Stress in Bar of Uniformly Tapering Rectangular Cross Section | Mechanical Engineering
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This document summarizes stress in a bar with a uniformly tapering rectangular cross section. It defines the width of the larger and smaller ends (b1 and b2), length (L), thickness (t), and modulus of elasticity (E). It describes how to calculate the cross-sectional area (A) as a function of position (x), tensile stress (σ), and total elongation or extension (δL) of the bar when an axial pull force P is applied. As an example, it gives values to calculate the extension of a steel plate that tapers from 200mm to 100mm width over 500mm length, under an axial force of 40kN.
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Stress in Bar of Uniformly Tapering Rectangular Cross Section | Mechanical Engineering
- 2. Introduction Stress in a Bar of Uniformly Tapering Rectangular Cross Section Example
- 3. Forces Simple Stress Simple Strain Deformation
- 4. Let, b1 and b2 = Width of the larger and smaller end of the bar respectively L and t = Length and thickness of the bar respectively b2b1P P t x dx
- 5. Let, b1 and b2 = Width of the larger and smaller end of the bar respectively L and t = Length and thickness of the bar respectively E = Modulus of elasticity or Young’s modulus of the material b2b 1 P P t x dx
- 6. The cross sectional area of the element, Ax = Width × Thickness = (b1 – kx) × t Tensile stress induced in the small element = P / A Total elongation or extension of the element length b b log bbEt PL δL 2 1 e 21
- 7. A steel flat plate of 20 mm thickness, uniformly tapers from 200 mm to 100 mm width in the a length of 500 mm. Find the extension of the plate if an axial pull of 40 kN is applied at its ends.
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