O 4,E 2 P L Problem: Determine the support reaction forces at the two ends of the bar shown above, given the following, P = 6.0× 10ʻ N, E=2.0×10* N / mm², A = 250 mm², L=150mm, A=1.2 mm %3D
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- Solve the preceding problem (W 250 × 44.8) if the resultant force P equals 110 kN and E = 200 GPa.Two separate cables AC and BC support a sign structure of weight W = 1575 lb attached to a building. The sign is also supported by a pin support at O and a lateral restraint in the '-direction at D. (a) Find the tension in each cable. Neglect the mass of the cables. (b) Find the average stress in each cable if the area of each cable is Ae= 0.471 in2.A 150-lb rigid bar AB. with friction less rollers al each end. is held in the position shown in the figure by a continuous cable CAD. The cable is pinned at C and D and runs over a pulley at A. (a) Find reactions at supports A and B. (b) Find the force in the cable.
- The figure shows an idealized structure consisting of rigid bars ABC And DEF joined by a linearly elastic spring ß between C and D. The structure is also supported by translational elastic support ß at B and rotational elastic support ßRat E. Determine the critical load Pcrfor the structure.A long re Lai nine: wall is braced by wood shores set at an angle of 30° and supported by concrete thrust blocks, as shown in the first part of the figure. The shores are evenly spaced at 3 m apart. For analysis purposes, the wall and shores are idealized as shown in the second part of the figure. Note that the base of the wall and both ends of the shores are assumed to be pinned. The pressure of the soil against the wall is assumed to be triangularly distributed, and the resultant force acting on a 3-meter length of the walls is F = 190 kN. If each shore has a 150 mm X 150 mm square cross section, what is the compressive stressSlender column ABC is supported at A and C and is subjected to axial load P. Lateral support is provided at mid-height if but only in the plane of the figure; lateral support perpendicular to the plane of the figure is provided only at ends A and C. The column is a steel W shape with modulus of elasticity E = 200 GPa and proportional limit pl= 400 MPa. The total length of the column L = 9 m. If the al low-able load is 150 kN and the factor of safety is 2.5, determine the lightest W 200 section that can be used for the column. (See Table F-l(b), Appendix F).
- The fixed-end bar ABCD consists of three prismatic segments, as shown in the figure. The end segments have a cross-sectional area A1= 840 mm2and length Lt= 200 mm. The middle segment has a cross-sectional area A2= 1260 mm2 and length L2= 250 mm. Loads PBand Pcare equal to 25.5 kN and 17.0 kN, respectively. (a) Determine the reactions RAand RDat the fixed supports. (b) Determine the compressive axial force FBCin the middle segment of the bar.A rigid bar of weight W = SOO N hangs from three equally spaced vertical wines( length L = 150 mm, spacing a = 50 mm J: two of steel and one of aluminum. The wires also support a load P acting on the bar. The diameter of the steel wires is ds= 2 mm, and the diameter of the aluminum wire is d = A mm. a Assume £,=210 GPa and EB« 70 GPa. What load Pallowcan be supported at the mitl-point of the bar (x = a) if the allowable stress in the steel wires is 220 MPa and in the aluminum wire is 80 MPa? (See figure part (b) What is /*,Ikw» if the load is positioned at .v = all1? (See figure part a.) (c) Repeat part (b) if the second and third wires are switched as shown in the figure part b.An L-shaped reinforced concrete slab 12 Ft X 12 ft, with a 6 Ft X 6 ft cut-out and thickness t = 9.0 in, is lifted by three cables attached at O, B, and D, as shown in the figure. The cables are are combined at point Q, which is 7.0 Ft above the top of the slab and directly above the center of mass at C. Each cable has an effective cross-sectional area of Ae= 0.12 in2. (a) Find the tensile force Tr(i = 1, 2, 3) in each cable due to the weight W of the concrete slab (ignore weight of cables). (b) Find the average stress ov in each cable. (See Table I-1 in Appendix I for the weight density of reinforced concrete.) (c) Add cable AQ so that OQA is one continuous cable, with each segment having Force T, which is connected to cables BQ and DQ at point Q. Repeat parts (a) and (b). Hini: There are now three Forced equilibrium equations and one constrain equation, T1= T4.
- The hoisting arrangement for lifting a large pipe is shown in the figure. The spreader is a steel tubular section with outer diameter 70 mm and inner diameter 57 mm. Its length is 2.6 m, and its modulus of elasticity is 200 GPa. Based upon a factor of safety of 2.25 with respect to Euler buckling of the spreader, what is the maximum weight of pipe that can be lifted? (Assume pinned conditions at the ends of the spreader.)An idealized column consists of rigid bar ABCD with a roller support at B and a roller and spring support at D. The spring constant at D. is ß = 750 N/m. Find the critical load Pcrof the column.A column, pinned at top and bottom, is made up of two C 6 x 13 steel shapes (see figure) that act together. Find the buckling load (kips) if the gap is zero. Find required separation distance d(inches) so that the buckling load is the same in y and z directions. Assume that E = 30,000 ksi and L = 18 ft. Note that distance d is measured between the centroids of the two C shapes.