Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
10th Edition
ISBN: 9780073398204
Author: Richard G Budynas, Keith J Nisbett
Publisher: McGraw-Hill Education
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Chapter 2, Problem 33P
To determine

The prove of constant β=23 for the Eβρ if cantilever beam loaded in bending by using Figure “Strength S verses density ρ for various materials”.

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An 8 m long I-beam made of mild steel is used to support an overhead crane in a workshop, as shown in Figure 2(a). Figure 2(b) gives the dimensions of the I-beam. When answering the following questions, include the weight of the beam in your calculations. At what horizontal position on the beam would the load cause the maximum bending moment?   Please note: this question is would potentially be worth around marks and the answer has to justify this.
An 8 m long I-beam made of mild steel is used to support an overhead crane in a workshop, as shown in Figure 2(a). Figure 2(b) gives the dimensions of the I-beam. When answering the following questions, include the weight of the beam in your calculations.  At what horizontal position on the beam would the load cause the maximum bending moment? What is the minimum load that can initiate plastic deformation on the beam? What will be its location on the beam? For the mild steel, take the elastic modulus as 210 GPa, yield stress as 350 MPa, and density as 7850 kg m−
A design requires that a solid cantilever beam carry the largest possible end load, F,without plastically deforming. The beam length, L, is fixed. The square cross-section (t2)is not specified and the beam must be as light as possible. a.Determine the material index for this design. Assume the maximum end load depends on the yield stress accordingly: Start this problem by listing the objective, the constraints and the free variables. b.Determine the magnitude and units of the derived material index for the following materials:Aluminum 6061-T6, Titanium, Polycarbonate,and Polyether ether ketone (PEEK). Among these, which is the optimal material for this design?
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