The beam shown in figure has across-sectional area of 2000 mm2and depth 50mm. (40x50). The second moment of the area is 0.516x106mm4. The beam is subjected to a uniformly distributed load of 30kN/m. The modulus of elasticity of the beam is E=200GPa. Determine the vertical displacement and rotation at node 2.
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- The Z-section of Example D-7 is subjected to M = 5 kN · m, as shown. Determine the orientation of the neutral axis and calculate the maximum tensile stress c1and maximum compressive stress ocin the beam. Use the following numerical data: height; = 200 mm, width ft = 90 mm, constant thickness a = 15 mm, and B = 19.2e. Use = 32.6 × 106 mm4 and I2= 2.4 × 10e mm4 from Example D-7A beam supporting a uniform load of intensity q throughout its length rests on pistons at points A, C and B (sec figure). The cylinders are filled with oil and are connected by a tube so that the oil pressure on each piston is the same. The pistons at A and B have diameter d1and the piston at C has diameter D2. (a) Determine the ratio of d2to d1so that the largest bending moment in the beam is as small as possible. Under these optimum conditions, what is the largest bending moment Mmaxin the beam? What is the difference in elevation between point C and the end supports?Find expressions for shear force V and moment Mat x = 2L/3 of beam (a) in terms of peak load intensity q0and beam length variable L. Repeat for beam (b) but at x = L/2.
- Find expressions for shear force V and moment Mat x = 2L/3 of beam (a) in terms of peak load intensity q0 and beam length variable L. Repeat for beam (b).Find expressions for shear force V and moment M at x = x0of beam AB in terms of peak load intensity q0and beam length variable L. Let x0= 2L/3.A fixed-end beam AB of a length L is subjected to a uniform load of intensity q acting over the middle region of the beam (sec figure). Obtain a formula for the fixed-end moments MAand MBin terms of the load q, the length L, and the length h of the loaded part of the beam. Plot a graph of the fixed-end moment MAversus the length b of the loaded part of the beam. For convenience, plot the graph in the following nondimensional form: MAqL2/l2versusbL with the ratio b/L varying between its extreme values of 0 and 1. (c) For the special case in which ù = h = L/3, draw the shear-force and bending-moment diagrams for the beam, labeling all critical ordinates.
- Find expressions for shear force V and moment M at mid-span of beam AB in terms of peak load intensity q0and beam length variables a and L Let a = 5L/b.The cross section of a sign post of constant thickness is shown in the figure. Derive the formula for the distance e from the cent crime of the wall of the post to the shear center S: where I2. = moment of inertia about the z axis. Also, compare this formula with that given in Problem 6.9-11 for the special case of ß = 0 here and a = h/2 in both formulas.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.
- 3. Determine the displacement and slope (i.e. 0) at the load point for the stepped beam shown in the following figure. Also determine the reaction forces and moments. Each element has E = 200 GPa. The area moment of inertia are given as I₁ = 1.25 × 105 mm4, and 2 = 4 x 104 mm. Clearly show the elemental stiffness matrices (k) for each element, assembly of k matrices to get global stiffness matrix (K) and application of boundary conditions. Then solve the reduced K matrix to get displacements and reactions 3000 N 150 mm 75 mm 125 mmFor the beam illustrated in the figure, find the locations and magnitudes of the maximum tensile bending stress due to M and the maximum shear stress due to V. Parameters are a = 290 mm, b= 135 mm, c = 20 mm, h = 39 mm, and F = 4300 N. a mm FN bmm C mm hmm The moment of inertia is 6.673x105 mm4 The maximum tensile bending stress due to Mis The maximum shear stress due to Vis 0 MPa. * MPa.The shape of the beam made of U profile ensures safe loading. Find the length c of the overhangs so that it can move. Of the material Safety stress (ç) emn = 50 N / mm2 for tension and compression conditions, (ob) emn = 80 N / mm2. Support spacing of the beam L = 6 m, cross section its dimensions are a = %D 210 mm, b = 150 mm and wall thickness t = 40 mm. The loading condition is P = 30 kN and qo = 40 kN / m. P B (Kesit)