 Ch 6. Advanced Beams Multimedia Engineering Mechanics CompositeBeams UnsymmetricBending
 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 Cantilever Beam Loaded in Two Directions Example Two distributed line loads act on a cantilever beam as shown in the diagram on the left. Both loads act through the center of the rectangular cross section in the directions shown. What is the maximum absolute bending stress in the wall? Solution Moments at Wall due to Distributed Loads To determine the bending stresses, the maximum moment needs to known. Since this is a cantilevered beam, the maximum bending moment will occur at the fixed end, or the wall.      Mz = Fy d  = -[(1.5)(0.5)] (1.5 + 0.75)           = -1.6875 kN-m      My = Fz d = [(1.5)(0.5)] (0.75)           = 0.5625 kN-m The moment of inertia around each axis is       Iz = (0.1)3(0.06)/12 = 5×10-6 m4       Iy = (0.06)3(0.1)/12 = 1.8×10-6 m4 Beam Cross-Section at Wall The maximum moment at one of the four corners. From inspection, both the My and Mz moments will cause tension stress in the upper left corner, point A (don't forget that Mz is negative value). Similarly, both moments will cause compression stress at point D. These two points, A and D, will be the maximum tension and conpression stress, respectively. In this case, the magnitudes for both the maximum compression and maximum tension will be equal. Maximum stress at point A, y = 0.05 m, z = 0.03 m, is = 26.25 + 16.875 MPa      σA = 26.25 MPa

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