Third Edition
MECHANICS OF
                     MATERIALS
                       Ferdinand P. Beer
                       E. Russell Johnston
                                                                Combined Stresses
                                                                        © 2002 The McGraw-Hill Companies, Inc. All rights reserved.
      MECHANICS OF MATERIALS
Edition
Third
                                                                                                     Beer • Johnston • DeWolf
          Loading and Stress
             The relationships for determining the state of
             stress and deformation in members due to the
             fundamental types of loads which are;
             • axially centric load,
                                                                                                         P
                                                                                                
                                                                                                         A
             • torsional load,
                                                                                                              T
                                                                                                       
                                                                                                               J
          © 2002 The McGraw-Hill Companies, Inc. All rights reserved.                                                    8-2
                                                                                                                                      1
      MECHANICS OF MATERIALS
Edition
Third
                                                                                          Beer • Johnston • DeWolf
          Loading and Stress
             • bending loading
                                                                                                      My
                                                                                              
                                                                                                       I
             • shear loading
                                                                                                     VQ
                                                                                               
                                                                                                      It
          © 2002 The McGraw-Hill Companies, Inc. All rights reserved.                                      8-3
      MECHANICS OF MATERIALS
Edition
Third
                                                                                          Beer • Johnston • DeWolf
          Loading and Stress
             • Thin-walled pressure vessel
                   – Cylinder
                                                                               pr            pr
                                                                        1           2 
                                                                               t             2t
                   – Sphere
                                                                                     pr
                                                                        1   2 
                                                                                     2t
             have been demonstrated previously.
          © 2002 The McGraw-Hill Companies, Inc. All rights reserved.                                      8-4
                                                                                                                     2
      MECHANICS OF MATERIALS
Edition
Third
                                                                        Beer • Johnston • DeWolf
          Combined Stresses
             Structural and machine components often
             resist more than one type of loading acting
             simultaneously.
             For example, a shaft in torsion may be
             subjected to bending because of its own
             weight at the same instance.
             Therefore, the effects of combined loadings
             should be considered.
          © 2002 The McGraw-Hill Companies, Inc. All rights reserved.                    8-5
      MECHANICS OF MATERIALS
Edition
Third
                                                                        Beer • Johnston • DeWolf
          Combined stresses
             The combined loadings which will be studied
             are:
             1.Shear load + Bending moment
             2.Axial load + Bending moment
             3.Axial load + Torsional loads
             4.Bending moment + Torsional load
          © 2002 The McGraw-Hill Companies, Inc. All rights reserved.                    8-6
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