Exam 11: Analysis of Stress and Strain

A rectangular plate in plane stress is subjected to normal stresses $\sigma _ { x } = 35 \mathrm { MPa } , \sigma _ { y } = 26 \mathrm { MPa }$ , and shearstress $\tau _ { x y } = 14 \mathrm { MPa } .$ The ratio of the magnitudes of the principal stresses $\left( \sigma _ { 1 } / \sigma _ { 2 } \right)$ is approximately:

$\text { A cantilever beam with rectangular cross section } ( b = 95 \mathrm {~mm} , h = 300 \mathrm {~mm} ) \text { supports load } P = 160 \mathrm { kN }$ at its free end. The ratio of the magnitudes of the principal stresses $\left( \sigma _ { 1 } / \sigma _ { 2 } \right)$ at point $A$ (at distance $c = 0.8 \mathrm {~m}$ from the free end and distance $d = 200 \mathrm {~mm}$ up from the bottom) is approximately:

A simply supported beam (L = 4.5 m) with rectangular cross section (b = 95 mm, h = 280 mm) supports uniform load $q = 25 \mathrm { kN } / \mathrm { m }$ . The ratio of the magnitudes of the principal stresses $\left( \sigma _ { 1 } / \sigma _ { 2 } \right)$ at a point $a = 1.0 \mathrm {~m}$ from the left support and distance $d = 100 \mathrm {~mm}$ up from the bottom of the beam is approximately:

A rectangular plate (a =120 mm, b = 160 mm) is subjected to compressive stress $\sigma _ { x } = - 4.5 \mathrm { MPa }$ tensile stress $\sigma _ { y } = 15 \mathrm { MPa }$ . The ratio of the normal stress acting perpendicular to the weld to the shear stress acting along the weld is approximately: