# Determine the force in each member of the truss. state of the members are in tension or compression

6–3.

Determine the force in each member of the truss.

State if the members are in tension or compression.

## General guidance

Concepts and reason
When slender members are attached together at their ends, then it forms a truss. Members that are used to form a truss are metal bars and wood. Planar trusses are the trusses which lie on a single plane. Each member of truss is considered as two force member. Either the member is subjected to tensile force or member is subjected to compressive force. Usually members that are subjected to compression are very thick than members that are in tension.

To solve this problem, make a cut across the three forces that have to be determined. Use force equilibrium or moment equilibrium to determine the forces.

Fundamentals

There are three equilibrium conditions of forces:

• Horizontal equilibrium

Summation of Forces in the direction of x will be equal to zero. It is mathematically represented as .

• Vertical equilibrium:

Summation of Forces in the direction of y will be equal to zero. It is mathematically represented as .

• Moment equilibrium:

Summation of Forces about a point will be zero. It is mathematically represented as .

## Step-by-step

### Step 1 of 2

Consider the joint A.

Write the force equilibrium along y direction.

Here, is the force in member .

Write the force equilibrium along x direction.

Here, is the force in member .

Consider the joint B.

Write the force equilibrium along x direction.

Here, is the force in member.

Write the force equilibrium in vertical direction.

Force in member AC,AB, BD, BC is , , , respectively.

Using the equilibrium of force, forces in each members are determined.

### Step 2 of 2

Consider the following diagram at joint C.

Write the force equilibrium along y direction.

Here, force in member CD is .

Write the force equilibrium along x direction.

Here, force in member CE is .

Draw the forces at joint D.

Write the force equilibrium along y direction.

Here, force in member DE is .

Write the force equilibrium along x direction.

Here, force in member DF is .

Consider the forces at joint D.

Write the force equilibrium along x direction.

Here, force in member EF is .

The force in member CD, CE,DE, DF,EF is , , , , respectively.

Using force equilibrium conditions, the force in each member is calculated.

Force in member AC,AB, BD, BC is , , , respectively.

The force in member CD, CE,DE, DF,EF is , , , , respectively.

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