 Ch 4. Beam Stresses Multimedia Engineering Mechanics Bending Strainand Stress BeamDesign Shear Stress Built-upBeams
 Chapter 1. Stress/Strain 2. Torsion 3. Beam Shr/Moment 4. Beam Stresses 5. Beam Deflections 6. Beam-Advanced 7. Stress Analysis 8. Strain Analysis 9. Columns Appendix Basic Math Units Basic Equations Sections Material Properties Structural Shapes Beam Equations Search eBooks Dynamics Statics Mechanics Fluids Thermodynamics Math Author(s): Kurt Gramoll ©Kurt Gramoll MECHANICS - EXAMPLE Example Cantilever Beam with Loads A cantilever I-Beam needs to support a distributed load of 300 lb/ft for the last 2 feet, as shown in the diagram on the left. The beam is a standard I-Beam S18x70. What is the maximum shear stress in the web section at location a-a? Account for the weight of the beam. Solution The actual shear load at the specified location, a-a, needs to be determined before the shear stress can be calculated. Both the applied load, 600 lb, and the beam weight need to considered. Using the appendix Structural Shapes, the beam weight is 70 lb/ft. Shear Load at Section a-a Cutting the beam at a-a, and summing forces in the vertical gives,      V = 300(2) + 70(7)         = 1,090 lb Recall, the shear stress at any location can be calculated from      τ = VQ / It I-Beam Cross Section Using the appendix, the moment of inertia, web thickness, and flange thickness are given as,      I = 926 in4      tw = 0.711 in      tf = 0.691 in All that is missing is Q. Since the maximum shear is needed, the largest Q is required. The largest Q of most symmetrical cross sections occurs at the middle. Thus, determining Q for top half of cross section is      Qmax = A1 y1 +A2 y2         = 0.691 (6.251) [(9 - 0.691 / 2)]             + (9 - 0.691) (0.711) [(9 - 0.691)/2]         = 37.38 + 24.54 = 61.92 in2 This gives the final shear stress as      τ = VQ / It        = (1,090)(61.93) / [(926)(0.711)]      τ = 102.5 psi

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