Show the zero force members on the figure (label them on the figure and list them on the side). Note: you don't have to solve the entire structure) D E 60 kips В F A M L K G H 180 kips 120 kips
Plane Trusses
It is defined as, two or more elements like beams or any two or more force members, which when assembled together, behaves like a complete structure or as a single structure. They generally consist of two force member which means any component structure where the force is applied only at two points. The point of contact of joints of truss are known as nodes. They are generally made up of triangular patterns. Nodes are the points where all the external forces and the reactionary forces due to them act and shows whether the force is tensile or compressive. There are various characteristics of trusses and are characterized as Simple truss, planar truss or the Space Frame truss.
Equilibrium Equations
If a body is said to be at rest or moving with a uniform velocity, the body is in equilibrium condition. This means that all the forces are balanced in the body. It can be understood with the help of Newton's first law of motion which states that the resultant force on a system is null, where the system remains to be at rest or moves at uniform motion. It is when the rate of the forward reaction is equal to the rate of the backward reaction.
Force Systems
When a body comes in interaction with other bodies, they exert various forces on each other. Any system is under the influence of some kind of force. For example, laptop kept on table exerts force on the table and table exerts equal force on it, hence the system is in balance or equilibrium. When two or more materials interact then more than one force act at a time, hence it is called as force systems.
![### Diagram Analysis of Truss Structure
The image depicts a truss structure with various members and joints. The purpose is to identify and label the zero-force members. These members do not carry any force and are critical in analyzing the stability and efficiency of the structure.
#### Description of the Truss Structure:
- **Joints and Members:**
- The structure consists of joints labeled from A to M.
- The members connect these joints forming triangular and rectangular shapes typical in trusses.
- **External Forces:**
- A downward force of 60 kips is applied at joint B.
- There are upward reactions at the supports: 180 kips at joint I and 120 kips at joint H.
- **Primary Components:**
- **Horizontal Members:** AM, DE, EF
- **Vertical Members:** EJ, FG, HI
- **Diagonal Members:** Connect various joints forming triangles.
#### Zero-Force Members:
To identify zero-force members in such structures, use the following rules common in truss analysis:
1. **At a Joint with No External Load or Support:**
If two non-collinear members meet at a joint without any external load or support, these members are zero-force.
2. **At a Joint with Two Members:**
If three members form a truss joint and two of them are collinear, the third member is a zero-force member.
### Application on the Structure:
- Identify joints where the above rules can be applied to determine zero-force members.
- Label these members on the diagram for clear distinction.
This analysis helps in simplifying the structure for further calculations related to forces and moments in the truss. Understanding which members do not contribute to the force distribution allows for optimizing the design and material use in construction projects.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F502330eb-9fa1-41eb-8716-374edceb5782%2F3c083b48-72d7-4463-b81e-439e45f8c831%2Fvllrpm4_processed.jpeg&w=3840&q=75)
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