고체역학 (Gere) — Axially Loaded Members: Problem 2.3-8

2.3-8 A rectangular bar of length \(L\) has a slot in the middle half of its length (see figure). The bar has width \(b\), thickness \(t\), and modulus of elasticity \(E\). The slot has width \(b/4\). (a) Obtain a formula for the elongation \(\delta\) of the bar due to the axial loads \(P\). (b) Calculate the elongation of the bar if the material is high-strength steel, the axial stress in the middle region is 160 MPa, the length is 750 mm, and the modulus of elasticity is 210 GPa. (c) If the total elongation of the bar is limited to \(\delta_{\text{max}} = 0.475\) mm, what is the maximum length of the slotted region? Assume that the axial stress in the middle region remains at 160 MPa.