![Consider a cantilever beam of length L with a fixed vertical load, Po, applied at a random distance, z, fron the fixed end of the beam. Assumeェis uniformly distributed, fx (z) = CIH (z-L/2)-H(z-L)]. (a) What is C? (b) What is the expected value of the bending moment at the root of the cantilever? (c) Suggest two possible modes in which the structure could fail to perform properly under the specified load. (d) For one of the two failure modes you described in (c), derive a general formula that expresses the reliability of the structure. You dont need to evaluate it numerically, but the expression should be in a form that is ready to be evaluated if necessary. (e) Suppose the load now also has a random magnitude that is independent of the loads position. Assume that P follows a uniform distribution of width Po that is also symmetric about Po. What is the expected value of the bending moment at the root of the cantilever? How do you think the additional randomness affects the reliability of the structure? You do not have to derive the new reliability, but you must give adequate reasoning to justify your conclusion. It will help if you draw a qualitative picture of the relevant pdfs for comparison.](http://img.homeworklib.com/questions/6a5248f0-5d3e-11eb-b527-89e071dce631.png?x-oss-process=image/resize,w_560)
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Consider a cantilever beam of length L with a fixed vertical load, Po, applied at a...
HW16.11. Cantilever beam with distributed load Consider a cantilever beam subjected to a uniform distributed load...
HW16.11. Cantilever beam with distributed load Consider a cantilever beam subjected to a uniform distributed load as indicated below. ty L/4 L/2 Draw the free-body diagram and corresponding shear force and bending moment diagrams. To draw the shear force and bending moment diagrams, you MUST use the minimum number of lines (straight or curved), i.e., the minimum number of objects created by clicking the two buttons under "V and M lines" FBD FBD Concentrated forces: FBD Distributed loads: ttt ???
Problem 5: A cantilever beam AB of length L supports a uniform load of intensity q...
Problem 5: A cantilever beam AB of length L supports a uniform load of intensity q (see figure) has a fixed support at A and spring support at B with rotational stiffness kR. Rotation at B, OB results in a reaction moment MB*Rx θ8. Beginning with the second-order differential equation of the deflection curve (the bending-moment equation), find rotation GB and di the end B. (Hint- You will need third boundary condition so read the problem statement carefully) (20 points)...
I need help with this problem. A cantilever beam is subjected to a linearly distributed load,...
I need help with this problem.
A cantilever beam is subjected to a linearly distributed load, with W, = 10 kN/m and to an inclined point load F equal to 20 kN, as shown in the figure. The length of the beam is L=10 m. Make a cut at distance x from the free end of the cantilever, as shown in the figure, and use the method of sections to derive expressions for the internal resultant loadings at the cross-section...
Q2 The simply supported beam of length L is subjected to a vertical point load P...
Q2 The simply supported beam of length L is subjected to a vertical point load P at its middle, as shown in Figure Q2. Both young's modulus and second moment of area of this structure are given as E and I. Please provide your answers in terms of letters P,L,1, E. Self-weight of the beam is neglected. P L/2 L/2 Figure Q2 (a) Determine the reactions, bending moment equation along the beam and draw the corresponding bending moment diagram. [10]...
Q2 The simply supported beam of length L is subjected to a vertical point load P...
Q2 The simply supported beam of length L is subjected to a vertical point load P at its middle, as shown in Figure Q2. Both young's modulus and second moment of area of this structure are given as E and I. Please provide your answers in terms of letters P,L,1,E. Self-weight of the beam is neglected P L/2 L/2 Figure Q2 (a) Determine the reactions, bending moment equation along the beam and draw the corresponding bending moment diagram. [10] (b)...
Q13. Consider a cantilever beam of 10m length fixed at right end. It carries 5 stones...
Q13. Consider a cantilever beam of 10m length fixed at right end. It carries 5 stones of length 2 m each placed on the beam. The load of each stone is 5 kN/m. A rod of 10 kN load is placed on the beam at 2 m from fixed end and another rod of load 12kN at midpoint of the beam. All the loads are acting downwards. Draw the beam with the loads and fixed condition. Mark the fixed end...
QI A cantilever steel beam of length L 7.5 m carries both a uniformly distributed load...
QI A cantilever steel beam of length L 7.5 m carries both a uniformly distributed load w of 20 kN/m throughout its length and a point load P of 10 kN at its free end, as shown in Figure QI (a). The beam is made from a rectangular hollow box section with a width of 300 mm and a depth of 450 mm (refer to Figure Q1 (b)). The wall thickness of the box section is constant throughout which is...
The simply supported beam of length L is subjected to uniformly distributed load of w and...
The simply supported beam of length L is subjected to uniformly distributed load of w and a vertical point load P at its middle, as shown in Figure Q3. Both young's modulus and second moment of area of this structure are given as E and I. Please provide your answers in terms of letters w, P,L,1, E. Self-weight of the beam is neglected. P W L/2 L/2 Figure Q3 (a) Determine the reactions, bending moment equation along the beam and...
The cantilever beam shown is subjected to a moment at A and a distributed load that...
The cantilever beam shown is subjected to a moment at A and a
distributed load that acts over segment BC, and is fixed at C.
Determine the reactions at the support located at C. Then write
expressions for shear and bending moment as a function of their
positions along the beam. Finally, use these expressions to
construct shear and bending moment diagrams.
Part A - Reactions at support C
Draw a free-body diagram of the beam on paper. Use your...
A cantilever beam of length L and constant EI carries a concentrated load P at a...
A cantilever beam of length L and constant EI carries a
concentrated load P at a distance of L/4 from the free end. Use any
method that you chose to develop an expression for the deflection
of the free end. VEI = ?
Loading Loading Function wwx) Shear V /w(xdx Moment M-Vax 1/4 M = M-a) V-M, M-M V-a) N-P) 03 V- M- (3 shop
HW16.11. Cantilever beam with distributed load Consider a cantilever beam subjected to a uniform distributed load as indicated below. ty L/4 L/2 Draw the free-body diagram and corresponding shear force and bending moment diagrams. To draw the shear force and bending moment diagrams, you MUST use the minimum number of lines (straight or curved), i.e., the minimum number of objects created by clicking the two buttons under "V and M lines" FBD FBD Concentrated forces: FBD Distributed loads: ttt ???
Problem 5: A cantilever beam AB of length L supports a uniform load of intensity q (see figure) has a fixed support at A and spring support at B with rotational stiffness kR. Rotation at B, OB results in a reaction moment MB*Rx θ8. Beginning with the second-order differential equation of the deflection curve (the bending-moment equation), find rotation GB and di the end B. (Hint- You will need third boundary condition so read the problem statement carefully) (20 points)...
I need help with this problem.
A cantilever beam is subjected to a linearly distributed load, with W, = 10 kN/m and to an inclined point load F equal to 20 kN, as shown in the figure. The length of the beam is L=10 m. Make a cut at distance x from the free end of the cantilever, as shown in the figure, and use the method of sections to derive expressions for the internal resultant loadings at the cross-section...
Q2 The simply supported beam of length L is subjected to a vertical point load P at its middle, as shown in Figure Q2. Both young's modulus and second moment of area of this structure are given as E and I. Please provide your answers in terms of letters P,L,1, E. Self-weight of the beam is neglected. P L/2 L/2 Figure Q2 (a) Determine the reactions, bending moment equation along the beam and draw the corresponding bending moment diagram. [10]...
Q2 The simply supported beam of length L is subjected to a vertical point load P at its middle, as shown in Figure Q2. Both young's modulus and second moment of area of this structure are given as E and I. Please provide your answers in terms of letters P,L,1,E. Self-weight of the beam is neglected P L/2 L/2 Figure Q2 (a) Determine the reactions, bending moment equation along the beam and draw the corresponding bending moment diagram. [10] (b)...
Q13. Consider a cantilever beam of 10m length fixed at right end. It carries 5 stones of length 2 m each placed on the beam. The load of each stone is 5 kN/m. A rod of 10 kN load is placed on the beam at 2 m from fixed end and another rod of load 12kN at midpoint of the beam. All the loads are acting downwards. Draw the beam with the loads and fixed condition. Mark the fixed end...
QI A cantilever steel beam of length L 7.5 m carries both a uniformly distributed load w of 20 kN/m throughout its length and a point load P of 10 kN at its free end, as shown in Figure QI (a). The beam is made from a rectangular hollow box section with a width of 300 mm and a depth of 450 mm (refer to Figure Q1 (b)). The wall thickness of the box section is constant throughout which is...
The simply supported beam of length L is subjected to uniformly distributed load of w and a vertical point load P at its middle, as shown in Figure Q3. Both young's modulus and second moment of area of this structure are given as E and I. Please provide your answers in terms of letters w, P,L,1, E. Self-weight of the beam is neglected. P W L/2 L/2 Figure Q3 (a) Determine the reactions, bending moment equation along the beam and...
The cantilever beam shown is subjected to a moment at A and a
distributed load that acts over segment BC, and is fixed at C.
Determine the reactions at the support located at C. Then write
expressions for shear and bending moment as a function of their
positions along the beam. Finally, use these expressions to
construct shear and bending moment diagrams.
Part A - Reactions at support C
Draw a free-body diagram of the beam on paper. Use your...
A cantilever beam of length L and constant EI carries a
concentrated load P at a distance of L/4 from the free end. Use any
method that you chose to develop an expression for the deflection
of the free end. VEI = ?
Loading Loading Function wwx) Shear V /w(xdx Moment M-Vax 1/4 M = M-a) V-M, M-M V-a) N-P) 03 V- M- (3 shop
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