# A steel rod of rectangular cross-section (b = 15 mm, h = 30 mm) lengthened by 7.5 mm under the action

A steel rod of rectangular cross-section (b = 15 mm, h = 30 mm) lengthened by 7.5 mm under the action of tensile forces p = 72000 N. determine the initial length of the bar.

To find the initial length of the steel bar taken, apply the formula: F = E * S * Δl / l, from where we express: l = E * S * Δl / F = E * b * h * Δl / F.

Constants and variables: E – Young’s modulus for steel (E = 200 * 109 kg / m3); b – section length (b = 15 mm = 0.015 m); h – section width (h = 30 mm = 0.03 m); Δl – elongation of the steel bar (Δl = 7.5 mm = 0.0075 m); F is the resulting tensile force (F = 72000 N).

Calculation: l = E * b * h * Δl / F = 200 * 109 * 0.015 * 0.03 * 0.0075 / 72000 = 9.375 m.

Answer: The steel bar had an initial length of 9.375 m.

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