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A steel bar 100 mm (4.0 in.) long and having a square cross section 20 mm (0.8 in.) on an edge is pulled in tension with a load of 89,000 N (20,000 lbf), and experiences an elongation of 0.10 mm (4.0 × 10−3 in.). Assuming that the deformation is entirely elastic, calculate the elastic modulus of the steel.

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Answer:

This problem asks us to compute the elastic modulus of steel.    For a square cross-section, A0  =  , where b0 is the edge length.    Combining Equations 6.1, 6.2, and 6.5 and solving for E, leads to

E   = σε = FA0Δll0= Fl0b02Δl= (89, 000  N)(100×10−3m)(20×10−3m)2(0.10×10−3m)= 223 × 109 N/m2 = 223 GPa    (31.3 × 106 psi)  

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