Determine the maximum normal stress (MPa) due to bending for the beam and loading condition shown in the figure.
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- The Z-section of Example D-7 is subjected to M = 5 kN · m, as shown. Determine the orientation of the neutral axis and calculate the maximum tensile stress c1and maximum compressive stress ocin the beam. Use the following numerical data: height; = 200 mm, width ft = 90 mm, constant thickness a = 15 mm, and B = 19.2e. Use = 32.6 × 106 mm4 and I2= 2.4 × 10e mm4 from Example D-7Solve 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 sign of weight W is supported at its base by four bolls anchored in a concrete footing. Wind pressure P acts normal to the surface of the sign; the resultant of the uniform wind pressure is force fat the center of pressure (C.P). The wind force is assumed to create equal shear forces F/4 in the y direction at each boll (see figure parts a and c). The overturning effect of the wind force also causes an uplift force R at bolts A and C and a downward force (— R) al bolts B and D (see figure part b). The resulting effects of the wind and the associated ultimate stresses for each stress condition are normal stress in each boll (h — 60 ksi); shear through the base plate (th = 17 ksi); horizontal shear and bearing on each bolt ( tfur = 25 ksi and cr^ = 75 ksi): and bearing on the bottom washer at B (or D) (abor = 50 ksi).
- Repeat Problem 11.3-9. Use two C 150 × 12.2 steel shapes and assume that E = 205 GPa and L = 6 m.-7 Repeat Problem 2.3-5, but n include the weight of the bar. See Table I-I in Appendix I for the weight density of steel.Derive a formula for the strain energy U of the cantilever bar shown in the figure. The bar has circular cross sections and length L. It is subjected to a distributed torque of intensity t per unit distance. The intensity varies linearly from r = 0 at the free end to a maximum value t = /0 at the support.
- A statically indeterminate stepped shaft ACE is fixed at ends A and B and loaded by a torque TQat point C (see figure). The two segments of the bar are made of the same material, have lengths L4and LB, and have polar moments of inertia IAand Ipb. Determine the angle of rotation 4>of the cross section at Cby using strain energy. Hint: Use Eq, (3-55b) to determine the strain energy Urn terms of the angle d?. Then equate the strain energy to the work done by the torque to. Compare your result with Eq. (3-52) of Example 3-9.The stresses acting on a stress element on the arm of a power excavator (see figure) are ax= 52 MPa and txy= 33 MPa (sec figure). What is the allowable range of values for the stress if the maximum shear stress is limited to = 37 MPa?A seesaw weighing 3 lb/ft of length is occupied by two children, each weighing 90 lb (see figure). The center of gravity of each child is 8 ft from the fulcrum. The board is 19 ft long, 8 in. wide, and 1.5 in. thick. What is the maximum bending stress in the board?
- Derive the following formula for the distance e from the centerline of the wall to the shear center S for the hat section of constant thickness shown in the figure: Also, check the formula for the special case of a channel section (a = 0).Two rigid bars are connected to each other by two linearly elastic springs. Before loads are applied, the lengths or the springs are such, that the bars are parallel and the springs are without stress. (a) Derive a formula for the displacement E4at point 4 when the load P is applied at joint 3 and moment PL is applied at joint 1. as shown in the figure part a. (Assume that the bars rotate through very small angles under the action of load P.) (b) Repeat part (a) if a rotational spring, kr= kL2, is now added at joint 6. What is the ratio of the deflection d4 in the figure part a to that in the figure part b ?Repeat 1.3-9 but use the method of sections go find member forces in AC and BD.