The steel rod shown below has a uniform cross-section. When it is suspended from

Question

The steel rod shown below has a uniform cross-section. When it is suspended from the top its own weight would cause the elongation e of 0.09mm. Calculate the unstressed length L of the rod. Give your answer in meters with three decimal places.
Steel has the elastic modulus of 210GPa and density of 7850kg/m3.

The steel rod shown below has a uniform cross-section. When it is suspended from the top its own weight would cause the elongation e of 0.09mm. Calculate the unstressed length L of the rod. Give your answer in meters with three decimal places. Steel has the elastic modulus of 210GPa and density of 7850kg/m3. Correct answer approximately 22m. Need full working though, because I can't understand how the question can be done as no information about area of the rod has been given.

Explanation / Answer

Assuming uniform cross-section A, we get the weight of the rod = mass of rod* g = (density * volume) *g = density*(A*L)*g So stress under self weight = Load on the rod per unit cross-section= Weight of the rod/A= (density*A*L*g)/A = density*L*g Strain = e/L. We are dealing with elongation under "self weight". For a rod of "uniform" cross-section this weight acts at the Centre of Mass of the rod which lies at the middle of the rod. Hence, effectively we'll have to consider only half of the rod length for calculating the strain. Elastic modulus = Stress / strain Putting values, 210*10^9 = (7850*L*9.81) / ((0.09*10^-3)/(L/2)) Solving this we get, L= 22.155 m

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