## Engineering mechanics of materials |

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Page 267

6-2 Moment-

pure bending is depicted in Figure 6.1(a). Cross-sectional centroidal axes u and

v, which are also principal axes, are shown in Figure 6.1(b). To simplify the ...

6-2 Moment-

**Curvature**Relationship A differential element of a beam subjected topure bending is depicted in Figure 6.1(a). Cross-sectional centroidal axes u and

v, which are also principal axes, are shown in Figure 6.1(b). To simplify the ...

Page 269

... Eq. 6.2 into Eq. 6.1 leads to 1 Mu (6.2) (63) Equation 6.3 expresses the fact that

the beam

moment Mu at that section and inversely proportional to the bending stiffness EIu

...

... Eq. 6.2 into Eq. 6.1 leads to 1 Mu (6.2) (63) Equation 6.3 expresses the fact that

the beam

**curvature**at any beam section is directly proportional to the appliedmoment Mu at that section and inversely proportional to the bending stiffness EIu

...

Page 270

To derive the governing differential equation for beam deflections (or

displacements), an approximation will be developed for beam

will be substituted into the moment-

beginning ...

To derive the governing differential equation for beam deflections (or

displacements), an approximation will be developed for beam

**curvature**and thiswill be substituted into the moment-

**curvature**relationship given by Eq. 6.3. Inbeginning ...

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### Contents

Introduction | 1 |

Torsionally Loaded Members in Equilibrium | 14 |

Shear and Bending Moment in Beams | 23 |

Copyright | |

19 other sections not shown

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### Common terms and phrases

absolute maximum shear allowable stress aluminum angle of twist applied Assume axes axial force axially loaded beam shown bending cantilever beam Castigliano's second theorem circular column components compressive Compute constant construct coordinate cross section cross-sectional area cylinder deflection deformation depicted in Figure Determine diameter differential elastic curve equal equation equilibrium factor of safety flexural stress free-body diagram function given by Eq Homework Problems k-ft k-in kN-m length longitudinal material maximum shear stress modulus of elasticity Mohr's circle neutral axis normal stress obtained perpendicular plane stress plot principal centroidal axis principal strains principal stresses radius Refer to Figure respect rotation section a-a segment shear center shear force shear strain shown in Figure slope solution Solve static statically indeterminate steel stress element subjected Substitution tension tion torque torsional uniform load vertical yield strength yield stress zero