Chapter 1 Normal Stress and Strain

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1. A hollow circular post ABC (see figure) supports a load P1 = 7.5 KN acting at the top. A second load P2 is uniformly distributed around the cap plate at B. The diameters and thicknesses of the upper and lower parts of the post are dAB = 32 mm, tAB = 12 mm, dBC = 57 mm, and tBC = 9 mm, respectively.

   (a) Calculate the normal stress deltaAB in the upper part of the post.

   (b) If it is desired that the lower part of the post have the same compressive stress as the upper part, what should be the magnitude of the load P2?

   (c) If P1 remains at 7.5 KN and P2 is now set at 10 KN lb, what new thickness of BC will result in the same compressive stress in both parts?

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2. A bicycle rider would like to compare the effectiveness of cantilever hand brakes [see figure part (a)] versus V brakes [figure part (b)].

   (a) Calculate the braking force RB at the wheel rims for each of the bicycle brake systems shown. Assume that all forces act in the plane of the figure and that cable tension T =200 N. Also, what is the average compressive normal stress dealtaC on the brake pad (A = 4 cm²)?

   (b) For each braking system, what is the stress in the brake cable (assume effective cross-sectional area of 1.077 mm²)?

(HINT: Because of symmetry, you only need to use the right half of each figure in your analysis.)

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3. The cross section of a concrete corner column that is loaded uniformly in compression is shown in the figure.

   (a) Determine the average compressive stress deltaC in the concrete if the load is equal to 14.5 MN.

   (b) Determine the coordinates xc and yc of the point where the resultant load must act in order to produce uniform normal stress in the column.

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4. Two steel wires support a moveable overhead camera weighing W = 110 N (see figure) used for close-up viewing of field action at sporting events. At some instant, wire 1 is at an angle alfa = 20^o to the horizontal and wire 2 is at an angle beta = 48^o. Both wires have a diameter of 0.76 mm.

   Determine the tensile stresses delta1 and delta2 in the two wires.

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5. A pickup truck tailgate supports a crate (WC = 900 N), as shown in the figure. The tailgate weighs WT = 270 N and is supported by two cables (only one is shown in the figure). Each cable has an effective cross-sectional area Ae = 11 mm². A horizontal force (F = 450 N) is applied at the top of the crate (h = 275 mm).

   (a) Find the tensile force T and normal stress delta in each cable.

   (b) If each cable elongates segma = 0.42 mm due to the weight of both the crate and the tailgate, what is the average strain in the cable?

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7. Two gondolas on a ski lift are locked in the position shown in the figure while repairs are being made else-where. The distance between support towers is L = 30.5 m. The length of each cable segment under gondola weights WB = 2000 N and WC = 2900 N are DAB = 3.7 m, DBC = 21.4 m, and DCD = 6.1 m. The cable sag at B is deltaB = 1.3 m and that at C(deltaC) is 2.3 m. The effective cross-sectional area of the cable is Ae = 77 mm².

   (a) Find the tension force in each cable segment; neglect the mass of the cable.

   (b) Find the average stress (delta) in each cable segment.

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