The beam shown in the figure below, has a pin support at A and roller support at C. Determine the reactions at A and C. A 3 kip/ft 40 ft 30 kip B 20 ft ft C 20ft 60 kip D
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- 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.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.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.
- Find the controlling buckling load (kN) for the steel column shown in the figure. The column is pinned at top and bottom and is made up of two C 150 x 12,2 shapes that act together. Assume that E = 205 GPa and L = 6 m.A 10-ft rigid bar AB is supported with a vertical translational spring at A and a pin at B. The bar is subjected to a linearly varying distributed load with maximum intensity q0. Calculate the vertical deform at ion of the spring if the spring constant is 4 kips/in.A plane Frame is restrained at joints A and D, as shown in the figure. Members AB and BCD are pin connected at B. A triangularly distributed lateral load with peak intensity of SO N/m acts on CD. An inclined concentrated force of 200 N acts at the mid-span of BC. (a) Find reactions at supports A and D. (b) Find resultant forces in the pins at B and C.
- 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?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 temporary wood flume serving as a channel for irrigation water is shown in the figure. The vertical boards forming the sides of the flume are sunk in the ground, which provides a fixed support. The top of the flume is held by tic rods that are tightened so that there is no deflection of the boards at that point. Thus, the vertical boards may be modeled as a beam AB, supported and loaded as shown in the last part of the figure. Assuming that the thickness t of the boards is 1,5 in., the depth d of the water is 40 in., and the height h to the tie rods is 50 in., what is the maximum bending stress in the boards? Hint: The numerically largest bending moment occurs at the fixed support.
- A truss ABC supports a load W at joint B, as shown in the figure. The length L, of member Aß is fixed, but the length of strut BC varies as the angle is changed. Strut BC has a solid circular cross section. Joint B is restrained against displacement perpendicular to the plane of the truss. Assuming that collapse occurs by Etiler buckling of the strut determine the angle for minimum weight of the strut.A rectangular column with cross-sectional dimensions b and h is pin-supported at ends A and C (see figure). At mid-height, the column is restrained in the plane of the figure but is free to deflect perpendicularly to the plane of the figure. Determine the ratio h/b such that the critical load is the same for buckling in the two principal planes of the column.A cylindrical brick chimney of height H weighs w = 825 lb/ft of height (see figure). The inner and outer diameters are d1= 3 ft and d2= 4 ft, respectively. The wind pressure against the side of the chimney is p = 10 lb/ft2 of projected area. Determine the maximum height H if there is to be no tension in the brickwork.