GATE Mechanical Engineering (ME) 2020 Shift 2 Solved Paper

Question : 12 of 65

Marks: +1, -0

A machine member is subjected to fluctuating stress

σ=σ_{0} \cos (8 π {t})

. The endurance limit of the material is

350 {MPa}

. If the factor of safety used in the design is

3.5

then the maximum allowable value of

σ_{0}

is _____________MPa (round off to 2 decimal places).

Solution:

Fluctuating stress

(σ)=σ_{0} \cos (8 π t)

Endurance strength

(σ_{ {e}})=350 {MPa}

{\FOS}=3.5

σ_{\max }=σ ×(1)=σ_{0}

σ_{\min }=σ 0 ×(-1)=-σ_{0}

Mean stress

(σ_{ {m}})=\;{σ_{\max }+σ_{ {min}}}/{2}=0

Amplitude stress

(σ_{a})=\;{σ_{\max }-σ_{\min }}/{2}=σ_{0}

Now

\;{σ_{ {m}}}/{ {S}_{ {yt}}}+\;{σ_{ {a}}}/{ {S}_{ {e}}}=\;{1}/{ {Fos}}

\;{0}/{ {S}_{ {yt}}}+\;{σ_{0}}/{350}=\;{1}/{3.5}

σ_{0}=100 {MPa}

Thus,

σ_{\max }=100 {MPa}

Go to Question:

Prev Question

Next Question