The 4 Steps for Solving a Truss Problem

The 4 Steps for Solving a Truss Problem

1.  Determine all of the angles and dimensions for the truss.

2.  Create the “Free Body Diagram.”

3.  Determine the reaction forces for the truss.

4.  Determine the forces in each member.

The Important General Equations

For a right triangle:

Alternately:

For a static object:

Moment = (Force) (Distance)

Example 1

Find

(1)

(2)

(3)

Find length of side H

(4)

(5)

(6)

(7)

(8)

Find angle

Since, for this triangle,

(9)

(10)

(11)

(12)

Find angle

Noting that the triangle is isosceles, we can use symmetry to determine

(13)

so

(14)

Create Free Body Diagram

Find the Reaction Forces

Recall

Moment = Force x Distance

Pick C as the point around which the moment is determined, because this eliminates Fcx and Fcy from the calculation. Also note that the force used in determining the moment must be perpendicular to the distance. Thus, we use the 20’ length rather than the length of member CD.

Find reaction force Fay

(15)

(16)

(17)

(18)

(19)

(20)

Find FCY

Recall

so

(21)

Substituting in the values for the forces

(22)

(23)

(24)

Find FRCX

Recall

so

(25)

Substituting in the values for the forces

(26)

(27)

Determine the forces at point A

Recall

Any force can be broken down into

so

Since only one of the forces in the Y-direction is unknown, we will find FABY first.

Recall

so

(28)

Substituting in the values for the forces

(29)

(30)

Recall

Find FABX

(31)

Substituting in the values for the forces

(32)

(33)

At this point, we can go no farther, so lets try another equation

Find

(34)

Substituting in the values for the forces

(35)

(36)

(37)

(38)

Find

Recalling equation (33),

(33)

Substituting in our value for FABX

(39)

(40)

To apply the force in this direction the member needs

(Tension) (41)

Find

We also know FABY from equation (8), so we can find FAB.

(42)

(43)

(44)

(45)

(46)

To apply the force in this direction the member needs

(Compression) (47)

Find

Noting that the triangle is isosceles, we can us symmetry to determine that

(Compression) (48)

Example 2

Determine the angles between the members in the truss

Find

(1)

(2)

Find

Noting that, for this right triangle,

(3)

(4)

(5)

Find

(6)

(7)

Find

Noting that, for this right triangle,

(8)

(9)

(10)

Find

(11)

(12)

Find

Since, for this triangle,

(13)

(14)

(15)

The lengths of two members remain unspecified, member AD and member DE

Find the length of member AD

For this right triangle

(16)

(17)

(18)

(19)

Find the length of member DE

Similarly,

(20)

(21)

(22)

(23)

Create the free Body Diagram

Find the reaction forces

Recall

Moment = Force x Distance

and

Pick B as the point around which the moment is determined. Also note that the force used in determining the moment must be perpendicular to the distance.

Find FRAX

(24)

(25)

(26)

(27)

(28)

Find

Recall

so

Substituting in the values for the forces

(29)

(30)

Find

Recall

so

(31)

Substituting in the values for the forces

(32)

(33)

Since joint E is one of the simplest joints, we will analyze it first,

Recalling that

Any force can be broken down into

so

Since only one of the forces in the Y-direction is unknown, we will find FEDY first

Recall

so

(34)

Substituting in the values for the forces

(35)

(36)

Find

(37)

Substituting in the values for the forces

(38)

(39)

(40)

(41)

Find

(42)

Substituting in the values for the forces

(43)

(44)

(45)

(46)

To apply the force in this direction the member needs to be

(Tension) (47)

Find FECX

Recall

Now the forces will get solved in the X direction

(48)

Substituting in the values for the forces

(49)

so

(50)

Substituting in our values for

(51)

To apply the force in this direction the member needs to be

(Compression) (52)

Find FCD

Recall

(53)

Since member CE is horizontal, its Y-component is 0, so

(54)

Similarly, since member CD is vertical, it has an X-component of O

(55)

Member CD carries no load

(56)

Find FCA

Recall

(57)

Substituting in our values for the forces

(58)

(59)

Since member CA is horizontal, its Y-component is 0, so

(60)

Then

(61)

To apply the force in this direction the member needs to be

(Compression) (62)

Find FBA

Recall

(63)

Substituting in the values for the forces

(64)

(65)

Since member BA is vertical, it has an X-component of 0

(66)

Then

(67)

To apply the force in this direction the member needs to be

(Tension) (68)

Find FBD

Recall

(69)

Substituting in our values for the forces

(70)

(71)

Since member BD is horizontal, it has an Y-component of 0

(72)

Then

(73)

To apply the force in this direction the member needs to be

(Tension) (74)

Find

Cosine (75)

(76)

(77)

(78)

To apply the force in this direction the member needs to be

(Compression) (79)