A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of $ \theta=30^\circ $ as shown in the figure.
The glue used at the interface fails if
Criterion 1: the maximum normal stress exceeds 2.5 MPa.
Criterion 2: the maximum shear stress exceeds 1.5 MPa.
Assume that the interface fails before the logs fail. When a uniform tensile stress of 4 MPa is applied, the interface
A simply supported beam of width 100 mm, height 200 mm and length 4 m is carrying a uniformly distributed load of intensity 10 kN/m. The maximum bending stress (in MPa) in the beam is __________ (correct to one decimal place).
A cantilever beam of length L and flexural modulus EI is subjected to a point load P at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear) is
A simply-supported beam of length 3L is subjected to the loading shown in the figure.
A shaft with a circular cross-section is subjected to pure twisting moment. The ratio of the maximum shear stress to the largest principal stress is
The cross-sections of two solid bars made of the same material are shown in the figure. The square cross-section has flexural (bending) rigidity $I_1$, while the circular cross-section has flexural rigidity $I_2$. Both sections have the same cross-sectional area. The ratio $I_1/I_2$ is
A gas is stored in a cylindrical tank of inner radius 7 m and wall thickness 50 mm. The gage pressure of the gas is 2 MPa. The maximum shear stress (in MPa) in the wall is
In a plane stress condition, the components of stress at a point are ${\sigma}_{x}=20\mathrm{MPa}$, ${\sigma}_{y}=80\mathrm{MPa}$ and ${\tau}_{xy}=40\mathrm{MPa}$. The maximum shear stress (in MPa) at the point is
A cylindrical tank with closed ends is filled with compressed air at a pressure of 500 kPa. The inner radius of the tank is 2 m, and it has wall thickness of 10 mm. The magnitude of maximum in-plane shear stress (in MPa) is____________
Consider the two states of stress as shown in configurations I and II in the figure below. From the standpoint of distortion energy (von-Mises) criterion, which one of the following statements is true?
Two solid circular shafts of radii R_{1} and R_{2} are subjected to same torque. The maximum shear stresses developed in the two shafts are ${\tau}_{1}$ and ${\tau}_{2}$. If R_{2}/ R_{2}=2, then ${\tau}_{2}$/${\tau}_{1}$ is _______
Consider a simply supported beam of length, 50h, with a rectangular cross-section of depth, h, and width, 2h. The beam carries a vertical point load, P, at its mid-point. The ratio of the maximum shear stress to the maximum bending stress in the beam is
The transverse shear stress acting in a beam of rectangular cross-section, subjected to a transverse shear load, is