the beam shown in Figure (2), determine transverse shear stresses E, F and G on the cross section. The load P-100 kN and INA = 470016 mr 12 mm IP H
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- A simply supported beam is subjected to point load P at mid-span. The normal stress on an element at mid-span is known to be ??x= 1.5 ksi. Determine the element stresses lilt is rotated through angle ? = 450• Show these stresses on a sketch of an element oriented at that angle.Solve the preceding problem for a W 200 × 41,7 shape with h = 166 mm, h = 205 mm. rw = 7.24 mm, tE= ILS mm,andV = 38 kN.A punch for making a slotted hole in ID cards is shown in the figure part a. Assume that the hole produced by the punch can be described as a rectangle (12 mm X 3 mm) with two half circles (r = 1.5 mm) on the left and the right sides. If P = 10 N and the thickness of the ID card is 1 mm, what is the average shear stress in the card?
- An aluminum tube has inside diameter dx= 50 mm, shear modulus of elasticity G = 27 GPa, v = 0.33, and torque T = 4.0 kN · m. The allowable shear stress in the aluminum is 50 MPa, and the allowable normal strain is 900 X 10-6. Determine the required outside diameter d2 Re-compute the required outside diameter d2, if allowable normal stress is 62 MPa and allowable shear strain is 1.7 X 10-3.A sign is supported by a pipe (see figure) having an outer diameter 110 mm and inner diameter 90 mm. The dimensions of the sign are 2.0 m X 1.0 m, and its lower edge is 3.0 m above the base. Note that the center of gravity of the sign is 1.05 m from the axis of the pipe. The wind pressure against the sign is 1.5 kPa. Determine the maximum in-plane shear stresses due to the wind pressure on the sign at points /I, B, and C, located on the outer surface at the base of the pipe.Cable DB supports canopy beam OABC as shown in the figure. Find the required cross-sectional area of cable BD if the allowable normal stress is 125 MPa. Determine the required diameter of the pins at 0, B, and D if the allowable stress in shear is 80 MPa. Assume that canopy beam weight is w = 8 kN. note The pins at 0, A, D and D are in double shear. Consider only the weight of the canopy; disregard the weight of cable DB.
- A cantilever beam(Z, = 6 ft) with a rectangular cross section (/> = 3.5 in., h = 12 in.) supports an upward load P = 35 kips at its free end. (a) Find the state of stress ((7T, o^., and r in ksi) on a plane-stress element at L/2 that is i/ = 8 in. up from the bottom of the beam. Find the principal normal stresses and maximum shear stress. Show these stresses on sketches of properly oriented elements. (b) Repeat part (a) if an axial compressive centroidal load N = 40 kips is added at BTwo steel tubes are joined at B by four pins (dp= 11 mm), as shown in the cross section a—a in the fiaure. The outer diameters of the tubes are dAB= 41 mm and dBC= 28 mm. The wall thickness are tAB= 6.5 mm and tBC= 7.5 mm. The yield stress in tension for the steel is sy = 200 MPa and the ultimate stress in tension is ??U:= 340 MPa. The corresponding yield and ultimate values in shear for the pm are 80 MPa and 140 MPa, respectively. Finally, the yield and ultimate values in bearing R between the pins and the tubes are 260 MPa, and 450 MPa, respectively. Assume that the factors safety with respect to yield stress and ultimate stress are 3.5 and 4.5. respectively. (a) Calculate the allowable tensile force P allowconsidering tension in the tube (b) Recompute P allowfor shear in the pins.(c)Finaly, recomputed Pallowfor bearing between the pm and the tubes. Which is the tubes. Which is the controlling value value of P?A single steel strut AB with a diameter (a) Find the strut force Fs and average normal stress ds= 8 mm supports the vehicle engine hood of a in the strut. mass 20 kg that pivots about hinges at C and D (see (b) Find the average shear stress t aver in the bolt at A,figure parts a and b). The strut is bent into a loop at (C) Find the average bearing stress bon the bolt at A. its end and then attached to a bolt at A with a diameter db= 10 mm. Strut AB lies in a vertical plane.