INTRODUCTION - Arizona State University



6. STRUCTURES IN EQUILIBRIUM

6.1 TRUSSES

Trusses - structures supported and loaded at their joints (places where the bars are pinned together), with bar weights neglected

- each bar is a two-force member, so the forces at the ends of a member

must be equal in magnitude, opposite in direction, and directed along the line

between the joints (the force is called the axial force in the member);

when the forces are directed away from each other, the member is in tension,

when the forces are directed toward each other, the member is in compression

- examples: structures used to support bridges and the roofs of houses

6.2 The method of joints - preferred approach when the axial forces in all members

are to be determined

- involves drawing free-body diagrams of the joints of a

truss one by one, and using the equilibrium equations to

determine the axial forces in the members.

Procedure:

1. Draw a free-body diagram of the entire truss (treat the truss as a single object) and

determine the reactions at its supports.

2. Choose a joint (isolate it by “cutting” members pinned at considering joint) and

draw its free-body diagram (suppose the directions of unknown axial forces as

tension forces for a member).

3. Use the equilibrium equations to determine the unknown forces (if the result/force

is positive, the member is in tension, and if negative – in compression); for 2-D

problems, there are only 2 independent equilibrium equations (the forces are

concurrent and summing the moments about a point does not result in an additional

independent equation).

4. Repeat 2. and 3. for other joints

Particular types of joints:

Truss joints with two collinear members and no load

The sum of forces must equal zero ( T1 = T2 (the axial forces are equal)

Truss joints with two noncollinear members and no load

From the sum of the forces for the joint ( T2 = 0 = T1 (the axial forces are zero)

Truss joints with three members, two of which are collinear, and no load

From the sum of the forces in the x-direction ( T3 = 0, and from the sum of the

forces in the y-direction ( T1 = T2 (the axial forces in the collinear members are

equal, and the axial force in the third member is zero)

6.3 The method of sections - preferred approach when the axial forces only in a

few members are to be determined

- involves drawing a single free-body diagram of a

section of the truss, and using the equilibrium

equations to determine the axial forces in specific

members

Procedure:

1. Draw a free-body diagram of the entire truss (treat the truss as a single object) and

determine the reactions at its supports.

2. Choose a section - cut several members (usually no more then 3) including member(s)

whose axial force(s) are to be determined, and draw a free-body diagram of a section

(suppose the directions of unknown axial forces as tension forces for a member).

3. Use the equilibrium equations to determine the unknown forces

(if the result is positive, the member is in tension, and if negative – in compression);

for 2-D problems, there are 3 independent equilibrium equations

(the forces are not usually concurrent and summing the moments about a point does

result in an additional independent equation).

6.4 Space trusses

Supports

6.5 Frames and machines

Analyzing the Entire Structure - objects subjected to a system of forces and

Analyzing the Members - objects subjected to a system of forces and moments

Two-force Members

Loads applied at joints

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download