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EGM 3520 Department of Mechanical and Aerospace Engineering Contents Introduction 8.1 Principal Stresses in a Beam 8.2 Design of Transmission Shafts 8.3 Stresses under Combined Loadings 2
EGM 3520 Department of Mechanical and Aerospace Engineering Introduction 3 In Chapter 1 and 2, you learned how to determine the normal stress due to centric loads. In Chapter 3, you analyzed the distribution of shearing stresses in a circular member due to a twisting couple. In Chapter 4, you determined the normal stresses caused by bending couples. In Chapters 5 and 6, you evaluated the shearing stresses due to transverse loads. In Chapter 7, you learned how the components of stress are transformed by a rotation of the coordinate axes and how to determine the principal planes, principal stresses, and maximum shearing stress at a point. In Chapter 8, you will learn how to determine the stress in a structural member or machine element due to a combination of loads and how to find the corresponding principal stresses and maximum shearing stress.

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EGM 3520 Department of Mechanical and Aerospace Engineering 8.1 Principle Stresses in a Beam 4 Prismatic beam subjected to transverse loading Principal stresses determined from methods of Chapter 7 Can the maximum normal stress within the cross-section be larger than no for a rectangular beam ; maybe otherwise I Mc m m Mc I m VQ It , x xy My VQ I It    
EGM 3520 Department of Mechanical and Aerospace Engineering 8.1 Principle Stresses in a Beam 5 axial stress at top principal stresses at y I Mc m

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EGM 3520 Department of Mechanical and Aerospace Engineering 8.1 Principle Stresses in a Beam 6 plot the direction of the principal axes I Mc m
EGM 3520 Department of Mechanical and Aerospace Engineering 8.1 Principle Stresses in a Beam 7 Cross-section shape results in large values of xy near the surface where x is also large. max may be greater than m

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EGM 3520 Department of Mechanical and Aerospace Engineering Sample Problem 8.1 8 A 160-kN force is applied at the end of a W200x52 rolled-steel beam. Neglecting the effects of fillets and of stress concentrations, determine whether the normal stresses satisfy a design specification that they be equal to or less than 150 MPa at section A-A’. SOLUTION: Determine shear and bending moment in Section A-A’ Calculate the normal stress at top surface and at flange-web junction. Evaluate the shear stress at flange- web junction. Calculate the principal stress at flange-web junction
EGM 3520 Department of Mechanical and Aerospace Engineering Sample Problem 8.1 9 SOLUTION: Determine shear and bending moment in Section A-A’ Calculate the normal stress at top surface and at flange-web junction.

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