CHAPTER 4fauzipuojkm.weebly.com/uploads/6/8/3/1/68313979/struture.pdf · Plane Trusses • Truss - structure consisting of two-force members (represented as pin connected) designed

CHAPTER 4

Structure Analysis

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Introduction

• An engineering structure is any connected system of members

built to support or transfer forces and to safely withstand the

loads applied to it. Two types of engineering structures, plane

truss and frame, will be discussed in this lesson.

• To determine the forces internal to an engineering structure,

we must dismember the structure and analyze separate free-

body diagrams of individual members or combinations of

members.

• In this statics class, only statically determinate structures,

which do not have more supporting constraints than are

necessary to maintain an equilibrium configuration, will be

considered.

• The analysis of trusses and frames under concentrated loads

constitutes a straightforward application of the material

developed in the previous two topics, force systems and

equilibrium.

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• Examples of Truss Structures

3

Example of Truss Joint connection

Gusset plate

Pin

Large bolt 4

Definitions

• Trusses

– Consist exclusively of straight members connected at joints located at the ends of each member. Member of a truss, therefore, are two-force members that is, members each acted upon by two equal and opposite forces directed along the member.

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Planar Trusses

• Lie in a single plane & are often used to support roofs and bridges.

A B

C D A

B

C

D

E

Figure 1a

Figure 1b

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1-Bridge (Figure 1a)

• In the case of a bridge ,such as shown in Figure 1a,the load on the deck is first transmitted to stringers, then to floor beams, & finally to the joints B,C, & D of the two supporting side trusses.

• The bridge truss loading is also coplanar, like arrow in the Figure 1a.

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2-Roof (Figure 1b)

• Figure 1b is an example of a typical roof-supporting truss.

• The roof load is transmitted to the truss at the joint .

• Since the imposed loading acts in the same plane as the truss.

• The analysis of the force developer in the truss members is two dimensional.

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Plane Trusses

• Truss - structure consisting of two-force members

(represented as pin connected) designed to support loads large

in comparison to its weight and applied at joints connecting

members

• Simple trusses - build on triangles

– simplest stable geometric shape

– add two members and one joint at a time

• Plane Trusses:

– all members lie in a single plane

– forces parallel to plane of truss, but not “in” the plane can

be transmitted via non-coplanar load bearing members 9

Simple Truss

• Consider the truss of figure (a), which are made of four members connected by pins at A, B, C, and D.

• If a load applied at B, the truss will greatly deform, completely losing its original shape.

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• In contrast, the truss of figure (b), which is made of three members connected by pins at A, B, and C, will deform only slightly under a load applied at B.

• The truss of figure (b) is said to be rigid truss, that is, the truss will not collapse.

• As shown in figure (c), a larger rigid truss can be obtained by adding two members BD and CD to the basic triangular truss of figure (b).

• A truss which can be constructed in this manner is called simple truss.

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Space Truss

• When several straight members are joined together at their extremities to form a three-dimensional configuration, the structure obtained is called a space truss.

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Techniques for Truss Analysis

• Method of joints - usually used to determine

forces for all members of truss.

• Method of sections - usually used to

determine forces for specific members of truss.

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Method of Joints • Do FBDs of the joints

• Forces are concurrent at each joint → no moments, just

∑Fx = 0 , ∑Fy = 0

• Procedure:

1) Choose joint with

• at least one known force

• at most two unknown forces

2) Draw FBD of the joint

• draw just the point itself

• draw all known forces at the point

• assume all unknown forces are tension forces and draw

– positive results → tension

– negative results → compression

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3) Solve for unknown forces by applying equilibrium

conditions in x and y directions:

∑Fx = 0 , ∑Fy = 0

4) Note: if the force on a member is known at one end,

it is also known at the other (since all forces are

concurrent and all members are two-force members)

5) Move to new joints and repeat steps 1-3 until all

member forces are known

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Method of Sections • Do FBDs of sections of truss cut through various members.

• Procedure:

1) Determine reaction forces external to truss system.

• Draw FBD of entire truss.

• Note: can find up to 3 unknown reaction forces.

• Use ∑Fx = 0, ∑Fy = 0, ∑ M = 0 to solve for the

reaction forces.

2) Draw a section through the truss cutting no more than 3

members.

3) Draw an FBD of each section .one on each side of the cut.

• Show external support reaction forces

• Assume unknown cut members have tension forces

extending from them 16

4) Solve FBD for one section at a time using :

∑Fx = 0, ∑Fy = 0, ∑ M = 0

Note: choose pt for moments that isolates one

unknown if possible

5) Repeat with as many sections as necessary to find

required unknowns

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