average shear stress ( P/ A), where the constant is a function of the cross-sectional form. Problems involving various types of cross sections can be solved by following procedures identical to that for rectangular sections. 5.7.2 Various Cross Sectionsīecause the shear formula for beams is based on the flexure formula, the limitations of the bending formula apply when it is used. (5.39) yields only approximate values of the shearing stress. ![]() More generally, for wide rectangular sections and for other sections, Eq. (5.42) is the exact distribution of shear stress. ![]() As observed in Section 5.4, for a thin rectangular beam, Eq. Note that the maximum shear stress (either horizontal or vertical: τ xy = τ yx) is 1.5 times larger than the average shear stress V/A. Where A = 2 bh is the area of the rectangular cross section. ![]()
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