1. MEC 0011 Statics
Lecture 7
Prof. Sanghee Kim
Fall_ 2012

2. Chapter Objectives Chapter Outline
Determine the forces in the members of a truss using the method of joints and the method of sections
Analyze forces acting on the members of frames and machines composed of pin-connected members
Chapter Outline
Simple Trusses
The Method of Joints
Zero-Force Members
The Method of Sections

3. 6.1 Simple Trusses
A truss composed of slender members joined together at their end points
Planar Trusses (평면트러스)
Planar trusses used to support roofs and bridges
Roof load is transmitted to the truss at joints(연결부) by means of a series of purlins(마룻대)

4. The analysis of the forces developed in the truss members is 2D
Similar to roof truss, the bridge truss loading is also coplanar (동일평면선상)

5. Deck
Stringer
(종재)
Floor beam
(바닥보)
Joint
- Load transmitting

6. Assumptions for Design
“All loadings are applied at the joint”
- Weight of the members neglected
“The members are joined together by smooth pins”
- Assume connections provided the center lines of the joining members are concurrent
Gusset plate
(bolting & welding)
(bolting & pin

7. Importance of actual design of truss
To state whether the nature of the force is tensile or compressive
Compression members made thicker (due to bucking or column effect)
Force tend to elongate member  tensile force
Force tend to shorten member  compressive force

8. Form of a truss must be rigid to prevent collapse
The simplest form that is rigid or stable is a triangle
Expanding the basic triangular truss
(connect more members to new joint D)

9. 6.2 The Method of Joints
For truss, we need to know the force in each members
Forces in the members are internal forces equilibrium not be applied
For external force members, equations of equilibrium can be applied
Force system acting at each joint is coplanar and concurrent
∑Fx = 0 and ∑Fy = 0 must be satisfied for equilibrium

10. Procedure for Analysis
Draw the FBD with at least 1 known and 2 unknown forces
Find the external reactions at the truss support
Determine the correct sense of the member
Orient the x and y axes
Apply ∑Fx = 0 and ∑Fy = 0
Use known force to analyze the unknown forces

11. Example 6.1
Determine the force in each member of the truss and indicate whether the members are in tension or compression.

12. Solution
2 unknown member forces at joint B
1 unknown reaction force at joint C
2 unknown member forces and 2 unknown reaction forces at point A
For Joint B,

13. For Joint C,

14. For Joint A,

15. FBD of each pin shows the effect of all the connected members and external forces applied to the pin
FBD of each member shows only the effect of the end pins on the member

16. Example 6.2
Determine the force in each member of the truss and indicate whether the members are in tension or compression.