## Strength of Materials |

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Page 167

By definition, J y2da = /, the moment of

axis (because y is measured from the neutral axis). On the basis of equilibrium, M

, must be equal in magnitude and opposite in direction to the net moment M ...

By definition, J y2da = /, the moment of

**inertia**of the whole area about its neutralaxis (because y is measured from the neutral axis). On the basis of equilibrium, M

, must be equal in magnitude and opposite in direction to the net moment M ...

Page 403

AREA MOMENTS OF

small area dA about a point that is r distance away (Fig. A-6) is defined as / =

r2dA (A-3) dA Fig. A-6. Definition of moment * P of

concept.

AREA MOMENTS OF

**INERTIA**The moment of**inertia**(or second moment) of asmall area dA about a point that is r distance away (Fig. A-6) is defined as / =

r2dA (A-3) dA Fig. A-6. Definition of moment * P of

**inertia**. This is an abstractconcept.

Page 404

Some understanding may be obtained by considering rotational acceleration as

an analogy. If the area dA is accelerated around point P, the rotational

resistance to change in velocity) depends on the mass associated with the area ...

Some understanding may be obtained by considering rotational acceleration as

an analogy. If the area dA is accelerated around point P, the rotational

**inertia**(orresistance to change in velocity) depends on the mass associated with the area ...

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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