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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Page 315
... tion will be equal in magnitude to the deflections at the applied loads P. Use the area - moment method and note that the beam and its loading are symmetric . P A B Constant El E D Fig . P6.57 . Express your answers in terms of w , L ...
... tion will be equal in magnitude to the deflections at the applied loads P. Use the area - moment method and note that the beam and its loading are symmetric . P A B Constant El E D Fig . P6.57 . Express your answers in terms of w , L ...
Page 318
... tion of P , a , E , and I1 . 6.78 Use the area - moment method to find the deflec- tion at point B of the beam depicted in Fig . P6.78 . Express the answer in terms of w , a , E , and I1 . A Ri W 2w ΕΙ El 2E11 B 2E11 B A R2 RI R2 2a a ...
... tion of P , a , E , and I1 . 6.78 Use the area - moment method to find the deflec- tion at point B of the beam depicted in Fig . P6.78 . Express the answer in terms of w , a , E , and I1 . A Ri W 2w ΕΙ El 2E11 B 2E11 B A R2 RI R2 2a a ...
Page 568
... tion . 12.10 Refer to Example 12.6 and use the given infor- mation except for rotating the beam such that the 2 - in . side is placed horizontally . Compare your answers with the answers for Example 12.6 . 12.11 Refer to Fig . 12.9 ( a ) ...
... tion . 12.10 Refer to Example 12.6 and use the given infor- mation except for rotating the beam such that the 2 - in . side is placed horizontally . Compare your answers with the answers for Example 12.6 . 12.11 Refer to Fig . 12.9 ( a ) ...
Contents
Stresses in Beams | 198 |
Deflections of Beams | 265 |
Combined Stresses and Theories of Failure | 336 |
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absolute maximum shear aluminum angle of twist applied Assume axes axial force axially loaded beam shown bending C₁ cantilever beam Castigliano's second theorem column compressive constant coordinate cross section cross-sectional area cylinder deflection deformation depicted in Fig diameter elastic curve equal equation equilibrium Euler EXAMPLE factor of safety FIGURE flexural stress FORTRAN free-body diagram k-ft k-in kN-m lb/ft length longitudinal M₁ material maximum shear stress modulus of elasticity Mohr's circle moment of inertia neutral axis normal stress obtained perpendicular plane stress plane stress condition plot principal centroidal axis principal stresses r₁ radius ratio rectangular Refer to Fig rotation shaft shear force shear strain shown in Fig slope SOLUTION statically indeterminate steel stress element T₁ t₂ tensile Tmax torque torsional uniform load V₁ yield stress zero