Design For Static Loading · Machine Design · GATE ME

Consider the schematic of a riveted lap joint subjected to tensile load $$F,$$ as shown below. Let $$d$$ be the diameter of the rivets, and $${S_f}$$ be the maximum permissible tensile stress in the plates. What should be the minimum value for the thickness of the plates to guard against tensile failure of the plates? Assume the plates to be identical.

A machine element $$XY,$$ fixed at end $$X,$$ is subjected to an axial load $$P,$$ transverse load $$F,$$ and a twisting moment $$T$$ at its free end $$Y.$$ The most critical point from the strength point of view is

The uniaxial yield stress of a material is $$300$$ $$MPa.$$ According to Von mises criterion, the shear yield stress $$(in$$ $$MPa)$$ of the material is ___________.

Which one of the following is NOT correct?

Match the following criteria of material failure, under biaxial stresses $${\sigma _1}$$and $${\sigma _2}$$ and yield stress $${\sigma _y}$$ with their corresponding graphic representations:
$$P.$$ Maximum normal stress criterion
$$Q.$$ Maximum distortion energy criterion
$$R.$$ Maximum shear stress criterion

Which theory of failure will you use for aluminium components under steady loading is

A solid shaft can resist a bending moment of $$3.0$$ $$kNm$$ and a twisting moment of $$4.0$$ $$kNm$$ together, then the maximum torque that can be applied is

Two shafts $$A$$ and $$B$$ are made of the same material. The diameter of shaft $$B$$ is twice that of shaft $$A.$$ The ratio of power which can be transmitted by shaft $$A$$ to that of shaft $$B$$ is

The outside diameter of a hollow shaft is twice its inside diameter. The ratio of its torque carrying capacity to that of a solid shaft of the same material and the same outside diameter is

A large uniform plate containing a rivet hole is subjected to uniform uniaxial tension of $$95$$ $$MPa.$$ The maximum stress in the plate is

Strength to weight ratio for a circuit shaft transmitting power is directly proportional to the

In the design of shafts made of ductile materials subjected to twisting moment and bending moment, the recommended theory of failure is

The principal stresses at a point in a critical section of a machine component are $${\sigma _1} = 60\,\,MPa,\,\,{\sigma _2} = 5\,\,MPa$$ and $${\sigma _3} = - 40\,\,MPa.$$ For the material of the component, the tensile yield strength is $${\sigma _y} = 200\,\,MPa.$$ According to the maximum shear stress theory, the factor of safety is

The principal stresses at a point inside a solid object are $${\sigma _1} = 100\,\,MPa,\,\,{\sigma _2} = 100\,\,MPa$$ and $${\sigma _3} = 0\,\,MPa.$$ The yield strength of the material is $$200$$ $$MPa.$$ The factor of safety calculated using Tresca (maximum shear stress) theory is $${n_T}$$ and the factor of safety calculated using Von Mises (maximum distortional energy) theory is $${n_V}$$. Which one of the following relations is TRUE?

A machine element is subjected to the following bi-axial state of stress: $$\,\,{\sigma _x} = 80MPa;\,\,{\sigma _y} = 20MPa;\,\,{\tau _{xy}} = 40MPa.$$ If the shear strength of the material is $$100 MPa,$$ the factor of safety as per Tresca’s maximum shear stress theory is

A shaft is subjected to pure torsional moment. The maximum shear stress developed in the shaft is $$100$$ $$MPa.$$ The yield and ultimate strengths of the shaft material in tension are $$300$$ $$MPa$$ and $$450$$ $$MPa,$$ respectively. The factor of safety using maximum distortion energy (Von - Mises) theory is __________.

Consider the two states of stress as shown in configurations $${\rm I}$$ and $${\rm II}$$ in the figure below. From the standpoint of distortion energy (Von - Mises) criterion, which one of the following statements is true?

The state of stress at a point is given by $$\,\,{\sigma _x} = - 6\,MPa,\,\,{\sigma _y} = 4\,\,MPa,$$ and $${\tau _{xy}} = - 8\,\,MPa.$$ The maximum tensile stress (in MPa) at the point is ____________.

The homogeneous state of stress for a metal part undergoing plastic deformation is $$$T = \left( {\matrix{ {10} & 5 & 0 \cr 5 & {20} & 0 \cr 0 & 0 & { - 10} \cr } } \right)$$$

Where the stress component values are in $$MPa.$$ Using von Mises yield criterion, the value of estimated shear yield stress, in $$MPa$$ is

A solid circular shaft needs to be designed to transmit a torque of $$50$$ $$N.m.$$ If the allowable shear stress of the material is $$140$$ $$MPa,$$ assuming a factor of safety of $$2,$$ the minimum allowable design diameter in $$mm$$ is

A small element at the critical section of a component in bi-axial state of stress with the two principal stresses being $$360$$ $$MPa$$ and $$140$$ $$MPa.$$ The maximum working stress according to distortion energy theory is