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- ‘11.5-2 A steel bar having a square cross section (50 mm × 50 mm)and length L = 2.0 in is compressed by axial loads that have a resultant P = 60 kN acting at the midpoint of one side of the cross section (sec figure). Assuming that the modulus of elasticity £is equal to 210 GPa and that the ends of the bar are pinned, calculate the maximum deflection S and the maximum bending moment Mmax.An aluminum bar having a rectangular cross section (2.0 in. × 1.0 in.) and length L = 30 in. is compressed by axial loads that have a resultant P = 2800 lb acting at the midpoint of the long side of the cross section (sec figure). Assuming that the modulus of elasticity E is equal to 10 × 106 psi and that the ends of the bar are pinned, calculate the maximum deflection and the maximum bending moment Mmax.A tie-down on the deck of a sailboat consists of a bent bar boiled at both ends, as shown in the figure. The diameter dBof the bar is 1/4 in., the diameter D Wof the washers is 7/8 in., and the thickness is of the fiberglass deck is 3/8 in. If the allowable shear stress in the fiberglass is 300 psi, and the allowable bearing pressure between the washer and the fiberglass is 550 psi, what is the allowable load P allowon the tie-down?
- An aluminum box column with a square cross section is fixed at the base and free at the top (sec figure). The outside dimension b of each side is 100 mm and the thickness t of the wall is 8 mm. The resultant of the compressive loads acting on the top of the column is a force P = 50 kN acting at the outer edge of the column at the midpoint of one side. What is the longest permissible length Lmaxof the column if the deflection at the top is not to exceed 30 mm? (Assume E = 73 GPaA retaining wall (Fig. a) is constructed using steel W-shape columns and concrete panel infill (Fig, b). Each column is subjected to lateral soil pressure with peak intensity q0(Figs, b and c). The tensile and compressive strength of the beam is 600 MPa. Select the most economical W 360 section from Table F-l(b) based on safety factor of 3.0.During construction of a highway bridge, the main girders are cantilevered outward from one pier toward the next (see figure). Each girder has a cantilever length of 48 m and an I-shaped cross section with dimensions shown in the figure. The load on each girder (during construction) is assumed to be 9,5 kN/m, which includes the weight of the girder. Determine the maximum bending stress in a girder due to this load.
- The cross section of a narrow-gage railway bridge is shown in part a of the figure. The bridge is constructed with longitudinal steel grinders that support the wood cross ties. The bridge is constructed with longitudinal steel girders that support the wood cross ties. The girders are restrained against lateral buckling by diagonal bracing, as indicated by the dashed lines. The spacing of the girders is S1= 50 in. and the spacing of the rails is s2= 30 in. The load transmitted by each rail to a single tie is P = 1500 1b. The cross section of a tie, shown in part b of the figure, has a width b =5.0 in. and depth d. Determine the minimum value of d based upon an allowable bending stress of 1125 psi in the wood tie. (Disregard the weight of the tie itself.)A framework A BCD is acted on by force P at 2L/3 from 8(see figure). Assume that 7f/is constant. Find expressions for reactions at supports B and C. Find expressions for angles of rotation at A, B* C, and D. Find expressions for horizontal deflections èAand ôD. If length LAB= L i 2, find length LCDin terms of L for the absolute value of the ratioBeam ABC has simple supports at A and B and an overhang from B to C. The beam is constructed from a steel W 16 × 3L The beam must carry its own weight in addition to uniform load q = 150 lb/ft. Determine the maxima m tensile and compressive stresses in the beam.
- A flying but tress transmit s a load P = 25 kN, acting at an angle of 60º to the horizontal, to the top of a vertical buttress AB (see figure). The vertical buttress has height h = 5.0 m and rectangular cross section of thickness t = 1.5 m and width b = 1.0 m (perpendicular to the plane of the figure). The stone used in the construction weighs y = 26 kN/m3. What is the required weight W of the pedestal and statue above the vertical buttress (that is, above section A) to avoid any tensile stresses in the vertical buttress?A heavy object of weight W is dropped onto the midpoint of a simple beam AB from a height h (see figure). Obtain a formula for the maximum bending stress ^ma* due to tne filing weight in terms of h, st, and 5st, where it is the maximum bending stress and Sstis the deflection at the midpoint when the weight W acts on the beam as a statically applied load. Plot a graph of the ratio o"max/ö"it (that is, the ratio of the dynamic stress to the static stress) versus the ratio iifS^r(Let h/S^ vary from 0 to 10.)-12 A "trapeze bar" in a hospital room provides a means for patients to exercise while in bed (see figure). The bar is 2.1 m long and has a cross section in the shape of a regular octagon. The design load is 1.2 kN applied at the midpoint of the bar. and the allowable bending stress is 200 M Pa. Determine the minimum height h of the bar. (Assume that the ends of the bar are simply supported and that the weight of the bar is negligible.)