(b) A simple beam ABCD with a uniformly loading and a single load at point C is shown in Figure Q2(b). If the value of Young's modulus, E = 200 GPa and moment of inertia I= 6.87 x 106 mm², determine (i) The slope at end of the point A (ii) The deflection at point C
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- A simple beam with an overhang is subjected to d point load P = 6kN. If the maximum allowable deflect ion at point C is 0.5 mm, select the lightest W360 section from Table F-l{b) that can be used for the beam. Assume that L = 3 m and ignore the distributed weight of the beam.Question 2 A beam ABC of length 3m has one support at the left end and the other support at a distance 2m from the left end. The beam carries an uniformly distributed load W=16 kN/m. Given E = 2 x 10$ N/mm? and I = 80 × 106 mm4. a. Find the slopes at the left support A. b. Find the deflection at the right end c. Find the maximum deflection between the supports. W A C 2 m 3 m Figure 2.1. The cantilever beam shown in the following figure is subjected to a load P or a deflection & at its free end. Two gages A and B are mounted at the same location on the top and bottom faces of the beam. Gage A is used to measure E., and gage B is used to measure E,. Assume that: E-30(10) psi, Poisson's ratio v-0.3 a) Determine theoretical values of E., b) Determine theoretical values of Strain gage A Strain gage B 14 in 12 in (μin/in) for a load of P-6 lbf. Ey (µin/in) for a deflection of 8-0.5 in. Por & 0.25
- (b) A simple beam ABCD with a uniformly loading and a single load at point C is shownin Figure Q2(b). If the value of Young’s modulus, E = 200 GPa and moment ofinertia I = 6.87 x 106 mm4, determine(i) The slope at end of the point A(ii) The deflection at point CQ 2. Calculate the slope and deflection at the free end of the cantilever beam shown in figure using Method of super position Take. E = 2.05 x 10$ N/mm2 and I = Y x 10% mm“. %3D If the last two digits of student id 2 50, then take Y = last two digits of id /100. If the last two digits of student id < 50, then take Y = last two digits of id /10; If last two digits of id are zeroes, then take Y= 0.75 2 kN 6 kN/m 1.2 kN-m 3 m 2.2 EI3. Two beams are supported as shown in the diagram below, each 150mm x 200mm x 6 meters. Beam CD is a cantilever beam carrying a uniformly distributed load of 6 KN/m freely supported on beam AB. Beam AB is freely supported on each ends. E = 13.8 GPa for both beam. Neglect the weight of the beam. a. Compute the reaction at D. b. Compute the deflection at D. c. Compute the bending stress of beam CD. 6 ka lm бт 6m 6m
- Q3. For the beam (E = 4.176×106 ksf) shown below, find the deflection at point C. 10K 2' X 16k/ft 77777 6' 4k/ft QB 2' 10k +1.51 ہہFor the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, (b) the slope at A, (c) the slope at B, and (d) the deflection at midspan. Assume that El is constant for the beam. Let Mo = 50KN-m, L= 4.5 m, E= 180 GPa, and I = 115x 106 mm4. Mo B Answer: (b) 0A = i rad (c) Og = i rad (d) vmid = i mmFor the beam and loading shown, integrate the load distribution to determine (a) the equation of the elastic curve, (b) the deflection at the left end of the beam, and (c) the support reactions By and MB. Assume that EI is constant for the beam. Let w0 = 6 kN/m, L = 4.5 m, E = 210 GPa, and I = 140 x 106 mm4.
- Question Two For the shown simply supported beam, a deflection of 1.5 mm is developed in the beam at x 0.75 m when a L mm, of P=500 g is applied. If the beam has a rectangular cross section of b= 35 mm and h = 51 find the modulu: elasticity of the beam's material. 0.6 m 0.6 mProblem 2: The cantilever beam shown below consists of two structural steel channels, size 3 in x 5 lb./ft. It carries a 150 lb. force at end A and a distributed force of 5 lb./in. over the length OA. (a) Find the deflection of the beam at А. (b) If the deflection is to be reduced by at least 20%, what will be the size of the steel channels? 60 in 150 lbf Problem 4-15 5 lbf/in AFor a beam subjected to the load F at the center of the span as shown below, please 1. Find the maximum allowed load F, given a. Modulus of Rupture (MOR) of the material for the beam = 130 GPa b. Beam width b = 0.02m and depth d = 0.05m c. Span length L = 10m 2. If the maximum allowed load F is designed to be 40,000N, given all other conditions the same, what is the minimum MOR required for the material to make the beam? 3. If the maximum allowed load F is designed to be 50,000N, given all other conditions (MOR = 130 GPa) the same, what is the minimum depth d required? F b ✰ d ↓ D L