We want to find a fundamental solution of the stationary equation for a simply supported beam, i....
Q2. A simply supported beam AB (Figure 2) supports a uniformly distributed load of q = 18kN/m and a concentrated load of P = 23kN at the centre. Consider length of the beam, L = 3m, Young's modulus, E = 200GPa and moment of inertial, I = 30 x 10 mm-. Assume the deflection of the beam can be expressed by elastic curve equations of the form: y(x) = Ax4 + Bx3 + Cx2 + Dx + E. 1) Sketch...
Problem 2 Consider a simply supported symmetric I beam ABCD carrying a uniformly distributed load w and a concentrated load F as shown in Figure 2. Young's modulus of the beam is 200 GPa F- 8 kNN 8cm 3cm 3cm w- 6 kN/m 6cm 2cm Figure 2 1) Replace the support C with the reaction force Rc, and using static equilibrium find the reactions at point A and B in terms of Ro 2) Using the boundary conditions, calculate the...
Mohammed Abdurahman Active Now The defection slong s uniform beam with fecual rigdity B-andapplied lond f(x)ossatisfis the equation (a) Evaluate the deflection y (a). (b) Find the influence function (Green's function) G(z,0, where 0 < ξ < 2 for this problem. Hint: Since 0 < ξ < 2, H(0-E)=0, H(2-E)-1. (e) Henoe write the deflection of this beam as a definite integral. Do not attempt tp evaluate the integral. ((7+2+2)+(6+6+2)-25 marks) Repl Crop Share Scroll Draw capture
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5.8-3 A simply supported wood beam is subjected to uniformly distributed load q. The width of the beam is 150 mm and the height is 200 mm. Determine the nor- mal stress and the shear stress at point C. Show these stresses on a sketch of a stress element at point C q =5.8 kN/m 75 mm С B A Μ 1 m 3 m 200 mm Z 150 mm PROBLEM 5.8-3
Problem 2 Consider a simply supported symmetric I beam ABCD carrying a uniformly distributed load w and a concentrated load F as shown in Figure 2. Young's modulus of the beam is 200 GPa. F 8 kN 8cm 3cm 3cm 7 m 5 m 3 m 2cm W= 6 kN/m 6cm A D B 2cm 7TITT TITIT Figure 2 1) Replace the support C with the reaction force Rc, and using static equilibrium find the reactions at point A and...
(a) A simply supported beam of hollow rectangular section is to be designed for min mum weight to carry a vertical load Fy and an axial load P as shown in Fig. 2. The deflection of the beam in the y direction under the self-weight and Fy should not exceed 0.5 in. The beam should not buckle either in the yz or the xz plane under the axial load. Assuming the ends of the beam to be pin ended, formulate...
Problem. 1 Consider the simply supported beam in Fig. 1. We assume all loads as static (.e. does not change with time). The load density of the applied lond is represented by Eq 1, where (RMR) are reaction force and moment respectively at the support. W(I) = R<=>? +MR <= >-2-5<=> +5<:-> <!-4 -F<=-77-1 (1) Fig. 1: Problem. 1 1. Find the reactions at the support (1.6. (RM)) as a function of F (..R(F) and Mr(F)) 2. Find the deflection...
need help for this question in full answer
2. The deflection along a uniform beam with fexual Yigidity BI- and applied load f (x) = cos (-) satisfies the equation (a) Evaluate the deflection y (x). Hint: /cos(az)dz-asin (as)+C, /sin(as)dz=-a cos(az) +C (b) Find the influence function (Green's function) G (z,f), where 0 < ξ < 2, for this problem. Hint: Since 0 < ξ < 2, H(0-E)=0, H(2-E)=1. (c) Hence write the deflection of this beam as a definite...
Torsional vibration of a shaft is govened by e wave equation where e(z,t) is the anqular displacement (angle of twist) along the shaft, z is the distance from the end of the shaft and t is time. For a shaft of length that is supported by frictionless bearings at each end, boundary conditions are 0(0,t) 0(4x,t) 0, t> 0. Suppose that the initial angular displacement and angular velocity are e(z,0) 3cos(2r), 0(z,0)= 4+cos(2r), 0<z< 4m, respectively You may use the...
Torsional vibration of a shaft is govened by e wave equation where e(z,t) is the anqular displacement (angle of twist) along the shaft, z is the distance from the end of the shaft and t is time. For a shaft of length that is supported by frictionless bearings at each end, boundary conditions are 0(0,t) 0(4x,t) 0, t> 0. Suppose that the initial angular displacement and angular velocity are e(z,0) 3cos(2r), 0(z,0)= 4+cos(2r), 0<z< 4m, respectively You may use the...