5003 Lectures - Faculty of Engineering and Applied Science

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E5003 - Ship Structures I 80 © C.G. Daley 8.5. For elastic beam bending, complete Figure 1. The shear force diagram is sketched. You need to infer from the shear what the load (including support reactions) may be, as well as an estimate of the bending moment diagram, the slope diagram and the deflected shape. Draw the support conditions and the applied load on the beam, and sketch the moment, slope and deflection is the areas given. 8.6. Beam Mechanics. For the beam sketch below: a) sketch by hand the shear, moment, slope and deflection diagrams
E5003 - Ship Structures I 81 © C.G. Daley b) Assuming the beam is a 10cm x 10cm square steel bar, solve the problem to find the bending stress at the fixed support. Use any method you like. 8.7. There is a length of steel that is 3.1416 m long, 50mm wide. It has a yield strength of 500 MPa (N/mm 2 ), and a Young’s Modulus of 200 GPa. If the steel is thin enough it can be bent into a perfect circle without yielding. a) What is the maximum thickness 't' for the steel to be bent elastically (and not yield)? b) If the steel thickness is 1mm, what is the stress when it is bent into a 1m Dia circle. c) What would the shear force diagram look like? (Hint :this relates directly to the derivation of the differential equations for beam bending) 8.8. Sketch the shear, bending, slope and deflection patterns for the four cases shown below. No numerical values are required.
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5003 Lectures - Faculty of Engineering and Applied Science

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