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 229
... supported by W14 x 22 ( see Appendix E ) beams which are parallel and spaced at a distance of 8 ft from each other . These beams may be assumed to be simply supported over a span of 20 ft . The roofing material weighs 30 lb / ft2 and ...
... supported by W14 x 22 ( see Appendix E ) beams which are parallel and spaced at a distance of 8 ft from each other . These beams may be assumed to be simply supported over a span of 20 ft . The roofing material weighs 30 lb / ft2 and ...
Page 289
... supported beam of length L and con- stant bending stiffness EI , has an elastic curve given by v = EI ( Wi 9012 x6 1 Wi x5 + 30 L WI W1 L x3 W1 w1 L3 X 18 30 where the origin for x is located at the left end , v is directed positively ...
... supported beam of length L and con- stant bending stiffness EI , has an elastic curve given by v = EI ( Wi 9012 x6 1 Wi x5 + 30 L WI W1 L x3 W1 w1 L3 X 18 30 where the origin for x is located at the left end , v is directed positively ...
Page 466
... supported at end B at the midpoint of cross beam CD , which is simply supported . Both beams are steel for which E 30 x 106 psi and have the same moment of inertia I method of superposition to determine the force acting on beam CD and ...
... supported at end B at the midpoint of cross beam CD , which is simply supported . Both beams are steel for which E 30 x 106 psi and have the same moment of inertia I method of superposition to determine the force acting on beam CD and ...
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