Fundamentals Of Structural Analysis:
Fundamentals Of Structural Analysis:
5th Edition
ISBN: 9781260083330
Author: Leet, Kenneth
Publisher: MCGRAW-HILL HIGHER EDUCATION
Question
Book Icon
Chapter 9, Problem 29P
To determine

Find the reactions and all bar forces for the truss.

Expert Solution & Answer
Check Mark

Explanation of Solution

Given information:

The Young’s modulus E of the beam is 200GPa.

The area of all the bars is 1000mm2.

Calculation:

Show the free body diagram of the truss as shown in Figure 1.

Fundamentals Of Structural Analysis:, Chapter 9, Problem 29P , additional homework tip  1

Refer Figure 1.

Find the length of the inclined members of the truss as follows:

Consider the length of the inclined members AE, EB, BD, DC is l.

l=32+42=25=5m

By symmetry of truss,

AE=EB=BD=DC=5m

Find the angle θ as follows:

tanθ=43θ=tan1(43)θ=53.130°

Consider the horizontal reaction at D as the redundant.

Remove the redundant at D to get the released structure.

Show the released structure with applied load as shown in Figure 2.

Fundamentals Of Structural Analysis:, Chapter 9, Problem 29P , additional homework tip  2

Refer Figure 2.

Find the reactions at A and D as follows:

Apply Equation of Equilibrium,

Fx=0Ax1=0

MA=0(Dy1×9)(100×3)(60×6)(60×12)=0Dy1=(13809)Dy1=153.3kN

Fy=0Ay1+Dy1=60+60+100Ay1=220Dy1Ay1=220153.3Ay1=66.7kN

Find the forces FP in the bars of released structure due to applied load as follows:

Refer Figure 2.

Consider Joint A.

Apply Equation of Equilibrium,

Fy=0Ay1FAE1sinθ=066.7FAE1sin(53.130°)=066.70.8FAE1=0FAE1=83.3kN(T)

Fx=0Ax1+FAB1+FAE1cosθ=00+FAB1+FAE1cos(53.130°)=0FAB1+0.6(83.3)=0FAB1=50kNFAB1=50kN(C)

Consider joint C.

Apply Equation of Equilibrium,

Fy=0FCD1sinθ60=0FCD1sin(53.130°)60=00.8FCD160=0FCD1=75kN(C)

Fx=0FBC1FCD1cosθ=0FBC1=(75)cos(53.130°)FBC1=45kN(T)

Consider joint B.

Apply Equation of Equilibrium,

Fy=060FBE1sin(53.130°)FBD1sin(53.130°)=00.8FBE1+0.8FBD1=60        (1)

Fx=0FBA1FBE1cos(53.130°)+FBD1cos(53.130°)+FBC1=0(50)0.6FBE1+0.6FBD1+45=00.6FBE1+0.6FBD1=95        (2)

Solve Equation (1) and (2).

FBE1=41.7kN(T)FBD1=116.7kN(C)

Consider joint D.

Apply Equation of Equilibrium,

Fx=0FEA1cosθ+FED1+FEB1cosθ=0(83.3)cos(53.130°)+FED1+(41.7)cos(53.130°)=050+FED1+25=0FED1=25kN(T)

Show the P forces in the members of the truss due to the applied load at D as shown in Table 1.

MembersFP forces (kN)
AB50 (C)
BC45 (T)
CD75 (C)
DE25 (T)
EA83.3 (T)
BE41.7 (T)
BD116.7 (C)

Table 1

Show the released structure loaded with unit horizontal load at D as shown in Figure 3.

Fundamentals Of Structural Analysis:, Chapter 9, Problem 29P , additional homework tip  3

Refer Figure 3.

By symmetry of the truss,

Fx=0Ax1=0Ax=1kN

MA=0Dy×9(1×4)=0Dy=0.444kN

Fy=0Ay+Dy=0Ay+0.444kN=0Ay=0.444kN

Find the FQ forces in the members of the released structure due to unit load as follows:

Refer Figure 3.

Consider Joint A.

Apply Equation of Equilibrium,

Fy=0AyFAEsinθ=00.444FAEsin(53.130°)=00.4440.8FAE=0FAE=0.556kN(C)

Fx=0Ax+FAB+FAEcosθ=01+FAB+FAEcos(53.130°)=0FAB+0.6(0.556)=1FAB=0.664kNFAB=0.664kN(C)

Consider joint C.

In a two member forces BC and CD, if both the members are not parallel and the no external loads or reactions acts at that joint. Then, the force in both the members is zero.

The forces in the member BC and CD is FBC=FCD=0.

Consider joint B.

Apply Equation of Equilibrium,

Fy=0FBEsin(53.130°)FBDsin(53.130°)=00.8FBE+0.8FBD=0FBE=FBD        (3)

Fy=0FBAFBEcos(53.130°)+FBDcos(53.130°)+FBC=0(50)0.6FBE1+0.6FBD1+45=00.6FBE1+0.6FBD1=95        (4)

Solve Equation (1) and (2).

FBE1=41.7kN(T)FBD1=116.7kN(C)

Consider joint D.

Apply Equation of Equilibrium,

Fx=0FEAcosθ+FED+FEBcosθ=0(0.556)cos(53.130°)+FED+(0.556)cos(53.130°)=0(0.556)cos(53.130°)+FED+(0.556)cos(53.130°)=00.3336+FED+0.3336=0FED=0.667kN(C)

Show the Q forces in the members of the truss due to the unit load at D as shown in Table 1.

MembersFQ forces (kN)
AB0.667 (C)
BC0
CD0
DE0.667 (C)
EA0.556 (C)
BE0.556 (T)
BD0.556 (C)

Table 2

Find the deflection ΔDO of the released structure due to the applied load and the deflection δDD of the released structure due to the unit load as follows:

MembersFP forces(kN)FQ forces (kN)L(m)ΔDO=FQFPLAEδDD=FQ2LAE
AB-50-0.6676200.1AE2.669AE
BC450600
CD-750500
DE25-0.6676100.05AE2.669AE
EA83.3-0.5565231.574AE1.5456AE
BE41.70.5565115.926AE1.5456AE
BD-116.7-0.5565324.426AE1.5456AE

Table 3

Refer Table 3.

ΔDO=FQFPLAEΔDO=309AE

δDD=FQ2LAE=10AE

Find the horizontal reaction at D as follows:

ΔD=ΔDD+δDDRD0=309AE+10AERDRD=30910RD=30.9kN()

Thus, the horizontal reaction at D is RD=30.9kN()_.

Find final forces in the truss as shown in Table 4.

MembersFP(kN)FQ(kN)RD()(kN)Fi=FP+FQRD(kN)
AB-50-0.667-30.9-29.4
BC450-30.945
CD-750-30.9-75
DE25-0.667-30.945
EA83.3-0.556-30.9100.5
BE41.70.556-30.924.5
BD-116.7-0.556-30.9-99.5

Table 4

Show the final support reaction as shown in Table 5.

Support Reactions
MembersPi(kN)PQ(kN) forcesRD(kN)()Reaction=Pi+PQRDkN
HA01-30.9-30.9
RA66.7-0.444-30.980.4
RD153.30.444-30.9139.6

Table 5

Thus, the reactions and all bar forces for the truss is tabulate in table 4 and table 5.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Note: Please accurately answer it!. I'll give it a thumbs up or down based on the answer quality and precision.  Question: What is the group name of Sample B in problem 3 from the image?. By also using the ASTM flow chart!. This unit is soil mechanics btw
Pick the rural location of a project site in Victoria, and its catchment area-not bigger than 25 sqkm, and given the below information, determine the rainfall intensity for ARI = 5, 50, 100 year storm event. Show all the details of the procedure. Each student must propose different length of streams and elevations. Use fig below as a sample only. Pt. E-ht. 95.0 200m 600m PLD-M. 91.0 300m Pt. C-93.0 300m PL.B-ht. 92.0 PL.F-ht. 96.0 500m Pt. A-M. 91.00 To be deemed satisfactory the solution must include: Q.F1.1.Choice of catchment location Q.F1.2. A sketch displaying length of stream and elevation Q.F1.3. Catchment's IFD obtained from the Buro of Metheorology for specified ARI Q.F1.4.Calculation of the time of concentration-this must include a detailed determination of the equivalent slope. Q.F1.5.Use must be made of the Bransby-Williams method for the determination of the equivalent slope. Q.F1.6.The graphical display of the estimation of intensities for ARI 5,50, 100 must be shown.
QUANTITY SURVEYING
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Structural Analysis
Civil Engineering
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:Cengage,
Text book image
Structural Analysis (10th Edition)
Civil Engineering
ISBN:9780134610672
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Principles of Foundation Engineering (MindTap Cou...
Civil Engineering
ISBN:9781337705028
Author:Braja M. Das, Nagaratnam Sivakugan
Publisher:Cengage Learning
Text book image
Fundamentals of Structural Analysis
Civil Engineering
ISBN:9780073398006
Author:Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:McGraw-Hill Education
Text book image
Sustainable Energy
Civil Engineering
ISBN:9781337551663
Author:DUNLAP, Richard A.
Publisher:Cengage,
Text book image
Traffic and Highway Engineering
Civil Engineering
ISBN:9781305156241
Author:Garber, Nicholas J.
Publisher:Cengage Learning