Figure 1 (a) shows an elevation view of a flexible weightless cable that is supp

Question

Figure 1 (a) shows an elevation view of a flexible weightless cable that is supported at points A and B. Please determine: reactions at A and B for the applied loads shown. The anchorage at A includes a 100 mm plate sandwiched between two 90 mm plates and bolted with three 13 mm diameter A325 bolts as shown in Fig. 1 (b). The effective diameter of the holes is 17 mm. The steel has Fy = 350 MPa, Fu = 450 MPa, = 0.9 and u= 0.75. Assume that plates are available in thicknesses of 3,4, 5, 6, 8, 9,10,12,16,20,25 and 30 mm. If the factored tensile force, due to a more severe loading condition than that shown in Fig. 5(a), is 105 kN, please determine: the necessary thickness of the 90 mm plates to resist this load. Will the failure of this member be ductile, or brittle? Figure 1(a): Suspended Cable for Problem 5 Figure 1(b): Detail at A for Problem 5

Explanation / Answer

The behavior of materials can be broadly classified into two categories; brittle and ductile. Steel and aluminum usually fall in the class of ductile materials. Glass and cast iron fall in the class of brittle materials. The two categories can be distinguished by comparing the stress-strain curves, such as the ones shown in Figure 8. Figure 8: Ductile and brittle material behavior The material response for ductile and brittle materials are exhibited by both qualitative and quantitative differences in their respective stress-strain curves. Ductile materials will withstand large strains before the specimen ruptures; brittle materials fracture at much lower strains. The yielding region for ductile materials often takes up the majority of the stress-strain curve, whereas for brittle materials it is nearly nonexistent. Brittle materials often have relatively large Young's moduli and ultimate stresses in comparison to ductile materials. Key note: The energy absorbed (per unit volume) in the tensile test is simply the area under the stress strain curve. These differences are a major consideration for design. Ductile materials exhibit large strains and yielding before they fail. On the contrary, brittle materials fail suddenly and without much warning. Thus ductile materials such as steel are a natural choice for structural members in buildings as we desire considerable warning to be provided before a building fails. The energy absorbed (per unit volume) in the tensile test is simply the area under the stress strain curve. Clearly, by comparing the curves in Figure 8, we observe that ductile materials are capable of absorbing much larger quantities of energy before failure. Finally, it should be emphasized that not all materials can be easily classified as either ductile or brittle. Material response also depends on the operating environment; many ductile materials become brittle as the temperature is decreased. With advances in metallurgy and composite technology, other materials are advanced combinations of ductile and brittle constituents. Quick Quiz: Question 1: A steel sample has a Young's modulus of 1.2e+7 and proportionality limit .0015 strain. The sample is a cylinder with radius .58 inches and length 3.48 inches. Find the total energy absorbed in the tensile test from zero strain to the proportionality limit. 50 in*lbs = 5.65 J 66,240 in*lbs = 7,484 J 14.27 in*lbs = 1.61 J None of the above

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