F1=55 lb Calculated the forces in members DC, HC, and HI using method of section determine whether they are in Tension or Compression. Tension or Compression Member DC: Member HC: A Member HI: Tension or Compression Tension or Compression 4)
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.
Need help finding:
Memeber DC ( answer cannot be -368.969 but is compression
).
![**Structural Analysis using Method of Sections**
**Objective:** Calculate the forces in members DC, HC, and HI of the truss. Use the method of sections to determine whether the forces in these members are in tension or compression.
**Given Data:**
1. Two vertical loads are applied on the truss:
- A 100 lb load at point E.
- A 150 lb load at point D.
2. Horizontal and vertical distances between the joints are provided along with another vertical load and a horizontal load at the base.
- Distance between E and D: 3 ft.
- Distance between C and D, C and E: 3 ft.
- Distance between B and C vertically: 4 ft.
- Distance between joints I and B vertically: 2 ft.
- Distance between joints I and A vertically: 2 ft.
- Load acting horizontally to the right at joint B: 200 lb.
3. External force F1=55 lb acting upwards at point C.
**Diagram Layout:**
The diagram shows a truss with joints labeled from A to I:
- Joints are connected with members forming triangles and rectangles.
- Points of interest for calculation are members DC, HC, and HI.
**Analysis:**
To complete the analysis, follow these steps:
1. Identify the section of the truss that includes members DC, HC, and HI.
2. Apply the method of sections:
- Make an imaginary cut through the truss to isolate members DC, HC, and HI.
- Ensure the truss is statically determinate.
- Apply equilibrium equations to solve for the unknown forces in the cut members.
- Determine the nature of each force (tension or compression).
**Equilibrium Equations:**
1. Sum of forces in the x-direction: \( \sum F_x = 0 \)
2. Sum of forces in the y-direction: \( \sum F_y = 0 \)
3. Sum of moments about a point: \( \sum M = 0 \)
**Force Evaluation:**
1. **Member DC:**
Force Characteristics - Tension or Compression: [Input field for answer]
2. **Member HC:**
Force Characteristics - Tension or Compression: [Input field for answer]
3. **Member HI:**
Force Characteristics - Tension or Compression: [Input field for answer]
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