Using the method of joints, determine the force in each member of the roof truss shownin Figure -07. State whether each member is in tension or compression.
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.
Using the method of joints, determine the force in each member of the roof truss shownin Figure -07. State whether each member is in tension or compression.
![**Title: Analysis of Truss Structure**
**Description:**
This image represents a truss structure used in engineering and architectural contexts. A truss is a framework, typically consisting of rafters, posts, and struts, supporting a roof, bridge, or other structure.
**Diagram Explanation:**
**Structure Layout:**
- The truss system in the image is composed of multiple triangles, which are the fundamental shapes used in truss designs because of their inherent structural stability.
- The truss spans horizontally 9 meters from point A to point C and another 9 meters from point C to point E, summing a total length of 18 meters.
- Vertically, the truss extends upwards to a height of 7.5 meters from point E to point F.
**Forces Acting on the Structure:**
- The forces acting on specific points of the truss are illustrated with red arrows, indicating their direction and magnitude.
- A downward force of 1.2 kN is applied vertically at point A.
- Another downward force of 2.4 kN is applied vertically at point B.
- A downward force of 2.4 kN acts vertically at point D.
- Finally, another force of 1.2 kN is applied in a downward direction at point F.
**Dimensions:**
- The horizontal segments from A to B, B to D, and D to F each measure 6 meters.
- The vertical height from E to any point on the ground, such as A or C, is 7.5 meters.
**Support:**
- Points A and E are the supports of the truss structure. Point A is grounded and appears fixed, whereas point E seems to offer a roller support allowing horizontal movement but restricting vertical movement.
This truss structure can be analyzed for structural integrity, determining the forces in each member and ensuring that all forces and moments are balanced to maintain stability and ensure safety in practical applications.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79826512-1148-4736-b4a7-6e7f4ec13f28%2Ff3e64672-d5eb-47ec-8447-c0b8dad8006e%2Fzhyabqh_processed.png&w=3840&q=75)
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