department of architecture arch 261 structural...
TRANSCRIPT
1
Asst. Prof. Dr. Ferhat PAKDAMARN Blok 1-17
Department of ArchitectureARCH 261
Structural Analysis
Analysis of Truss Structures
We will discuss the determinacy, stability, and analysis of three forms of statically determinate trusses.
2
2
Analysis of Truss Structures
3
Analysis of Truss Structures
4
3
Analysis of Truss Structures
5
Analysis of Truss Structures
6
4
Analysis of Truss Structures
7
Analysis of Truss Structures
Definition of a Truss;
A truss is a structure composed of slender members joined together at their end points.
Planar trusses lie in a single plane.
Typically, the joint connections are formed by bolting or welding the end members together to a common plate, called a gusset plate.
8
5
To design both the members and connections of a truss, the force in each member for a given loading must be determined.
Two important assumptions are made in truss analysis
Truss members are connected by smooth pins
All loading is applied at the joints of the truss
Because of these two assumptions, each truss member is a two-force member with either a compressive (C) or a tensile (T) axial force
9
Assumptions for Truss Design
10
Analysis of Truss Structures
6
Analysis of Truss Structures
11
Classification of Coplanar Trusses
Simple Trusses Compound Trusses Complex Trusses
Area of usage of truss systems;
Roofs;
12
Analysis of Truss Structures
7
Bridges;
13
Bridges;
14
Analysis of Truss Structures
8
Determinacy of Coplanar Trusses
Determinate Truss systems;
n=m+r-2j=0
n= degree of freedom
m= the total parts of structure members
r= the total number of unknown reactive force and moment components
j= the total number of connection points
15
16
m=5
r=3
j=4
n=m+r-2j
5+3-8=0
Analysis of Truss Structures
9
17
m=10
r=4
j=7
n=m+r-2j
=0
Analysis of Truss Structures
18
m=14
r=4
j=8
n=m+r-2j
=2
Analysis of Truss Structures
10
The analys type of truss systems;
1) The Method of Joints
2) The Method of Sections (Ritter)
3) (Maxwell-Cremona)
19
Analysis of Truss Structures
Method of Joints;
Procedure for analysis - the following is a procedure for analyzing a truss using the method of joints:
1. If possible, determine the support reactions
2. Draw the free body diagram for each joint. Ingeneral, assume all the force member reactionsare tension (this is not a rule, however, it ishelpful in keeping track of tension andcompression members).
20
Analysis of Truss Structures
11
21
Analysis of Truss Structures
•Procedure for analysis - the following is a procedure for analyzing a truss using the method of joints:
3. Write the equations of equilibrium for each joint,
∑ Fx =0 ∑ FY =0
Procedure for analysis - the following is a procedure for analyzing a truss using the method of joints:
4. If possible, begin solving the equilibrium equations at a joint where only two unknown reactions exist. Work your way from joint to joint, selecting the new joint using the criterion of two unknown reactions.
5. Solve the joint equations of equilibriumsimultaneously, typically using a computer or anadvanced calculator
12
23
Tension
Compression
Analysis of Truss Structures
24
Example:
13
25
Analysis of Truss Structures
Examples forWrong Structural Design
26