W LAB B LBC assume w = 4 kips/ft P= 5kips LAB=16 ft LBC=8 ft What is the vertical reaction at A ? answer in kips
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- Solve the preceding problem for a W 250 × 89 steel column having a length L = 10 m. Let E = 200 GPa..2 A ligmio.irc ii supported by two vorlical beams consistins: of thin-walled, tapered circular lubes (see ligure part at. for purposes of this analysis, each beam may be represented as a cantilever AB of length L = 8.0 m subjected to a lateral load P = 2.4 kN at the free end. The tubes have a constant thickness ; = 10.0 mm and average diameters dA = 90 mm and dB = 270 mm at ends A and B, re s pec lively. Because the thickness is small compared to the diameters, the moment of inerlia at any cross section may be obtained from the formula / = jrrf3;/8 (see Case 22, Appendix E); therefore, the section modulus mav be obtained from the formula S = trdhlA. (a) At what dislance A from the free end docs the maximum bending stress occur? What is the magnitude trllul of the maximum bending stress? What is the ratio of the maximum stress to the largest stress (b) Repeat part (a) if concentrated load P is applied upward at A and downward uniform load q {-x) = 2PIL is applied over the entire beam as shown in the figure part b What is the ratio of the maximum stress to the stress at the location of maximum moment?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 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..17 A mountain-bike rider going uphill applies torque T = Fd(F = l5lb, d = 4 in.) to the end of the handlebars ABCD by pulling on the handlebar extenders DE. Consider the right half of the handlebar assembly only (assume the bars are fixed at the fork at A). Segments AB and CD are prismatic with lengths L, = 2 in.andL3 = 8.5 in, and with outer diameters and thicknesses d01 = 1.25 in. 101 = 0.125 in. and d03 = O.87in.,i03 = 0.ll5in, respectively as shown. Segment BC’ of length L, = 1.2 in. however. is tapered, and outer diameter and thickness vary linearly between dimensions at B and C. Consider torsion effects only. Assume G = 4000 ksi is constant. Derive an integral expression for the angle of twist of half of the handlebar tube when it is subjected to torque T = Fd acting at the end. Evaluate ‘b1-, for the given numerical1ues.The inclined ladder AB supports a house painter (85 kg) at C and the weight iq = 40 K/m} of the ladder itself. Each ladder rail (t5= 4 mm) is supported by a shoe (ts= 5 mm) that is attached to the ladder rail by a bolt of diameter d = 8 mm
- -4-4 A cantilever beam is supported at B by cable BC. The beam carries a uniform load q = 200 N/M. If the length of the beam is L = 3 m, find the force in the cable and the reactions at A. Ignore the axial flexibility of the cable.Solve the preceding problem for the following data: diameter LO m, thickness 48 mm, pressure 22 MPa, modulus 210 GPa. and Poisson's ratio 0.29-4-13 A propped cantilever beam of a length 2L is loaded by a uniformly distributed load with intensity q. The beam is supported at B by a linearly elastic spring with stiffness k. Use the method of superposition to solve for all reactions. Also draw shear-force and bending-moment diagrams, labeling all critical ordinates. Let k = 6EI/L3.
- The horizon Lai rigid beam A BCD is supported by vertical bars BE and CF and is loaded by vertical Forces P, = 400 KN arid P2= 360 kN acting at points A and D, respectively (see figure). Bars BE and CF are made of steel (£ = 200 GPa} and have cross-sectional areas Ag=11,100 mm" and ABE= 9280 mm-. The distances between various points on the bars are shown in the figure. Determine the vertical displacements SAand SDof points A and D, respectively.A cable CD of a length H is attached to the third point of a simple beam AB of a length L (see figure). The moment of inertia of the beam is I, and the effective cross-sectional area of the cable is A. The cable is initially taut but without any initial tension, (a) Obtain a formula for the tensile force S in the cable when the temperature drops uniformly by T degrees, assuming that the beam and cable are made of the same material (modulus of elasticity E and coefficient of thermal expansion . Use the method of superposition in the solution, (b) Repeat part (a), assuming a wood beam and steel cable.Space frame A BCD is clamped at A, except it is Free to translate in the .v direction. There is also a roller support at D, which is normal to line CDE. A triangularly distributed Force with peak intensity q0 = 75 N/m acts along AB in the positive - direction. Forces Px= 60 N and Pz = = 45 N are applied at joint C, and a concentrated moment My = 120 N . m acts at the mid-span of member BC. (a) Find reactions at supports A and I). (b) Find internal stress resultants N. E’I T, and .11 at the mid-height of segment AB.