Scan 0002

Quiz 1

MAE 243

An aluminum rod is shown in the figure and has a circular cross-section. The rod is subjected to an axial load of 10 kN. Using the stress-strain diagram for the material as shown to: a) Determine the yield stress. [1 point] b) Compute the stresses and strains acting on AB and BC while loading. [2 points] c) Sketch on the 'stress-strain diagram the calculated stress-strain values. [1 point] d) Find the approximate elongation of the rod when the load is applied. [2 points] e) Find the permanent elongation of the rod after the load is removed. [2 points] f) Ensure all your units are correct. [2 l3eints]

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Quiz 2

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Two solid cylindrical rods are joined at B and loaded as shown. Rod AB is ----+ A made of steel (E=29 x 106 psi), and rod Be of brass (E=15 x 106 psi). B Determine (a) the total deformation of the composite rod [4 points], and (b) the deflection of point B [4 points]. Use correct units throughout [2 points]. 30in

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Three bars made of different materials are connected together and placed between two walls when the temperature is T1=12°C. Determine the force exerted on the (rigid) supports when the temperature becomes T2=18°C [8 Points]. The materials properties and cross-sectional area of each bar are given in the Figure. Use correct units [2 points]

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The shaft has an outer diameter of 1.25 in. and an inner diameter of 1 in. If it is subjected to the applied torques as shown, determine the absolute maximum shear stress developed in the shaft. The smooth bearings at A and B do not resist torque.

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For the simple beam shown, calculate the reactions at A & B. Plot the shear and moment diagrams below. Reactions Shear Diagram Moment Diagram Units <2.A.AA

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Take Home Quiz Due Wednesday October 25th For the beam shown. Calculate the maximum compressive stress and maximum tensile stress in the beam and where they occur.

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h: [ha[ ('Con 0;:. 2.F be-d LO a. cannle-:e: o.e..:....-:. 70.-:~ :c~ s..t..:-::..=:. shown in Fig. P6.3-34. The allowable tensile '- re" is 'L7~::.~ :- = 20 ksi; and the allowable compressive stress is (CTallow)C = 16 ksi. 2..:-

,:Prob.6.3·27. For beam AE in Fig. P6.3-16, (a) sketch shear and

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;- momentdiagrams, and (b) determine the maximum flexural stress inthe beam. : Prob.6.3-28. For beam AE in Fig, P6.3-17, (a) sketch shear and C·',moment diagrams, and (b) determine the maximum flexural stress J' inthe beam.

NA

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~Prob. 6.3·29. For beam AE in Fig. P6.3-18, (a) sketch shear and ~·niomentdiagrams, and (b) determine the maximum flexural stress ~;ln the beam. ~)~rtib. 6.3-30. For beam AD in Fig. P6.3-19, (a) sketch shear and ~/iiiomentdiagrams, and (b) determine the maximum flexural stress $inthe beam. ~':~ob. 6.3-31. For beam AE in Fi'!. P6.3-20, (a) sketch shear and ~:i:~omentdiagrams, and (b) determine me ma.ximum flexural srress ~fin the beam.

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P6.3-34 Prob. 6.3-35. Determine me ma.ximum uniform distributed load, lV, that can be applied to the beam with o"erhang shown in Fig. P6.3-35. The allo";able srress (magnitude) in tension or cornpression is 1"0 :vIPa, and the beam is a W310 X 97 (see Table D.2 of Appendix D).

~J!rob. 6.3·32. A channel section is used as a cantile"er beam to ~~:supporta uniformly distributed load of intensity \I' = 100 lb/it ~;[~da concentrated load of P = 100 lb, as shown in Fig. P63jIf;;: 2, (a) Sketch shear and moment diagrams for the beam, and )determine the maximum tensile flexural stress and the maxim compressive flexural stress in the beam. The relevant dinsions of the cross section are shown below, and the moment

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P6.3-35 Prob. 6.3-36. One of the assumptions made in deriving the flexure formula, Eq. 6-13, was that CTy and CT, are much smaller than CTx' (a) Using the cantilever beam with uniformly distributed load, shown in Fig. P63-36, derive an expression for the ratio of the magnitude of the maximum flexural stress at the top of the beam, CTxm "" ICTx(X, y = h/2)i, at an arbitrary cross section x to the maximum transverse normal stress in the beam, CTym = p/b. (b) Use your results from Part (a) to show that the stated assumption is satisfied practically everywhere in this cantilever beam with uniform distributed load.

P6.3-32

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,ob.6.3-33. A structural tee section is used as a cantilever beam . SUpporta triangularly distributed load of maximum intensity 0'", 3 kN/m a..'ld a concentrated load P = 750 N as shown in

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ent of inertia about the beam's neutral axis (NA) is

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The principal stresses [2 pts] Maximum in-plane shear stress [2 points] Normal stresses at maximum shear [2 points] Sketch the elements [2 points] Use correct units [2 points]

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