Problems Using the method of joints, determine the force in each member of the truss shown. Summarize the results on a force summation diagram, and indicate whether each mem- ber is in tension or compression. You may want to try the "quick" method for Problems 3.14 through 3.17. Fal 3.12 300 31 1000# E 10¹ F 1 10² 10¹ A s 1000# 1000
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.
![### Problem 3.12: Force Analysis on Truss
**Objective:**
Using the method of joints, determine the force in each member of the truss shown. Summarize the results on a force summation diagram, and indicate whether each member is in tension or compression.
**Instructions:**
You may want to try the "quick" method for Problems 3.14 through 3.17.
#### Truss Specifications:
- The truss has joints labeled as A, B, C, D, and E.
- The horizontal distance between joints is 10 feet.
- The vertical height between joints A and B, and between joints B and C is 10 feet each.
- A force of 1000 pounds is applied vertically downward at joint C.
- Another force of 1000 pounds is applied at an angle of 30 degrees to the horizontal at joint E.
#### Diagram:
The provided diagram illustrates a truss with members connected at different joints. Two external loads are acting on the truss:
- A downward load of 1000 pounds at joint C.
- An angled (30 degrees) load of 1000 pounds at joint E.
#### Steps to Solve:
1. **Isolate each joint**: Start with the joints having known forces (usually where external loads are applied) and proceed to adjacent joints.
2. **Apply equilibrium equations**: For each joint, use the conditions of equilibrium (sum of horizontal forces = 0 and sum of vertical forces = 0) to solve for the unknown forces.
3. **Determine force types**: Assess if each member force is in tension (pulling apart) or compression (pushing together).
This problem requires a systematic approach to solve for the internal forces in the truss members, ensuring that all equilibrium conditions are satisfied.
#### Annotations:
- A solid analysis diagram is crucial. Draw and label each force, including dimensions and angles.
- Use trigonometric relationships to resolve angled forces into horizontal and vertical components.
- Summarize findings indicating whether each member is in tension or compression to provide a clear understanding of the structural behavior under given loads.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff88f7a45-d574-4bc0-9954-11cb0a44c72b%2F20fdc7d9-8d00-45d1-b3b8-ecb10552afd8%2Fjkeajdn_processed.jpeg&w=3840&q=75)
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