Chegg 3 - Lecture notes dvxcv x PDF

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Engineering Design (5th Edition) 3 Bookmarks

Chapter 11, Problem 13PE

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Problem

A cantilever beam is loaded with force P at its free end to produce a deflection δ = PL 3/3EI . T beam has a circular cross section, I = πr4/4. Develop a figure of merit for selecting a material that minimizes the weight of a beam for a given stiffness (P/δ). By using the following material properties, select the best material (a) on the basis of performance and (b) on the basis of co and performance.

Step-by-step solution

Step 1 of 3 a) Consider the following calculations of steel:

Here, k is stiffness, I is moment of inertia, E is elasticity, L is length, r is radius of bar, d is displacement, P is load. Put C for

because radius and length will be constant for all materials.

Put 200 for E to calculate k in terms of C.

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Step 2 of 3 Tabulate the stiffness of each material on the basis of performance:

Therefore, performance factor is more for steel.

Comment

Step 3 of 3 b) Therefore, on the basis of cost and performance steel is better material for cantilever beam because cost of steel is 450 $/ton which is less than other materials and it has more performance factor compare to other materials.

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