Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition
Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition
5th Edition
ISBN: 9781259820960
Author: Leet, Kenneth
Publisher: McGraw-Hill Education
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Chapter 9, Problem 38P
To determine

Find the reactions and all bar forces for the truss.

Expert Solution & Answer
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Explanation of Solution

Given information:

EI is constant.

The Young’s modulus E of the beam is 30,000kips/in.2.

The area of all the bars are 2in2.

Calculation:

Consider the force in the member AC and the horizontal reaction at support B are the redundant.

Remove the redundant to get the released structure.

Sketch the released structure with external loading as shown in Figure 1.

Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition, Chapter 9, Problem 38P , additional homework tip  1

Refer Figure 1.

Consider the force in the member AC as zero.

Find the value of the angle θ as follows:

tanθ=1520θ=tan1(1520)θ=36.869°

Find the support reaction as follows:

Apply Equation of Equilibrium,

MA=060×15+By1×20=0By1=90020By1=45kips

Fy=0Ay1+By1=0Ay1=By1Ay1=45kips

Fx=0Ax1+60=0Ax1=60kips

Consider support A.

Apply Equation of Equilibrium,

Fy=0Ay1+FAD1=0FAD1=Ay1FAD1=(45)kipsFAD1=45kips(T)

Fx=0Ax1+FAB1=0FAB1=Ax1FAB1=(60)kipsFAB1=60kips(T)

Consider joint C.

Apply Equation of Equilibrium,

Fx=0FCD1+60=0FCD1=60kips(T)

Fy=0FBC1=0

Consider joint D,

Apply Equation of Equilibrium,

Fx=0FCD1+FBD1cosθ=0FCD1+FBD1cos(36.869°)=060+0.8FBD1=0FBD1=75kips(T)

Sketch the P system for Δ10 and Δ20 as shown in Figure 2.

Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition, Chapter 9, Problem 38P , additional homework tip  2

Sketch the released structure with unit member force in member AC as shown in Figure 3.

Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition, Chapter 9, Problem 38P , additional homework tip  3

Refer Figure 4.

Consider the force in the member AC is 1 kips.

The support reactions at A and B are zero as no external load acts on the truss.

Consider support A.

Apply Equation of Equilibrium,

Fx=0FACcosθ+FAB=01cos(36.869°)+FAB=0FAB=0.8kipsFAB=0.8kips(C)

Fy=0FACsinθ+FAD=01sin(36.869°)+FAD=0FAD=0.6kipsFAD=0.6kips(C)

Consider joint C.

Apply Equation of Equilibrium,

Fx=0FCAcosθFCD=0cos(36.869°)FCD=0FCD=0.8kipsFCD=0.8kips(C)

Fy=0FCAsinθFCB=0sin(36.869°)FCB=0FCB=0.6kipsFCB=0.6kips(C)

Consider joint D,

Apply Equation of Equilibrium,

Fx=0FCD+FBDcosθ=00.8+FBDcos(36.869°)=00.8+0.8FBD=0FBD=1kips(T)

Sketch the Q system for Δ10 as shown in Figure 4.

Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition, Chapter 9, Problem 38P , additional homework tip  4

Sketch the Q system for Δ20,δ21,δ22 and P system for δ22 as shown in Figure 5.

Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition, Chapter 9, Problem 38P , additional homework tip  5

Refer Figure 5.

Find the support reaction at A as follows:

Applying Equation of Equilibrium,

Fx=0Ax1=0Ax=1kips

There is no external load at joint D and C and no vertical reaction at A and B.

The force in all the members of the truss except AB is zero.

Consider joint A.

Applying Equation of Equilibrium,

Fx=0Ax+FAB2=01+FAB2=0FAB2=1kipsFAB2=1kips

Find the deflection Δ10 as follows:

Δ10=FQFPLAE=[(0.8)×60×(20ft×12in.1ft)2×30,000×2+(0.6)×45×(15ft×12in.1ft)2×30,000+1×(75)×(25ft×12in.1ft)4×30,000]=0.6525in.

Find the deflection Δ20 as follows:

Δ20=FQFPLAE=1×60×(20ft×12in.1ft)2×30,000=0.24in.

Find the deflection δ11 as follows:

δ11=FQ2LAE=[(0.8)2×(20ft×12in.1ft)2×30,000×2+(0.6)2×(15ft×12in.1ft)2×30,000+12×(25ft×12in.1ft)2×30,000+12×(25ft×12in.1ft)4×30,000]=0.0148in.

Find the deflection δ21 as follows:

δ21=FQFPLAE=(1)(0.8)×(20ft×12in.1ft)2×30,000=0.0032in.

Find the deflection δ12 as follows:

δ12=FQFPLAE=(0.8)(1)×(20ft×12in.1ft)2×30,000=0.0032in.

Find the deflection δ22 as follows:

δ22=FQFPLAE=(1)(1)×(20ft×12in.1ft)2×30,000=0.004in.

Show the compatibility Equation for Δ1,ACREL as follows:

Δ1,ACREL=0Δ10+δ11X1+δ12X2=00.6525+0.0148X1+0.0032X2=00.0148X1+0.0032X2=0.6525        (1)

Show the compatibility Equation for ΔBX as follows:

ΔBX=0Δ20+δ21X1+δ22X2=00.24+0.0032X1+0.004X2=00.0032X1+0.004X2=0.24        (2)

Solve Equation (1) and (2).

X1=37.62kips

X2=29.9kips

Find the reaction and bar forces in the members of the truss as shown in 6 and 7.

Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition, Chapter 9, Problem 38P , additional homework tip  6

Apply the sum shown in Figure 6 to get the final reactions and member forces shown in Figure 7.

Connect Access Card For Fundamentals Of Structural Analysis (one Semester Access) 5th Edition, Chapter 9, Problem 38P , additional homework tip  7

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