GATE Mechanical Engineering (ME) 2020 Shift 1 Solved Paper

Question : 40 of 65

Marks: +1, -0

Bars of square and circular cross-section with 0.5 m length are made of a material withshear strength of 20 MPa. The square bar cross-section dimension is 4 cm × 4 cm and thecylindrical bar cross-section diameter is 4 cm. The specimens are loaded as shown in thefigure.

Which specimen(s) will fail due to the applied load as per maximum shear stress theory?

None of the specimens
Tensile and compressive load specimens
Bending load specimen
Torsional load specimen

Validate

Solution:

σ=\;{80 × 10^{3}}/{40 × 40}=50 {MPa}

\Tmax=25

MPa which is greater than shear strength of material

\Tmax = –25

MPa which is greater than shear strength of material

τ=\;{16 {T}}/{π {d}^{3}}

=\;{16 × 64 π ×(100)^{3}}/{π × 4^{3}}

T=16

MPa which is less than shear strength of material

\;{σ}/{y}=\;{M}/{I}

σ=\;{M y}/{I}

=\;{320 × {4}/{2}}/{{a^{4}}/{12}}=30 ×(100)^{3}=30 {MPa}

T = 15 MPa which is less than shear strength of material

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