chapter6 (analysis of structures)

8/13/2019 Chapter6 (Analysis of Structures)

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CHAPTER SIX

ANALYSIS OFSTRUCTURES


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STRUCTURE DEFINED

A structure is a rigid body made up ofseveral connected parts or membersdesigned to withstand some externallyapplied forces. The analysis of structures is based on theprinciple that if a structure is in equilibrium,then each of its members is also inequilibrium.By applying the equations of equilibrium tothe various parts of simple truss, frame ormachine, the forces acting on theconnections can be determined.


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6.2 TRUSSES A truss is a structure made up of straightmembers which are connected at the joints,and having the joints at the ends of themembers. Trusses are used to supportroofs, bridges and other structures.


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6.2.1 Types of Trusses(a) Simple Trusses : A simple truss is onewhich is generated from a basic triangle. Toany two ends of a member, two additionalmembers are attached and connected at asingle new joint.


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Types of Trusses Contd.

(a) Non-Simple Truss-Fink's RoofTruss


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6.1.1 Analysis of Trusses- Method ofJoints

Example: Determine the force in eachmember of the truss shown. Indicatewhether the members are in tension orcompression.


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xterna orces eterm nat on


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2.3 Zero Force Members

These members are used to increase thestability of the truss during construction and

to provide support if the applied loading ischanged. There are two conditions:(i) If only two members form a truss joint andno external load or support reaction isapplied to the joint, the members must bezero force members.


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Zero Force Members Contd.


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Analysis of Trusses - Method of Sections

If there is no need to solve for all the forcesin the members, and all the external forces,then the method of joints would be laborious.Method of sections can be used.

Steps (i) Determine the external forces analytically(ii) Draw a line which splits the free bodydiagram into two halves such that the linecrosses the members whose forces arerequired.The line should not cross more than threemembers whose forces are unknown.


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Steps in the Method of SectionsContd.

(iii) Choose one of the halves and draw thefree body diagram. Use arbitrary directions

for the forces in the members. The solutionwill give the actual direction.(iv) Assuming the external forces have beenfound, then since the sections chosen must

be in equilibrium, the three equations ofequilibrium for a 2-dimension rigid body aresufficient to determine the maximum threeunknowns.


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Example

Determine the force in members GE, GC andBC of the truss shown in the Figure. Indicate

whether the members are in tension orcompression.


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6.1 Frames and Machines

Frames and machines are two commontypes of structures which are oftencomposed of pin-connecting multi-forcemembers i.e. subjected to three ormore forces.Frames are stationary and are used tosupport loads while machines containmoving parts and are designed totransmit and alter the effect of forces.


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6.1.1 Types of Frames :

Frames are divided into two:(a) Rigid Frames where the shape does notchange(b) Non-rigid frame : Where the removal oralteration of the supports of a frame causes

the shape to change e.g. diagram belowshows a four-link mechanism as an exampleof a non-rigid frame.


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Non-Rigid Frame


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Non-Rigid Frames

Non-rigid frames are analyzed in thesame way but not all the reactionforces can be obtained from theequilibrium of the entire non-rigidframe.

See diagram (b) above. There are fourunknowns and three equations ofequilibrium.


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Non-Rigid Frames Contd.

From (c), the free body diagrams of themembers show 8 unknown forces, the fourreaction forces Ax, Ay, Dx, Dy and fourinternal forces Bx, By, Cx and Cy. Since

there are eight independent equilibriumequations, the structure is staticallydeterminate.

E l


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Example

8 m

10 m

Ax

Ay

P = 10 kN R = 20 kN4 m

5 m

DyDx


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Rigid Frames

Rigid frames are analyzed by firstdrawing the free-body diagram of theentire structure so as to determine thereaction forces.

A free-body diagram of each member isthen drawn and equilibrium equationsare used to determine the internalforces. Consider the two-forcemembers first before the multi-forceones.


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Example


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Recognize that AB is a two-force member. See the free body diagrams:

Mc = 0 : 2000 x 2 m - 4 F AB sin 60 = 0; F AB = 1154.7 N

Fx = 0 : 1154.7 cos 60 - C x = 0 i.e. C x = 577 N

Fy = 0 : 1154.7 sin 60 - 2000 + C y = 0; C y = 1000 N


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6.3.2 Machines

A machine has moving parts and isusually not considered a rigid structure.Machines are designed to transmitloads rather than support theme.g the pair of tongs below has a forceP applied to each tong that transmitsthe gripping force Q.


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Machine Contd.


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chapter6 (analysis of structures)

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