Q2: For the beam shown in Figure (2), determine transverse shear stresses at points E, F and G on the cross section. The load P=100 kN and INA = 470016 mm*. %3D 12 mm P. Fi 4mmG NA 48 mm D 6 mm 12 mm -0.4 m- 0.2 m 0.2 m 96 mm Figure (2)
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- Solve the preceding problem for the following data: diameter LO m, thickness 48 mm, pressure 22 MPa, modulus 210 GPa. and Poisson's ratio 0.29A 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 BA simply supported wood beam is subjected to point load P at mid-span. The normal stress on element C is known to be sx= 12 MPa. Find the maximum shear stress on the element and show the state of stress on a sketch of a properly oriented element.
- 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 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.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.
- 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?A U-shaped cross section of constant thickness is shown in the figure. Derive the following formula for the distance e from the center of the semicircle to the shear center. Also, plot a graph showing how the distance e (expressed as the non dimensional ratio e/r varies as a function of the ratio b/r. (Let b/r range from 0 to 2.)A post having a hollow, circular cross section supports a P = 3.2 kN load acting at the end of an arm that is h = 1.5 m long (see figure). The height of the post is L = 9 m, and its section modulus isS = 2.65 x 10 mmJ. Assume that the outer radius of the post is r2= 123 mm, and the inner radius is r}=117 mm. (a) Calculate the maximum tensile stress and \ maximum in-plane shear stress Tm:ls at point A on the outer surface of the post along the x axis due to the load P. Load P acts at B along line BC. (b) If the maximum tensile stress and maximum in-plane shear stress at point A arc limited to 90 MPa and 38 MPa, respectively, what is the largest permissible value of the load PI
- . A cantilever beam (width b = 3 in. and depth h = 6 in,) has a length L = 5 ft and is subjected to a point load P and a concentrated moment M = 20 kip-ft at end B. If normal stress trx= 0 at point C, located 0.5 in. below the top of the beam and 1 ft to the right of point Atfind point load P. Also show the complete state of plane stress on the element at point C.A gondola on a ski lift is supported by two bent arms, as shown in the figure. Each arm is offset by the distance b = ISO mm from the line of action of the weight force W. The allowable stresses in the arms are 100 MPa in tension and 50 MPa in shear. If the loaded gondola weighs 12 kN, what is the minimum diameter roof the arms?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.