Truss Analysis
Ahmad Shufni bin Othman
Mei 2014
ANALYSISOFSTATICALLYDETERMINATE TRUSSES(Part 3)
Truss Analysis
Techniques for Truss Analysis
Truss Analysis
METHOD OF SECTIONS
Learning Objectives
Upon completion of this course, students should be able to;
• Explain the Method of Sections.• Determining the truss members forces using the Method
of Sections.
Truss Analysis
Assumptions for Design
Truss Analysis
Assumptions for Design• Axial Force Members
– Tension / Compression
– Compression Members Usually Thicker
Tension
Compression
Tensile (T) axial member force is indicated on the joint
by an arrow pulling away from the joint.
Compressive (C) axial member forceis indicated by an
arrow pushing toward the joint.
Truss Analysis
The Objectives:
Students will be able to determine forces in truss members using the method of sections.
In-Class Activities:
•Applications
•Method of sections
•Concept quiz
•Group Problem solving
• Attention quiz
Truss Analysis
APPLICATIONS
Long trusses are often used to construct bridges.
The method of joints requires that many joints be analyzed before we can determine the forces in the middle part of the truss.
Is there another method to determine these forces directly?
Truss Analysis
THE METHOD OF SECTIONS
In the method of sections, a truss is divided into two parts by taking an imaginary “cut” (shown here as a-a) through the truss.
Since truss members are subjected to only tensile or compressive forces along their length, the internal forces at the cut member will also be either tensile or compressive with the same magnitude. This result is based on the equilibrium principle and Newton’s third law.
Truss Analysis
Truss in Equilibrium Each PART in Equilibrium
THE METHOD OF SECTIONS
Efficient when forces of only a few members are to be found
Truss Analysis
STEPS FOR ANALYSIS
1. Decide how you need to “cut” the truss. This is based on: a) where you need to determine forces, and, b) where the total number of unknowns does not exceed three (in general).
2. Decide which side of the cut truss will be easier to work with (minimize the number of reactions you have to find).
3. If required, determine the necessary support reactions by drawing the FBD of the entire truss and applying the EofE.
Truss Analysis
4. Draw the FBD of the selected part of the cut truss. We need to indicate the unknown forces at the cut members. Initially we assume all the members are in tension, as we did when using the method of joints. Upon solving, if the answer is positive, the member is in tension as per our assumption. If the answer is negative, the member must be in compression.
PROCEDURE (continued)
Truss Analysis
PROCEDURE (continued)
5. Apply the equations of equilibrium (EofE) to the selected cut section of the truss to solve for the unknown member forces. Please note that in most cases it is possible to write one equation to solve for one unknown directly.
Truss Analysis
0
0
0
M
F
F
y
x
Equations of Equilibrium
Take moments about a
point that lies on the
intersection of the lines of
action of two unknown
forces
PROCEDURE (continued)
Truss Analysis
SOLUTIONS
NF
F
Mc
GF
GF
2000
0)4(1000)2(
0
(compression)
NF
F
M
BC
BC
G
1000
0)2(1000)2(
0
(tension)
NF
F
F
GCY
GCY
Y
1000
01000
0
NF
F
FFF
GCYGC
GCXGCYGC
21.141482
10008
2
228
(tension)
FGCY
FGCX
Truss Analysis
Example 1
For this truss :
1. Calculate the forces in
members AB, BE and DE.
2. Determine whether the
member is in compression or
tension.
20 kN
10 kN 10 kN
2 m 2 m
4 m
AB
CDE
Truss Analysis
Solution 1 :
For this truss :
1. Determine support reaction (if
needed)
2. Apply ‘a cut’ through the required
members (x – x)
3. Determine the forces in the members
(state : compression or tension)
Truss Analysis
Solution 1 : (Right Side)
Truss Analysis
Solution 1 : (Left Side) cont.
Truss Analysis
ATTENTION QUIZ
1. As shown, a cut is made through members GH, BG and BC to determine the forces in them. Which section will you choose for analysis and why?
A. Right, fewer calculations.
B. Left, fewer calculations.
C. Either right or left, same amount of work.
D. None of the above, too many unknowns.
Truss Analysis
ATTENTION QUIZ
2. When determining the force in member HG in the previous question, which one equation of equilibrium is best to use?
A. MH = 0
B. MG = 0
C. MB = 0
D. MC = 0
Truss Analysis
Example 2
For this truss :
1. Calculate the forces in
members CD, CG and GH.
2. Determine whether the
member is in compression
or tension.
Then ?
Which side of the “cut” ? WHY ?
Calculate the support reaction at A
Truss Analysis
Taking the right side of the truss :
1. Calculate FCD
2. Calculate FHG
3. Calculate FCG
Solution 2 :
Truss Analysis
By taking a moment to the joint G
+MG = 0 ;
300(6) + FCD(3) = 0
FCD = 600 N (compression)
By taking a moment to the joint C
+MC = 0 ;
300(6) – FCG(3) = 0 FED = 600 N (tension)
Solution 2 : (cont.)
Truss Analysis
Define FCGy:
Fy = 0 : -FCGy + 300 = 0
FCGy = 300 kN
18
F
3
F
3
FCGCGCG XY
YCGCG F*)3
18(F
(tension) N424.26N)(300*)3
18(
Solution 2 : (cont.)
Truss Analysis
CONCEPT QUIZ
If you know FED, how will you
determine FEB ?
A. By taking section b-b and using ME = 0
B. By taking section b-b, and using FX = 0 and FY = 0
C. By taking section a-a and using MB = 0
D. By taking section a-a and using MD = 0
Truss Analysis
Given: Loads as shown on the roof truss.
Find: The force in members DE, DL, and ML.
Plan:
a) Take a cut through the members DE, DL, and ML.
b) Work with the left part of the cut section. Why?
c) Determine the support reaction at A. What are they?
d) Apply the EofE to find the forces in DE, DL, and ML.
Example 3
Truss Analysis
Analyzing the entire truss, we get FX = AX = 0. By symmetry, the vertical support reactions are
AY = IY = 36 kN
+ MD = – 36 (8) + 6 (8) + 12 (4) + FML (5) = 0
FML = 38.4 kN ( T )
Solution 3 :
Truss Analysis
+ ML = –36 (12) + 6 (12) + 12 (8) + 12 (4) – FDE ( 4/17)(6) = 0
FDE = –37.11 kN or 37.1 kN (C)
+ FX = 38.4 + (4/17) (–37.11) + (4/41) FDL = 0 FDL = –3.84 kN or 3.84 kN (C)
Solution 3 : (cont.)
Truss Analysis
Given: Loading on the truss as shown.
Find: The force in members BC, BE, and EF.
Plan:
a) Take a cut through the members BC, BE, and EF.
b) Analyze the top section (no support reactions!).
c) Draw the FBD of the top section.
d) Apply the equations of equilibrium such that every equation yields answer to one unknown.
GROUP PROBLEM SOLVING
Truss Analysis
+ FX = 5 + 10 – FBE cos 45º = 0 FBE = 21.2 kN (T)
+ ME = – 5(4) + FCB (4) = 0 FCB = 5 kN (T)
+ MB = – 5 (8) – 10 (4) – 5 (4) – FEF (4) = 0
FEF = – 25 kN or 25 kN (C)
SOLUTION
Truss Analysis
For the truss shown, find the internal fore in member BE
Class Problem 1
Truss Analysis
The structure shown, is pinned to the floor at A and H. Determine the magnitude of all the support forces acting on the structure and find the force in member BF.
Class Problem 2
Answer : FBF = 128.06 kN (Tension)
Truss Analysis
Class Problem 3
Using method of sections determine the forces in members BC, GC and GF of the pin-jointed truss shown below.
Answer : FGC = 7.07 kN (Comp.) FBC = 25 kN (Tension) FGF = 20 kN (Comp.)
Truss Analysis
The truss below is pinned to the wall at point F, and supported by a roller at point C. Calculate the force (tension or compression) in members BC, BE, and DE.
Class Problem 4
Answer : FBC = 120 kN (Comp.) FBE = 150.78 kN (Tension) FDE = 64 kN (Tension)
Truss Analysis
The roof truss shown below is pinned at point A, and supported by a roller at point H. Determine the force in member DG.
Class Problem 5
Answer : FDG = 18.14 kN (Tension)
Truss Analysis
Determine the force in member BE and BC of the truss shown. State whether each member is in tension or compression. Member DE and EG is equal in length.
Answer : FBE = 4.17 kN (Comp.) FBC = 6.67 kN (Comp.)
Class Assignment 1
Truss Analysis
Class Assignment 2
Determine the forces in members BC, BF, and EF of the truss shown in Fig. below by using the method of sections.
Answer:
TBF = 3.75 kN (T)
TBC = 2.25 kN (T)
TEF = 4.5 kN (C)
Truss Analysis
A symmetrical fink roof truss is subjected to vertical loadings as shown. Determine the force in members IM, IJ and CJ.
GROUP PROBLEM SOLVING
Truss Analysis
Excercise : Determine the forces in the members of the truss
Truss Analysis
Answer :
Truss Analysis