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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...
(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,...
Problem 7.5 of your textbook (Haldar & Mahadevan): A simply supported beam of span L 360 inches is loaded by a uniformly distributed load w kip/in. and a concentrated kip applied at the midspan....
Problem 7.5 of your textbook (Haldar & Mahadevan): A simply supported beam of span L 360 inches is loaded by a uniformly distributed load w kip/in. and a concentrated kip applied at the midspan. The maximum deflection of the beam at the midspan can be calculated as: mar- 384 EI 48 E A beam with El 63.51 x 106 kip-in.2 Is selected to carry the load. Both w and P are statistically independent RVs with mean values estimated to be...
A simply supported uniform beam (with length L and flexural rigidity El) carries a moment Mo...
A simply supported uniform beam (with length L and flexural rigidity El) carries a moment Mo (clockwise) at a distance -21B away from the left end (x-0). Calculate the deflection () and slope (dv/de) at 21/3 by using the Rayleigh-Ritz Method. Assume a deflection curve of the form v-asin(rx/L), where a is to be determined
Q2. A simply supported beam AB (Figure 2) supports a uniformly distributed load of q =...
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...
SS two BMs midspan deflection The simply supported beam shown below has a span length L...
SS two BMs midspan deflection The simply supported beam shown below has a span length L = 4.1. Two applied bending moments Mo = 4.6 are applied at either support. Determine the midspan deflection of the beam. Assume El is constant. Show your results to two decimal point and no units. (Hibbeler) M M 2 Answer:
A simply supported bridge with a single span of L feet has a deck of uniform...
A simply supported bridge with a single span of L feet has a deck of uniform cross section with mass m per foot length and flexural rigidity EI. A single wheel load p0 travels across the bridge at a uniform velocity of v. Negelecting damping and assuming the shape function of the form ψ(x) = L2x−x3 , determine an equation for the deflection at midspan as a function of time. L = 200 ft, m = 11 kips/g per foot,...
Problem 4 (25 points) An overhang beam with negligible weight is loaded as shown. Knowing that...
Problem 4 (25 points) An overhang beam with negligible weight is loaded as shown. Knowing that the flexural rigidity of the beam is El = 100 x 106 Nm?, (a) derive the elastic curve for section AB of the beam and (b) determine the slope at supports A and B. 10 KN 5 kN/m А) M = 40 kN-m B. 4 m - 2 m (a) V= (b) өA = OB
Problem 4 (25 points) An overhang beam with negligible weight is loaded as shown. Knowing that...
Problem 4 (25 points) An overhang beam with negligible weight is loaded as shown. Knowing that the flexural rigidity of the beam is El = 100 x 106 Nm?, (a) derive the elastic curve for section AB of the beam and (b) determine the slope at supports A and B. 10 KN 5 kN/m А) M = 40 kN-m B. 4 m - 2 m (a) V= (b) өA = OB
5. Determine the mid-span short-term deflection of a simply supported beam with the section shown in...
5. Determine the mid-span short-term deflection of a simply supported beam with the section shown in Figure Q5. Design data: Concrete strength: fcu 30 MPa. Area of tensile steel reinforcement: As 1500 mm Area of compressive steel reinforcement: A,-1500 mm2 Instantaneous static modulus of elasticity of concrete = 25GPa. Span -8.0 m Loading: Dead load 5.0 kN/m (uniformly distributed load); Live load 5.0 kN/m (uniformly distributed load) (Hint: the height of neutral axis of the mid-span section under the service...
For the beam and loading shown in the figure, integrate the load distribution to determine the...
For the beam and loading shown in the figure, integrate the load
distribution to determine the equation of the elastic curve for the
beam, and the maximum deflection for the beam. Assume that
EI is constant for the beam. Assume EI=25000 kN⋅m2, L=2.4
m, and w0=61 kN/m.
(a) Use your equation for the elastic curve to
determine the deflection at x=1.5 m. Enter a negative value if
the deflection is downward, or a positive value if it is
upward.
(b)...
(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,...
Problem 7.5 of your textbook (Haldar & Mahadevan): A simply supported beam of span L 360 inches is loaded by a uniformly distributed load w kip/in. and a concentrated kip applied at the midspan. The maximum deflection of the beam at the midspan can be calculated as: mar- 384 EI 48 E A beam with El 63.51 x 106 kip-in.2 Is selected to carry the load. Both w and P are statistically independent RVs with mean values estimated to be...
A simply supported uniform beam (with length L and flexural rigidity El) carries a moment Mo (clockwise) at a distance -21B away from the left end (x-0). Calculate the deflection () and slope (dv/de) at 21/3 by using the Rayleigh-Ritz Method. Assume a deflection curve of the form v-asin(rx/L), where a is to be determined
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...
SS two BMs midspan deflection The simply supported beam shown below has a span length L = 4.1. Two applied bending moments Mo = 4.6 are applied at either support. Determine the midspan deflection of the beam. Assume El is constant. Show your results to two decimal point and no units. (Hibbeler) M M 2 Answer:
Problem 4 (25 points) An overhang beam with negligible weight is loaded as shown. Knowing that the flexural rigidity of the beam is El = 100 x 106 Nm?, (a) derive the elastic curve for section AB of the beam and (b) determine the slope at supports A and B. 10 KN 5 kN/m А) M = 40 kN-m B. 4 m - 2 m (a) V= (b) өA = OB
Problem 4 (25 points) An overhang beam with negligible weight is loaded as shown. Knowing that the flexural rigidity of the beam is El = 100 x 106 Nm?, (a) derive the elastic curve for section AB of the beam and (b) determine the slope at supports A and B. 10 KN 5 kN/m А) M = 40 kN-m B. 4 m - 2 m (a) V= (b) өA = OB
5. Determine the mid-span short-term deflection of a simply supported beam with the section shown in Figure Q5. Design data: Concrete strength: fcu 30 MPa. Area of tensile steel reinforcement: As 1500 mm Area of compressive steel reinforcement: A,-1500 mm2 Instantaneous static modulus of elasticity of concrete = 25GPa. Span -8.0 m Loading: Dead load 5.0 kN/m (uniformly distributed load); Live load 5.0 kN/m (uniformly distributed load) (Hint: the height of neutral axis of the mid-span section under the service...
For the beam and loading shown in the figure, integrate the load
distribution to determine the equation of the elastic curve for the
beam, and the maximum deflection for the beam. Assume that
EI is constant for the beam. Assume EI=25000 kN⋅m2, L=2.4
m, and w0=61 kN/m.
(a) Use your equation for the elastic curve to
determine the deflection at x=1.5 m. Enter a negative value if
the deflection is downward, or a positive value if it is
upward.
(b)...
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