.3 m B 5 kN 75 A 2 kN .5 m 2 kN FIGURE P3-21 -2m- 3-22. Determine the moment about point A for the system shown in Figure P3-22. 10 lb 8 b A 80° 80 10 16 FIGURE P3-22
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.
![### Engineering Mechanics: Statics
#### Problem 3-22: Determine the Moment About Point A
For the system shown in Figure P3-21 and Figure P3-22, calculate the moment about point A.
**Figure P3-21:**
- The diagram shows an object with forces acting on it. Key details include:
- Two forces of 2 kN acting horizontally at different heights.
- Another force of 5 kN acting at an angle of 75° to the horizontal.
- Dimensions are given for different parts of the object: 0.3 m vertically and 2 m horizontally.
- Points A and B are marked, and point A appears to be a support point or hinge.
**Figure P3-22:**
- The diagram depicts a horizontal structure subjected to forces.
- A force of 10 lb acts at an 80° angle on both the left side and the right side of the structure.
- Another force of 8 lb acts vertically downward.
- Dimensions are given: 4 ft horizontally where the forces are applied, 6 ft horizontally for the entire length of the structure, and 8 ft vertically.
- Points A and B are marked, with point A on the right end of the structure.
### Objective:
Determine the moment about point A for the system.
#### Steps to Solve:
1. **Identifying Forces and Their Components:**
- Break down each force into its horizontal and vertical components.
2. **Calculating Moments:**
- Use the moment formula: \( M = F \times d \times \sin(\theta) \)
- Sum the moments caused by each force about point A.
3. **Result:**
- The sum of all moments will give you the net moment about point A.
For detailed calculations, consider the geometry and forces at play explicitly. This will involve resolving the forces into their components and using the perpendicular distances from point A to each force's line of action.
Remember to consider the sign convention for moments (clockwise vs. counterclockwise) to ensure accurate summation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42c853c6-6184-4971-92a2-b66c5e1bdcfe%2F51ba723c-9553-4005-ae78-9064cd44372b%2F448ccka_processed.jpeg&w=3840&q=75)
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