1
GATE ME 2017 Set 2
+2
-0.6
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
A
$$1.67$$
B
$$2.00$$
C
$$3.60$$
D
$$4.00$$
2
GATE ME 2016 Set 1
+2
-0.6
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
$${n_T} = \left( {{{\sqrt 3 } \over 2}} \right){n_V}$$
B
$${n_T} = \left( {\sqrt 3 } \right){n_V}$$
C
$${n_T} = {n_V}$$
D
$${n_V} = \left( {\sqrt 3 } \right){n_T}$$
3
GATE ME 2015 Set 1
+2
-0.6
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
$$1.0$$
B
$$2.0$$
C
$$2.5$$
D
$$3.3$$
4
GATE ME 2014 Set 4
Numerical
+2
-0
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 __________.