5. Determine the resultant forces on pins B and C on member ABC on the four- member frame. 6ft 3ft 200 lb/ft B C 5ft E D 3ft 6ft
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 Statement:**
**5. Determine the resultant forces on pins B and C on member ABC on the four-member frame.**
**Description and Analysis:**
The diagram provided illustrates a four-member frame comprised of members ABC, DEF, and ED. The frame includes several pinned connections and is subjected to a uniformly distributed load across the upper member AC.
**Key Dimensions:**
- The length of member AB is 6 feet.
- The length of member BC is 3 feet.
- The vertical component BD is 5 feet.
- The length of member DE is 6 feet.
- The length of member EF is 3 feet.
**Loading:**
- A uniformly distributed load of 200 pounds per foot (lb/ft) is applied along the entire length of member AC, which spans 9 feet.
**Objective:**
- To determine the resultant forces acting on pins B and C due to the applied load.
This analysis will involve using principles of static equilibrium, including the summation of forces and moments, to solve for the unknown reactions at pins B and C. The primary steps include:
1. Summing forces in the horizontal and vertical directions to establish equilibrium conditions.
2. Taking moments about suitable points to solve for the unknown reactions.
3. Accounting for the effects of the distributed load by converting it to an equivalent point load acting at the centroid of the load application area (the midpoint of member AC).
Performing these calculations will provide the necessary resultant forces on pins B and C, ensuring the frame remains in equilibrium.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F859743d5-9578-4a68-94b4-09f68a5c3500%2F1e01bd3e-c334-4f2c-97f9-8e82c58e09e3%2Fnf9yo8c_processed.png&w=3840&q=75)
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