For the configuration of loading shown in the given figure, the stress in fibre AB is given by :a)b)c)d)Correct answer is option 'B'. Can you explain this answer?

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Answer

Answer

It is the case of eccentric axial compressive loading
In this case what we actually do is we apply an equal and opposite force at the longitudinal axis.
Because we only know how to find stress when load is acting along longitudinal axis.
By doing this, the given load forms a couple with the opposite direction force.

when we apply an equal and opposite force P on the longitudinal axis, the given load forms a couple =P.e(anticlockwise) with the tensile force at L.A., and we get a compressive force P at L.A.

the axial stress is given by P/A
the bending stress is given by (M*y/ Ixx) = [ P.e.(d/2)/ Ixx ]

Now the question asks stress in fibre AB
The axial stress is compressive that we know
The bending stress is in anti clockwise direction i.e. tensile at bottom fibre and compressive at top fibre

at top the total stress will be [ axial stress(compr.) + bending stress (compr.)]
at bottom the total stress = [ axial stress(compr.) + bending stress(tens.) ]

by incorporating the signs negative for compressive and positive for tensile we get the required answer.

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