Student Cestruc 04 Truss Analysis

6/12/2020
EXPECTED LEARNINGS:
At the end of this lecture, you are expected to:
1. Analyze a truss using the Method of Joints
ANALYSIS OF 2. Determine zero forces in a truss
PLANE TRUSSES 3. Analyze a truss using the Method of Sections
4. Draw Influence Diagrams of the axial force of a truss member
and apply the theorems for analysis for maximum forces
DLSU CIVIL ENGINEEERING DEPARTMENT STRUCTURAL ANALYSIS – AWC ORETA DLSU CIVIL ENGINEEERING DEPARTMENT STRUCTURAL ANALYSIS – AWC ORETA
METHOD OF JOINTS : EXAMPLE METHOD OF JOINTS : EXAMPLE

Analyze the truss using the method of joints

Draw FBD at each joint
Assume axial forces in tension (T)
Draw FBD Concurrent Force System
Use 2 Equilibrium Equations
Interpret results:
+P (T) or a “Tie”
–P (C) or a “Strut”
FBDs of selected joints
1
6/12/2020

Analyze the truss using the
method of joints
Draw FBD at each joint

Assume axial forces in tension (T)
Draw FBD Concurrent Force
System
Use 2 Equilibrium Equations
Interpret results:
+P (T) or a “Tie”
–P (C) or a “Strut”
ZERO FORCE MEMBERS ZERO FORCE MEMBERS
2
6/12/2020
ZERO FORCE MEMBERS ZERO FORCE MEMBERS : KNOWLEDGE CHECK
ZERO FORCE MEMBERS : KNOWLEDGE CHECK METHOD OF SECTIONS : EXAMPLE
METHOD OF SECTIONS : EXAMPLE METHOD OF SECTIONS : EXAMPLE

Choose either the left or right FBD & apply equilibrium equations.
3
6/12/2020
METHOD OF SECTIONS : CHALLENGE PROBLEM #1 METHOD OF SECTIONS : CHALLENGE PROBLEM #1
Using only one eqn of equilibrium, solve for axial force in bar DI.

Using only one eqn. of equilibrium, solve for axial force in bar HI.
Using only 2 equations of equilibrium, solve for the axial force in DG.
Eqn. 1: Sum moment at A to solve Ey
4
6/12/2020
METHOD OF SECTIONS : CHALLENGE PROBLEM #3
Eqn 2: Sum moment at O to get FDG.
Influence Lines for

Trusses
STRUCT Notes (Ref: Hibbeler)
INFLUENCE LINES INFLUENCE LINES - REACTIONS

An influence line is a curve the ordinate to which at any point • To draw an influence line, simply apply a unit load moving from the left end to
equals the value of some particular function (e.g. reaction, bending the right end of the beam and determine the value of the function at that
moment, axial force, or shear) due to a unit load acting at that position of the unit load.
point. • Draw the influence line for the reactions at A and B.
Influence lines can be used for two very important purposes:
1. To determine what position of live loads that will lead to a
maximum value of the particular function for which the
influence line has been constructed; and
2. To compute the value of that function due to the live loads.
INFLUENCE LINES : THEOREMS INFLUENCE LINES : THEOREMS

THEOREM 3 - To obtain the maximum value of the function due to a uniformly distributed
THEOREM 1 - To obtain the maximum value of a function due to a single concentrated live load, the load should be placed over all those portions of the structure for which the
live load, the load should be placed at the point where the ordinate to the influence ordinates to the influence line for that function have the sign of the character of the
line for that function is a maximum. function desired.
THEOREM 2 - The value of a function due to the action of a single concentrated live THEOREM 4 - The value of a function due to a uniformly distributed live load is equal to the
load equals the product of the magnitude of the load and the ordinate to the product of the intensity of the loading and the net area under that portion of the influence
influence line for that function, measured at the point of application of the load. line, for the function under consideration, which corresponds to the portion of the structure
loaded.
P = 10 kN w = 5 kN/m
Q: Where should a moving load P = 10 kN be positioned
to get the maximum reaction at A for a simple beam? Q: Where should a uniform live load (5 kN/m) be applied to
A: Theorem 1: At x = 0 where the influence line is get the maximum positive shear at C?
maximum. A: Draw the first the influence line for Vc. Using
Q: What is the value of the maximum rxn at A due to P = Theorem 3, apply the uniform load from C to B. +V
10 kN. Q: What is the value of the maximum positive Vc?
A: Theorem 2: RA = 10 kN x (1.0) = 10 kN A: Theorem 4: Vc = 5 kN/m x ½ (0.75 x 15 m) = 37.5 kN
-V
5
6/12/2020
INFLUENCE LINES : TRUSSES INFLUENCE LINES : TRUSSES

Hibbeler, Structural Analysis Hibbeler, Structural Analysis
Problem 1: Draw the IL for bar GB Problem 1: Draw the IL for bar GB
Here is the truss with the unit load at B.
Repeat the process by applying the unit load at A, C,

Apply the unit load at A, B, C, D & E and solve
D & E.
the bar force in G for each case.
The table shows the axial force at GF for each case.
Plot the points to obtain the influence line.

Hibbeler, Structural Analysis Hibbeler, Structural Analysis
Problem 2: Draw the IL for bar CG Problem No. 3
Apply the unit load at A, B, C, D and E. Here is the Apply the unit load at J, I, H, G & F.
FBD of joint C when the unit load is at joint C.

Hibbeler, Structural Analysis
Problem No. 3
6
6/12/2020
INFLUENCE LINES : TRUSSES INFLUENCE LINES : KNOWLEDGE CHECK

Hibbeler, Structural Analysis
1.5 kn Load at Point C
REFERENCES VIDEO TUTORIALS

ANALYSIS OF TRUSSES (METHOD OF JOINTS)
SA04: Truss Analysis: Method of Joints - https://www.youtube.com/watch?v=Evsjp0zKeGw 18:22
Hibbeler, Structural Analysis SA04U: Truss Analysis (Method of Joints) - 17:59
https://www.youtube.com/watch?v=wxAsjywBbMg
Chapter 3 (3.1 – 3.6)– Analysis of Statically Determinate Trusses ST13: Truss Analysis (Method of Joints) - https://www.youtube.com/watch?v=0agNov4JigA 10:40
Chapter 6 (6.5) – Influence Lines for Trusses ZERO FORCE MEMBERS
SA05: Truss Analysis: Zero-force Members - 8:06
Kassimali, Structural Analysis https://www.youtube.com/watch?v=LAb_ezELQ_Y
Chapter 4 (4.1 – 4.7)– Plane & Space Trusses METHOD OF SECTIONS
SA10: Truss Analysis: Method of Sections - 15:30
Chapter 8 (8.4) – Influence Lines for Trusses https://www.youtube.com/watch?v=Svv721BSte0
ST15: Truss Analysis Using The Method of Sections - 7:51
https://www.youtube.com/watch?v=GOKfuendjA4
INFLUENCE LINES 60
SA34: Influence Line in Trusses - https://www.youtube.com/watch?v=QGbUFqJdWuc 9:05
SA35: Influence Line and Moving Load Series in Trusses - 11:16
https://www.youtube.com/watch?v=Vg5LDGMoCO4&t=256s

Student Cestruc 04 Truss Analysis

Uploaded by

Copyright:

Available Formats

Student Cestruc 04 Truss Analysis

Uploaded by

Document Information

Original Description:

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Student Cestruc 04 Truss Analysis

Uploaded by

Copyright:

Available Formats

6/12/2020

METHOD OF JOINTS : EXAMPLE METHOD OF JOINTS : EXAMPLE

METHOD OF JOINTS : EXAMPLE METHOD OF JOINTS : EXAMPLE

FBDs of selected joints

METHOD OF JOINTS : EXAMPLE METHOD OF JOINTS : EXAMPLE

Draw FBD at each joint

METHOD OF JOINTS : EXAMPLE METHOD OF JOINTS : EXAMPLE

ZERO FORCE MEMBERS ZERO FORCE MEMBERS

ZERO FORCE MEMBERS ZERO FORCE MEMBERS : KNOWLEDGE CHECK

ZERO FORCE MEMBERS : KNOWLEDGE CHECK METHOD OF SECTIONS : EXAMPLE

METHOD OF SECTIONS : EXAMPLE METHOD OF SECTIONS : EXAMPLE

METHOD OF SECTIONS : CHALLENGE PROBLEM #1 METHOD OF SECTIONS : CHALLENGE PROBLEM #1

METHOD OF SECTIONS : CHALLENGE PROBLEM #2 METHOD OF SECTIONS : CHALLENGE PROBLEM #2

METHOD OF SECTIONS : CHALLENGE PROBLEM #3 METHOD OF SECTIONS : CHALLENGE PROBLEM #3

Eqn. 1: Sum moment at A to solve Ey

METHOD OF SECTIONS : CHALLENGE PROBLEM #3

Eqn 2: Sum moment at O to get FDG.

Influence Lines for

INFLUENCE LINES INFLUENCE LINES - REACTIONS

INFLUENCE LINES : THEOREMS INFLUENCE LINES : THEOREMS

INFLUENCE LINES : TRUSSES INFLUENCE LINES : TRUSSES

Repeat the process by applying the unit load at A, C,

INFLUENCE LINES : TRUSSES INFLUENCE LINES : TRUSSES

INFLUENCE LINES : TRUSSES INFLUENCE LINES : TRUSSES

INFLUENCE LINES : TRUSSES INFLUENCE LINES : KNOWLEDGE CHECK

REFERENCES VIDEO TUTORIALS

You might also like