## Strength of Materials |

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Otto

of a

follows: Eq. 1-11 Eq. 1-10 x = ae horizontal coordinate of a point on the

Otto

**Mohr**(1835-1918) first recognized that Eq. 1-10 is the same as the equationof a

**circle**: (x - fl)2 + (y - bY = c2 (1-11) Equations 1-10 and 1-11 are related asfollows: Eq. 1-11 Eq. 1-10 x = ae horizontal coordinate of a point on the

**circle**y ...Page 21

They must be points of a circle because they satisfy Eq. 1-8 and 1-9, which were

combined as the equation of a circle, Eq. ... The same change in stresses occurs

after a rotation of 180° in the

They must be points of a circle because they satisfy Eq. 1-8 and 1-9, which were

combined as the equation of a circle, Eq. ... The same change in stresses occurs

after a rotation of 180° in the

**Mohr's circle**, in going from point 1 to point 2 in Fig.Page 27

The reader should check carefully to see if any other combinations of stresses

may result in circles that are not within the large circle in Fig. 1-17. Positions and

Sizes of

is ...

The reader should check carefully to see if any other combinations of stresses

may result in circles that are not within the large circle in Fig. 1-17. Positions and

Sizes of

**Mohr's Circles**. It has been demonstrated that the center of**Mohr's circle**is ...

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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