Homework Answers
The problem can be solved using force method cosndiering the reactio force on beamat B as redundant
Deflection of point B due to q on the cantilever beam AB = qL4/8EI
deflection of point B due to concentrated force P at B = PL3/3EI
Let the net displacement at B be 
Force in bar =
(EbAb/Lb)*
net displacement is given by
qL4/8EI -
[(EbAb/Lb)*]L3/3EI
=
qL4/8EI =
[1+(EbAb/Lb)L3/3EI]
= (qL4/8EI
)/[1+(EbAb/Lb)L3/3EI]
axial load in bar
=(EbAb/Lb)*=(EbAb/Lb)*
(qL4/8EI
)/[1+(EbAb/Lb)L3/3EI]
vertical reaction at A=qL-axial lpoad in bar = qL-(EbAb/Lb)* (qL4/8EI )/[1+(EbAb/Lb)L3/3EI]
vertical deflection at B==(qL4/8EI
)/[1+(EbAb/Lb)L3/3EI]
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answer the four question please
A built-in beam AB with bending stiffness El is loaded as...
A rectangular cross section at a location along a beam in bending is
(a). A rectangular cross section at a location along a beam in bending is acted upon by a bending moment and a shear force. The cross section is \(120 \mathrm{~mm}\) wide, \(300 \mathrm{~mm}\) deep and is orientated such that it is in bending about its major axis of bending. The magnitudes of the bending moment and shear force are \(315 \mathrm{kNm}\) and \(240 \mathrm{kN}\) respectively. Determine the maximum bending and shear stresses on the cross section. Plot the bending and...
Q2 The simply supported beam of length is subjected to a vertical point load at its...
Q2 The simply supported beam of length is subjected to a vertical point load at its middle, as shown in Figure Q2. Both young's modulus and second moment of area of this structure are given as and. Please provide your answers in terms of letters. Self-weight of the beam is neglected. Figure Q2 (a) Determine the reactions, bending moment equation along the beam and draw the corresponding bending moment diagram [10] (b) Determine both the slope and deflection at the...
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...
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)...
A Semi-infinite beam is loaded by force P at distance a from its end, as shown...
A Semi-infinite beam is loaded by force P at distance a from its
end, as shown in figure. (a) Obtain formulas for deflection, slope,
moment, and shear force, Using the results from part (a), consider
a 2-m-long steel bar (E = 210 GPa) of 75mm´75mm square cross
section that rests with a side on a rubber foundation with a
modulus of k = 24 MPa. If a concentrated load P = 100 kN is applied
at the distance of a...
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...
Question 29 For the following simply supported beam AB, the beam is loaded with a concentrated...
Question 29 For the following simply supported beam AB, the beam is loaded with a concentrated load and a segment of uniform load as shown below 40 KN 20 kN/m 0.5m 2 m The reaction at support B is: 25 kN 35 kN 30 kN All the choices are incorrect
10. The slope and deflection at a section in a loaded beam can be found out...
10. The slope and deflection at a section in a loaded beam can be found out by which of the following methods? (a) Double integration method (b) Moment area method (c) Macaulay's method (d) Any of the above. 15. A cartilever AB of length 1 is carrying a distributed load whose intensity varies uniformly from zero at the free end to w per un run at the forced end. The deflection at the free end is given as: (3) 30E1...
For the cantilever beam shown in figure below, we have derived the deflection curve during the...
For the cantilever beam shown in figure below, we have derived the deflection curve during the lecture as: r(z)-하-둬뿌 부] 48 Consider the magnitude of the distributed load q 1 N/m, length of the beam L 1 m, Young's modulus E-200 GPa and the 2nd moment of area about the bending axis is 1 = 250 cm". What is the reaction bending moment at the left end in N.m? Ya 2
Q2 The simply supported beam of length is subjected to a vertical point load at its middle, as shown in Figure Q2. Both young's modulus and second moment of area of this structure are given as and. Please provide your answers in terms of letters. Self-weight of the beam is neglected. Figure Q2 (a) Determine the reactions, bending moment equation along the beam and draw the corresponding bending moment diagram [10] (b) Determine both the slope and deflection at the...
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...
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)...
A Semi-infinite beam is loaded by force P at distance a from its
end, as shown in figure. (a) Obtain formulas for deflection, slope,
moment, and shear force, Using the results from part (a), consider
a 2-m-long steel bar (E = 210 GPa) of 75mm´75mm square cross
section that rests with a side on a rubber foundation with a
modulus of k = 24 MPa. If a concentrated load P = 100 kN is applied
at the distance of a...
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...
Question 29 For the following simply supported beam AB, the beam is loaded with a concentrated load and a segment of uniform load as shown below 40 KN 20 kN/m 0.5m 2 m The reaction at support B is: 25 kN 35 kN 30 kN All the choices are incorrect
10. The slope and deflection at a section in a loaded beam can be found out by which of the following methods? (a) Double integration method (b) Moment area method (c) Macaulay's method (d) Any of the above. 15. A cartilever AB of length 1 is carrying a distributed load whose intensity varies uniformly from zero at the free end to w per un run at the forced end. The deflection at the free end is given as: (3) 30E1...
For the cantilever beam shown in figure below, we have derived the deflection curve during the lecture as: r(z)-하-둬뿌 부] 48 Consider the magnitude of the distributed load q 1 N/m, length of the beam L 1 m, Young's modulus E-200 GPa and the 2nd moment of area about the bending axis is 1 = 250 cm". What is the reaction bending moment at the left end in N.m? Ya 2
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