Calculating Truss Forces, Lecture notes of Acting

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Calculating Truss Forces

A body being squeezed

Forces

Compression

Tension

A body being stretched

Simple Truss

A simple truss is composed of triangles , which will retain their shape even when removed from supports.

Pinned and Roller Supports

A pinned support can

support a structure in two

dimensions.

A roller support can

support a structure in

only one dimension.

Static Determinacy

A statically determinate structure is one that can be mathematically solved.

J = Number of Joints

M = Number of Members

R = Number of Reactions

2J = M + R

A truss is considered statically indeterminate when the static equilibrium equations are not sufficient to find the reactions on that structure. There are simply too many unknowns. Try It

Did you notice the two pinned connections?

Statically Indeterminate

2J = M + R

C

D

A

B

FD = 500 lb

 

2

2 19 35 3

38 38

J  M  R

 



Each side of the main street bridge in Brockport, NY has 19 joints, 35 members, and three reaction forces (pin and roller), making it a statically determinate truss.

What if these numbers were different?

Static Determinacy Example

 M  0

The sum of the moments about a given point is zero.

Equilibrium Equations

The sum of the forces in the y-direction is zero.

A vector that acts up is positive, and a vector

that acts down is negative.

Equilibrium Equations

0 y

 F 

A force that causes a clockwise moment is negative. A

A force that causes a^ 3.0 ft^ 7.0 ft counterclockwise moment is positive.

Using Moments to Find RCY

B

C Ax D R

RAy 500 lb

RCy

 M A  0

 F (^) D (3.0 ft )  RCy (10.0 ft )  0  500 lb (3.0 ft )  RCy (10.0 ft )  0  1500 lb ft   RCy (10.0 ft )  0 RCy (10.0 ft )  1500 lb ft  RCy  150 lb

FD contributes a negative moment because it causes a clockwise moment.

RCy contributes a positive moment because it causes a counterclockwise moment.

0 x

 F 

Because joint A is pinned , it is capable of reacting to a force applied in the x -direction.

However, since the only load applied to this truss ( FD ) has no x-component, RAx must be zero.

Sum the x Forces to Find Ax

500. lb
501. lb

A

B

C Ax D R

350. lb

0 x

A 

Use cosine and sine to determine x and y vector components.

Assume all members to be in tension. A positive answer will mean the member is in tension , and a negative number will mean the member is in compression.

As forces are solved, update free body diagrams. Use correct magnitude and sense for subsequent joint free body diagrams.

B



Method of Joints

Using Truss Dimensions to Find Angles

3.0 ft 7.0 ft

4.0 ft

Method of Joints

A C

D

B

θ 1 θ 2

4.0 ft

tan (^1) opp adj

 

tan

ft

ft

 

1 1 tan 4.



 

  1 53.130 

Using Truss Dimensions to Find Angles

3.0 ft 7.0 ft

4.0 ft

Method of Joints

A C

D

B

θ 1 θ 2

4.0 ft

tan (^1) opp adj

 

tan

ft

ft

 

1 1 tan 4.



 

  29.745