## Strength of Materials |

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Page 195

R-y The radius of

R, a constant, so Eq. 7-18 can be written as a = 0 (7-19) da Solving for R, R = -+ (

7-20) \da/p where both integrals are over the same cross-sectional area. R is the

...

R-y The radius of

**curvature**of any fiber l(y) isp = R - y, and of the neutral axis it isR, a constant, so Eq. 7-18 can be written as a = 0 (7-19) da Solving for R, R = -+ (

7-20) \da/p where both integrals are over the same cross-sectional area. R is the

...

Page 213

the beam is directly proportional to the local bending moment and inversely

proportional to Young's modulus and the moment of inertia of the cross section.

**CURVATURES**OF BEAMS Equation 8-2 also means that the local**curvature**ofthe beam is directly proportional to the local bending moment and inversely

proportional to Young's modulus and the moment of inertia of the cross section.

Page 224

Solution The moment diagram and the

shown in Fig. 8-14b. The maximum

point of interest, A, to the centroid is \L - 2 m. Since the beam at point B is rigidly

fixed, ...

Solution The moment diagram and the

**curvature**diagram are triangular asshown in Fig. 8-14b. The maximum

**curvature**is PL/El. The distance x' from thepoint of interest, A, to the centroid is \L - 2 m. Since the beam at point B is rigidly

fixed, ...

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angle applied Assume axial beam bending brittle buckling calculated caused column compressive stress concrete Consider constant crack cross section cross-sectional area curvature cyclic cylindrical deflection Determine diameter ductile elastic strain element elongation equations equilibrium EXAMPLE extensometer external load factors of safety failure fatigue fibers fracture free-body diagram ft-lb given GPa Fig hardening horizontal implant increase inertia magnitude maximum shear stress maximum stress metal minimum modulus Mohr's circle neutral axis normal stress notch plane plastic deformation plate plot pole pressure Prob problems psi Fig radius residual stresses rivets shaft shear force shear strain shear strength shown in Fig softening Solution specimen static steel strain gages strength of materials stress and strain stress distribution stress-strain curve temperature tensile stress tension thickness torque torsion tube vertical weight weld wire yield strength zero