## Engineering Mechanics of Materials4. 2 Solid Circular Shafts-Angle of Twist and Shearing Stresses 159 4. 3 Hollow Circular Shafts-Angle of Twist and Shearing Stresses 166 4. 4 Principal Stresses and Strains Associated with Torsion 173 4. 5 Analytical and Experimental Solutions for Torsion of Members of Noncircular Cross Sections 179 4. 6 Shearing Stress-Strain Properties 188 *4. 7 Computer Applications 195 5 Stresses in Beams 198 5. 1 Introduction 198 5. 2 Review of Properties of Areas 198 5. 3 Flexural Stresses due to Symmetric Bending of Beams 211 5. 4 Shear Stresses in Symmetrically Loaded Beams 230 *5. 5 Flexural Stresses due to Unsymmetric Bending of Beams 248 *5. 6 Computer Applications 258 Deflections of Beams 265 I 6. 1 Introduction 265 6. 2 Moment-Curvature Relationship 266 6. 3 Beam Deflections-Two Successive Integrations 268 6. 4 Derivatives of the Elastic Curve Equation and Their Physical Significance 280 6. 5 Beam Deflections-The Method of Superposition 290 6. 6 Construction of Moment Diagrams by Cantilever Parts 299 6. 7 Beam Deflections-The Area-Moment Method 302 *6. 8 Beam Deflections-Singularity Functions 319 *6. 9 Beam Deflections-Castigliano's Second Theorem 324 *6. 10 Computer Applications 332 7 Combined Stresses and Theories of Failure 336 7. 1 Introduction 336 7. 2 Axial and Torsional Stresses 336 Axial and Flexural Stresses 342 7. 3 Torsional and Flexural Stresses 352 7. 4 7. 5 Torsional, Flexural, and Axial Stresses 358 *7. 6 Theories of Failure 365 Computer Applications 378 *7. |

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Results 1-5 of 5

Page 7

-L- - – - - (a) (b) (c) 11

axial force (

the free-body diagram shown in Fig. 1.5(c): 1 X F, = 0 FA – we(10) – wA(y – 10) ...

-L- - – - - (a) (b) (c) 11

**ft**) y/**ft**) |30 ||y +" 40 ||, +4 f = w = applied force intensity F =axial force (

**lb**) f = w (1b/**ft**) (tension is positive) (d) (e) FIGURE 1.5 Now, considerthe free-body diagram shown in Fig. 1.5(c): 1 X F, = 0 FA – we(10) – wA(y – 10) ...

Page 12

1.10 An 18-ft-long rod is suspended as shown in Fig. P1.10. The unit weights of

each part are wa = 6

body diagrams to determine the internal axial forces in each part of the rod. Use

an ...

1.10 An 18-ft-long rod is suspended as shown in Fig. P1.10. The unit weights of

each part are wa = 6

**lb**/**ft**, we = 8**lb**/**ft**, and we = 4**lb**/**ft**. Draw appropriate free-body diagrams to determine the internal axial forces in each part of the rod. Use

an ...

Page 30

P1.39 and compute the shear and moment at distances of 2 and 10 ft from the left

end of the beam. Include free-body diagrams for each solution. Linear 200

{ 14- ". |. R Ri 12 ft * FIGURE P1.39 1.40 Determine the reactions at D and E ...

P1.39 and compute the shear and moment at distances of 2 and 10 ft from the left

end of the beam. Include free-body diagrams for each solution. Linear 200

**lb**/**ft**| (){ 14- ". |. R Ri 12 ft * FIGURE P1.39 1.40 Determine the reactions at D and E ...

Page 51

1.82 A 6 ft x 3 ft sign is supported on a vertical post which is fixed at its foundation

as shown in Fig. P1.82. The wind loading has been reduced to a line loading of

120

1.82 A 6 ft x 3 ft sign is supported on a vertical post which is fixed at its foundation

as shown in Fig. P1.82. The wind loading has been reduced to a line loading of

120

**lb**/**ft**along the vertical which acts perpendicular to the sign and is applied ... Page 59

(a) A single-story building has column spacings: A = 20 ft, B = 20 ft, C = 30 ft, and

D = 30 ft. Roof loading intensities: W1 = W2 = W3 = W4 = 60

COLWT = 120

...

(a) A single-story building has column spacings: A = 20 ft, B = 20 ft, C = 30 ft, and

D = 30 ft. Roof loading intensities: W1 = W2 = W3 = W4 = 60

**lb**/**ft**”. Columns:COLWT = 120

**lb**/**ft**, STORYHT = 14 ft. Use this information to provide data for the...

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### Contents

60 | |

Stresses and Strains in Axially Loaded Members | 121 |

Torsional Stresses Strains and Rotations | 159 |

Stresses in Beams | 198 |

5 Deflections of Beams | 265 |

Combined Stresses and Theories of Failure | 336 |

Column Theory and Analyses | 384 |

Statically Indeterminate Members | 432 |

Introduction to Component Design | 484 |

Analysis and Design for Inelastic Behavior | 523 |

Analysis and Design for Impact and Fatigue Loadings | 552 |

Selected Topics | 590 |

APPEMDx Computer Programming for Mechanics of Materials | 647 |

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### Common terms and phrases

absolute maximum shear aluminum angle of twist applied Assume axes axial force axially loaded beam shown bending cantilever beam Castigliano's second theorem column compressive constant coordinate cross section cross-sectional area cylinder deflection deformation depicted in Fig elastic curve equal equation equilibrium Euler EXAMPLE factor of safety FIGURE flexural stress FORTRAN free-body diagram function given by Eq k-ft k-in kN-m lb-in lb/ft length longitudinal material maximum in-plane shear maximum shear stress modulus of elasticity Mohr’s circle moment of inertia neutral axis normal stress obtained perpendicular plane stress condition plot positive principal centroidal axis principal strains principal stresses radius Refer to Fig respect rotation shaft shear force shear strain shown in Fig simply supported beam slope SOLUTION statically indeterminate steel stress concentration stress element subjected torque torsional uniform load vertical yield strength yield stress zero