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Problem 2 A beam is clamped at left end. A linearly varying distributed load is applied...
The beam is subjected to the linearly varying distributed load.
The beam is subjected to the linearly varying distributed load.Part A Determine the maximum deflection of the beam. EI is constant. (Figure 1)
Problem-1 (15 points) A cantilever beam ACB supports a concentrated load P and a couple moment Mo, as shown in the figure below. (a) Determine the total strain energy of the beam, (b) Determine t...
Problem-1 (15 points) A cantilever beam ACB supports a concentrated load P and a couple moment Mo, as shown in the figure below. (a) Determine the total strain energy of the beam, (b) Determine the deflections δ and δ8 at points C and B respectively. (c) Determine the angle of rotations 0 and θι, at points C and B respectively. Use the Castigliano's theorem(s). Assume that the beam's flexural rigidity is EI Mo
Problem-1 (15 points) A cantilever beam ACB...
Problem 1 A cantilever beam of length L is clamped at its left end (x = 0) and is free at its rig...
Problem 1 A cantilever beam of length L is clamped at its left end (x = 0) and is free at its right end (x = L). Along with the fourth-order differential equation EIy(4) = w(x), it satisfies the given boundary conditions y(0) = y′(0) = 0,y′′(L) = y′′′(L) = 0. a) If the load w(x) = w0 a constant, is distributed uniformly, determine the deflection y(x). b) Graph the deflection curve when w0 = 24EI and L = 1....
QUESTION 4 (25 marks) A simply supported beam is loaded by an uniform distributed load, wkN/m, over the span of the beam, L, as shown in Figure Q4. (a) Determine the end reactions at point A and...
QUESTION 4 (25 marks) A simply supported beam is loaded by an uniform distributed load, wkN/m, over the span of the beam, L, as shown in Figure Q4. (a) Determine the end reactions at point A and B in terms of w and L. (4 marks) (b) At an arbitrary point, x, express the internal mom (c) Show that the deflection curve of the beam under the loading situation is ent, M(x), in x, w, and L. (5 marks) 24EI...
(2) A simply supported beam of flexural rigidity El carries a constant uniformly distributed load of...
(2) A simply supported beam of flexural rigidity El carries a constant uniformly distributed load of intensity p per unit length as shown Figure 2 below. Assume the deflection shape to be a polynomial in x, and is given by v (x) = a., + as+ a2 x, where ao, a.呙are constants to be determined. (a) State the boundary conditions for the deflection equation. Using the boundary conditions stated in (a) and the Rayleigh-Ritz method, determine (b) the constants a,...
A 9m span simply supported beam carries a load varying from 20KN/m at left end to 40KN/m at the r...
A 9m span simply supported beam carries a load varying from 20KN/m at left end to 40KN/m at the right end. The variation is reported to be linear. You are required to find the following: a) slopes at support b) position and magnitude of maximum deflection E=200GPa and I=12000cm4
2. A beam with a uniform flexural rigidity, EI, is loaded by a triangular distributed load,...
2. A beam with a uniform flexural rigidity, EI, is loaded by a triangular distributed load, Pz(x), as shown below: a) Find the deflection w(x) (10pts) b) Sketch the shear force V(x) and the beading moment M(x) along the length of the beam, labeling all significant points. (5pts) c) Calculate the maximum bending stress, Omax, and indicate where it occurs. (5pts) z, W Cross Section - 1/3 — * - 2/3 —
4N Problem 6. The beam shown is loaded with a linear distributed load for the left...
4N Problem 6. The beam shown is loaded with a linear distributed load for the left half and a constant distributed load for the right. At the center a 4 N load is applied. 6 N/m a) Use equilibrium to find the shear and moment equations for the beam. b) Draw the shear and moment diagrams for the beam. c) Integrate your answers to find the deflection of the beam. Leave your final answer as a piecewise function. (IE can...
The intensity of the distributed load on the simply supported beam varies linearly from zero to...
The intensity of the distributed load on the simply supported
beam varies linearly from zero to w0. (a) Derive the equation of
the elastic curve. (b) Find the location of the maximum deflection.
Use any method.
Wo| B AL 1
2) (15 pts) A steel beam is supported by a pin at A and a high-strength wire at B. Load P acts on the free end at C. The wire's axial rigidity EA - 300x10' lb, and the beam's flexural...
2) (15 pts) A steel beam is supported by a pin at A and a high-strength wire at B. Load P acts on the free end at C. The wire's axial rigidity EA - 300x10' lb, and the beam's flexural rigidity EI- 30x10% Ib/in2. Find the deflection at C P-220 lb 24 in 36 in 24 in
2) (15 pts) A steel beam is supported by a pin at A and a high-strength wire at B. Load P acts on...
Problem-1 (15 points) A cantilever beam ACB supports a concentrated load P and a couple moment Mo, as shown in the figure below. (a) Determine the total strain energy of the beam, (b) Determine the deflections δ and δ8 at points C and B respectively. (c) Determine the angle of rotations 0 and θι, at points C and B respectively. Use the Castigliano's theorem(s). Assume that the beam's flexural rigidity is EI Mo
Problem-1 (15 points) A cantilever beam ACB...
QUESTION 4 (25 marks) A simply supported beam is loaded by an uniform distributed load, wkN/m, over the span of the beam, L, as shown in Figure Q4. (a) Determine the end reactions at point A and B in terms of w and L. (4 marks) (b) At an arbitrary point, x, express the internal mom (c) Show that the deflection curve of the beam under the loading situation is ent, M(x), in x, w, and L. (5 marks) 24EI...
(2) A simply supported beam of flexural rigidity El carries a constant uniformly distributed load of intensity p per unit length as shown Figure 2 below. Assume the deflection shape to be a polynomial in x, and is given by v (x) = a., + as+ a2 x, where ao, a.呙are constants to be determined. (a) State the boundary conditions for the deflection equation. Using the boundary conditions stated in (a) and the Rayleigh-Ritz method, determine (b) the constants a,...
2. A beam with a uniform flexural rigidity, EI, is loaded by a triangular distributed load, Pz(x), as shown below: a) Find the deflection w(x) (10pts) b) Sketch the shear force V(x) and the beading moment M(x) along the length of the beam, labeling all significant points. (5pts) c) Calculate the maximum bending stress, Omax, and indicate where it occurs. (5pts) z, W Cross Section - 1/3 — * - 2/3 —
4N Problem 6. The beam shown is loaded with a linear distributed load for the left half and a constant distributed load for the right. At the center a 4 N load is applied. 6 N/m a) Use equilibrium to find the shear and moment equations for the beam. b) Draw the shear and moment diagrams for the beam. c) Integrate your answers to find the deflection of the beam. Leave your final answer as a piecewise function. (IE can...
The intensity of the distributed load on the simply supported
beam varies linearly from zero to w0. (a) Derive the equation of
the elastic curve. (b) Find the location of the maximum deflection.
Use any method.
Wo| B AL 1
2) (15 pts) A steel beam is supported by a pin at A and a high-strength wire at B. Load P acts on the free end at C. The wire's axial rigidity EA - 300x10' lb, and the beam's flexural rigidity EI- 30x10% Ib/in2. Find the deflection at C P-220 lb 24 in 36 in 24 in
2) (15 pts) A steel beam is supported by a pin at A and a high-strength wire at B. Load P acts on...
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