The negative sign indicates a negative moment, which was established from the sign convention for the moment, so the moment actually goes in the opposite direction. The obtained expression is valid for the entire beam (the region 0 < x < 3 ft). To compute the bending moment at section x dx, use the following: The total load acting through the center of the infinitesimal length is wdx. Let the shear force and bending moment at a section located at a distance of x from the left support be V and M, respectively, and at a section x dx be V dV and M dM, respectively. If distributed load is 0, then the shear will be constant and the slope of the moment will be linear (as shown in example 1 in the next section).įor the derivation of the relations among w, V, and M, consider a simply supported beam subjected to a uniformly distributed load throughout its length, as shown in the figure below. So, if there is a constant distributed load, then the slope of shear will be linear and the slope of the moment will be parabolic. There is a relationship between distributed loads and shear/moment diagrams. (Udoeyo)/01:_Chapters/1.04:_Internal_Forces_in_Beams_and_FramesĦ.2.2 Distributed Loads
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