Truss Analysis
ANALYSIS
OF
STATICALLY
DETERMINATE TRUSSES
(Part 3)
Ahmad Shufni bin Othman
Mei 2014
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
Tensile (T) axial member force is indicated on the joint
by an arrow pulling away from the joint.
Compression
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
Newtons third law.
Truss Analysis
THE METHOD OF SECTIONS
Truss in Equilibrium
Each PART in Equilibrium
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
PROCEDURE (continued)
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.
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
PROCEDURE (continued)
Equations of Equilibrium
F 0
F 0
M 0
x
Take moments about a
point that lies on the
intersection of the lines of
action of two unknown
forces
Truss Analysis
SOLUTIONS
Mc 0
FGCY
FGF (2) 1000(4) 0
FGCX
FGF 2000 N
(compression)
FY 0
FGCY 1000 0
FGCY 1000 N
FBC (2) 1000(2) 0
FBC 1000 N
(tension)
FGC FGCY FGCX
2
2
8
FGCY
1000
FGC
8
8 1414.21N
2
2
(tension)
Truss Analysis
Example 1
For this truss :
20 kN
1. Calculate the forces in
members AB, BE and DE.
2. Determine whether the
member is in compression or
tension.
4m
2m
D
10 kN
2m
C
10 kN
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.
Which side of the cut ?
Then ?
WHY ?
Calculate the support reaction at A
Truss Analysis
Solution 2 :
Taking the right side of the truss :
1. Calculate FCD
2. Calculate FHG
3. Calculate FCG
Truss Analysis
Solution 2 : (cont.)
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)
Truss Analysis
Solution 2 : (cont.)
Define FCGy:
Fy = 0 : -FCGy + 300 = 0
FCGy = 300 kN
FCGY
3
FCG
FCGX
3
FCG
18
18
(
) * FCG Y
3
18
(
) * (300 N) 424.26 N (tension)
3
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
Example 3
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.
Truss Analysis
Solution 3 :
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 )
Truss Analysis
Solution 3 : (cont.)
+ 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)
Truss Analysis
GROUP PROBLEM SOLVING
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.
Truss Analysis
SOLUTION
+ FX = 5 + 10 FBE cos 45 = 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)
Truss Analysis
Class Problem 1
For the truss shown, find the internal fore in member BE
Truss Analysis
Class Problem 2
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.
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
Class Problem 4
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.
Answer : FBC = 120 kN (Comp.)
FBE = 150.78 kN (Tension)
FDE = 64 kN (Tension)
Truss Analysis
Class Problem 5
The roof truss shown below is pinned at point A, and
supported by a roller at point H. Determine the force in
member DG.
Answer : FDG = 18.14 kN (Tension)
Truss Analysis
Class Assignment 1
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.)
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
GROUP PROBLEM SOLVING
A symmetrical fink roof truss is subjected to vertical loadings
as shown. Determine the force in members IM, IJ and CJ.
Truss Analysis
Excercise :
Determine the forces in the members of the truss
Truss Analysis
Answer :
Truss Analysis
