The bending moment diagram of a fixed ended beam with an external moment couple of 200 kip-ft applied at midspan is shown below.
The bending moment diagram of a fixed ended beam with an external moment couple of 200 kip-ft applied at midspan is shown below. The flexural rigidity EI is constant. In terms of El, determine
(a) The equations for the slope v'(x) for each segment of the beam.
(b) The equations for the deflection v(x) for each segment of the beam.
(c) The slope at midspan.
(d) BONUS 15%): Determine the maximum vertical deflection, the maximum slope, and the locations of each.
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The bending moment diagram of a fixed ended beam with an external moment couple of 200 kip-ft applied at midspan is shown below.
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...
Consider a cantilever beam under a concentrated force and moment as shown below. The deflections ofthe...
Consider a cantilever beam under a concentrated force and moment as shown below. The deflections ofthe beam under the force F (y) and moment M (y) are given by: 2. y' Mo L-x) , and y2 Me , where EI is the beam's flexural rigidity. The slope of the beam, 0, is the derivative of the deflection. Write a program that asks the user to input beam's length L, flexural rigidity EI (you may consider this as a single parameter,...
5.2 kip-ft 9.5 kip/ft I. PROBLEMS 3) (25 points) The cantilivered W16x45 beam is made of...
5.2 kip-ft 9.5 kip/ft I. PROBLEMS 3) (25 points) The cantilivered W16x45 beam is made of A-36 steel and is subjected to the loading shown. Determine: a) the shear and bending moment diagrams. b) the maximum deflection (in in) at the point B and maximum slope (in rad) of point B using superposition, and c) if a roller support is introduced at B, determine, the force on this additional roller. 1 1 1 1 1 1 1 WW 18 ft
Determine the maximum tensile and compressive bending stress in the beam if it is subjected to a moment of M = 6 kip-ft.
Problem 2 - Bending Stress Determine the maximum tensile and compressive bending stress in the beam if it is subjected to a moment of M = 6 kip-ft.
For the loading shown in the below figure, knowing that wo 2 kN/m, the length of the beam is L 2 ...
For the loading shown in the below figure, knowing that wo 2 kN/m, the length of the beam is L 2 m, and the bending rigidity EI-204 kN-m2, a) Find the deflection equation for the beam by integration. Clearly specify the conditions to determine the constants of integration b) Find the vertical force needed at point A to prevent vertical displacement at point A (v(0)-0) c) Find the moment needed at point A to have zero slope at point A...
(7) A moment of M = 4 kip-ft is applied on the cross section shown. Determine...
(7) A moment of M = 4 kip-ft is applied on the cross section shown. Determine (a) the normal stress at point a, (b) the maximum tensile and compressive bending stresses in the beam. Ans: (a) oa = 0.0523 ksi (b) om =-1.779 ksi, om' = 3.72 ksi 10.5 in.al -3 in. +0.5 in. 0.5 in. B 3 in. M 10 in. D +0.5 in.
The beam is subjected to a moment of 15 kip*ft. Determine the resultant force the bending stress produces on the top flange A and the bottom flange B.
The beam is subjected to a moment of 15 kip*ft. Determine the
resultant force the bending stress produces on the top flange A and the bottom
flange B. Also compute the maximum bending stress developed in the beam.
The cross-sectional dimensions of the beam shown in the figure are a = 4.2 in., b = 4.7 in., d = 4.2 in., and t = 0.31 in. The internal bending moment about the z centroidal axis is Mz = -3.60 kip-ft....
The cross-sectional dimensions
of the beam shown in the figure are a = 4.2 in., b = 4.7 in., d =
4.2 in., and t = 0.31 in. The internal bending moment about the z
centroidal axis is Mz = -3.60 kip-ft. Determine (a) the maximum
tension bending stress (a positive number) in the beam. (b) the
maximum compression bending stress (a negative number) in the beam.
Answers: (a) σmax T = psi (b) σmax C = psi
P8.012 The...
A beam is subjected to the distributed transverse load Wo = 5.1 kip/ft as shown below....
A beam is subjected to the distributed transverse load Wo = 5.1 kip/ft as shown below. The beam lengths are given by d= 6 ft. Determine the magnitude of the resultant internal bending moment acting on the cross section at point C, assuming the reactions at the supports A and B are vertical. Express your answer in kip-ft. ti I . Oly
Use the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let...
Use the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a=4.0 ft, b=9.0 ft, c=5.0 ft, d=4.0 ft, w = 8 kips/ft and P = 75 kips. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. W X A B C D E a b с For this loading, calculate the reaction forces Ay and Ey acting on the...
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...
Consider a cantilever beam under a concentrated force and moment as shown below. The deflections ofthe beam under the force F (y) and moment M (y) are given by: 2. y' Mo L-x) , and y2 Me , where EI is the beam's flexural rigidity. The slope of the beam, 0, is the derivative of the deflection. Write a program that asks the user to input beam's length L, flexural rigidity EI (you may consider this as a single parameter,...
5.2 kip-ft 9.5 kip/ft I. PROBLEMS 3) (25 points) The cantilivered W16x45 beam is made of A-36 steel and is subjected to the loading shown. Determine: a) the shear and bending moment diagrams. b) the maximum deflection (in in) at the point B and maximum slope (in rad) of point B using superposition, and c) if a roller support is introduced at B, determine, the force on this additional roller. 1 1 1 1 1 1 1 WW 18 ft
For the loading shown in the below figure, knowing that wo 2 kN/m, the length of the beam is L 2 m, and the bending rigidity EI-204 kN-m2, a) Find the deflection equation for the beam by integration. Clearly specify the conditions to determine the constants of integration b) Find the vertical force needed at point A to prevent vertical displacement at point A (v(0)-0) c) Find the moment needed at point A to have zero slope at point A...
(7) A moment of M = 4 kip-ft is applied on the cross section shown. Determine (a) the normal stress at point a, (b) the maximum tensile and compressive bending stresses in the beam. Ans: (a) oa = 0.0523 ksi (b) om =-1.779 ksi, om' = 3.72 ksi 10.5 in.al -3 in. +0.5 in. 0.5 in. B 3 in. M 10 in. D +0.5 in.
The cross-sectional dimensions
of the beam shown in the figure are a = 4.2 in., b = 4.7 in., d =
4.2 in., and t = 0.31 in. The internal bending moment about the z
centroidal axis is Mz = -3.60 kip-ft. Determine (a) the maximum
tension bending stress (a positive number) in the beam. (b) the
maximum compression bending stress (a negative number) in the beam.
Answers: (a) σmax T = psi (b) σmax C = psi
P8.012 The...
A beam is subjected to the distributed transverse load Wo = 5.1 kip/ft as shown below. The beam lengths are given by d= 6 ft. Determine the magnitude of the resultant internal bending moment acting on the cross section at point C, assuming the reactions at the supports A and B are vertical. Express your answer in kip-ft. ti I . Oly
Use the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a=4.0 ft, b=9.0 ft, c=5.0 ft, d=4.0 ft, w = 8 kips/ft and P = 75 kips. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. W X A B C D E a b с For this loading, calculate the reaction forces Ay and Ey acting on the...
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