A rectangular plate (a = 120 mm, b = 160 mm) is subjected to compressive stress $\sigma_{x}=-4.5 \mathrm{MPa} \text { and tensile stress } \sigma_{y}=15 \mathrm{MPa}$ . The
Ratio of the normal stress acting perpendicular to the weld to the shear
Stress acting along the weld is approximately:
A) 0.27
B) 0.54
C) 0.85
D) 1.22

Question

Quizplus · Accepted Answer

The normal stress ($\sigma_{n}$) and shear stress ($\tau$) acting on the weld can be calculated using the given stresses ($\sigma_{x}$ and $\sigma_{y}$) and the orientation of the weld. Since the problem does not specify the orientation of the weld, we assume the most common scenario where the weld is oriented at 45 degrees to the direction of the principal stresses for maximum shear stress calculation. At this orientation, the normal and shear stresses on the weld can be calculated using the equations for stresses on an oblique plane:$$\sigma_{n} = \frac{\sigma_{x} + \sigma_{y}}{2}$$$$\tau = \frac{\sigma_{y} - \sigma_{x}}{2}$$Substituting the given values:$$\sigma_{n} = \frac{-4.5 + 15}{2} = \frac{10.5}{2} = 5.25 \, \text{MPa}$$$$\tau = \frac{15 - (-4.5)}{2} = \frac{19.5}{2} = 9.75 \, \text{MPa}$$The ratio of the normal stress to the shear stress is:$$\frac{\sigma_{n}}{\tau} = \frac{5.25}{9.75} \approx 0.54$$However, my initial calculation led to an incorrect interpretation. Correcting this:The ratio should be calculated correctly based on the given scenario and the correct formulas. Given the mistake in the calculation process, the correct approach involves understanding that the ratio of normal to shear stress on the weld depends on the orientation and the correct application of stress transformation equations. Without specific orientation details or a mistake in the calculation, the correct answer should be directly derived from the problem's context and the formulas provided.

A Rectangular Plate (A = 120 Mm, B = 160 σx=−4.5MPa and tensile stress σy=15MPa\sigma_{x}=-4.5 \mathrm{MPa} \text { and tensile stress } \sigma_{y}=15 \mathrm{MPa}σx​=−4.5MPa and tensile stress σy​=15MPa

A Rectangular Plate (A = 120 Mm, B = 160 $\sigma_{x}=-4.5 \mathrm{MPa} \text { and tensile stress } \sigma_{y}=15 \mathrm{MPa}$