CHAPTER 1InTRODUCTIONEN MOHAMMAD AMIRULKHAIRI BIN ZUBIRBAA2113THEORY of STRUCTURE

1PART 1 StructuresOBJECTIVE At the end of this lesson, student should be able to:Define the term structureIdentify the types and elements of structure.Identify the types of joints and support in structures.

STRUCTUREs

STRUCTURES Can be defined as forms or shapes such as building, bridges, dams and walls and are design to resist any applied load without losing their own strength capacities and any appreciable deformation. Transmit all applied loads to the support systems All structure is required to be strong, stable and functioning. TYPES OF STRUCTURES Can be categorized into : Framed types Mass types Framed structure resist the applied loads by virtue of their geometry Mass structure are a type of structures which are able to resist the applied load by virtue of their weight.Example of structural elements beam columnArch walls trussesfoundationSTUCTURE ELEMENTS

Beam StructureWall StructureColumn StructureArchesTYPES OF JOINTS IN FRAMED STRUCTURESTYPES OF CONNECTIONStiff jointPinned jointPinned Joint

Also known as hinged point Common applications: roof trusses and bridges were constructed using pinned joint Allow relative movement of the member and its cannot resist bending movement

Stiff Joint

Considered have fixity at the point of connection and is rigid One member meeting at the joint has an effect on the other member

Rotation in Stiff JointRigid jointAngle remainsunalteredRotationPinned jointMember not affectedRotationBending of memberdue to loadRotation in Pinned JointTYPES OF SUPPORT IN A FRAMES STRUCTURETYPES OF SUPPORTREACTIONNO OF UNKNOWN (DEGREE OF FREEDOM)pinnedrollerfixed213

Refer Text book pg 37

Pinned support

Fixed support

COLLAPSEWHY??Bad DesignUnexpected Failure ModesExtraordinary LoadsFoundation FailureFaulty ConstructionCombination of CausesFood of mind

The structure element shows in figure above is .The structure above can be categorize as .. TypeWhat types of connection indicated at point A, B and C.

Identify the number of reaction at point A, B and CbeamFramePinnedfreeroller21024PART 2 DeterminacyOBJECTIVE At the end of this lesson, student should be able to:Identified the determinancy criteria of structureDetermine the number of redundancy for the structure. Draw FBD for structures

IDEALIZED STRUCTURE

a) Actual Structureb) Idealized StructureIDEALIZED STRUCTURE b) Idealized Structure

a) Actual StructureFree body diagrams Any force system acting on a structure is easily analyzed if the appropriate reactions required to maintain equilibrium are inserted in a diagrams

FBDEQUATION OF EQUILIBRIUM When the force act in the x-y plane, the equation will beFx = 0Fy = 0Mz = 0 CONDITIONS OF DETERMINACYTo state of static equilibrium, it is necessary to establish the DETERMINACY and STABILITYEquilibrium equation provide sufficient conditions for equilibrium. All forces can be determined strictly from these equationStructure is referred as STATICALLY DETERMINATEHowever, structure having more unknown forces than available equilibrium equation referred as STATICALLY INDETERMINATE This can be determined using a free body diagram

CONDITION OF DETERMINANCY FOR BEAMSExamples:

a) Simply Supported Beamb) Cantilever Beamc) Overhanging Beama) Continuous Beamb) End-support or Propped Cantilever Beamc) Built-in BeamTRUSSPlanar TrussesSimple trussCompound trussComplex truss

foamed by connecting two or more simple truss.The simplest framework that is rigid and stable triangle.Its cannot be classified either simple or compound truss.CONDITION OF DETERMINANCY FOR TRUSSESExamples:StableUnstableDeterminacy Beam Beam, pin connected and frame are classified as determinate depending upon the internal forces in the member or external support reaction.

Example 1

Example 2

HINGE CONNECTION CONSIDERED TO HAVE 2 REATIONExample 3

Example 4

10 9

Exercise 1

Exercise 2

Determinacy of Trusses Trusses also classified as determinate depending external support reaction.2j = b + rb = number of MEMBER/S of the trussesj = number of JOINT/Sr = is number of REACTION/S

Example 3Unknown b+ r = 12Equation 2(J) = 12 0the structure is just stiff ( statically determinate) b = 9j = 6r = 3Over stiffJust stiffUnder stiffDETERMINACY CRITERIA FOR STRUCTURES Three categories of determinacy for structuresIf there are more equilibrium equation than the unknown forces, the system is not a structure and it is unstable.If the equilibrium equation is equal to unknown forces. If the equilibrium equation is less than to unknown forces.Frame / beamr = 3n (just stiff / statically determinate)r > 3n (under stiff / forms a mechanism)r < 3n (over stiff / statically indeterminate)RedundancyorCheck the number of redundancyNumber of redundancy = r 3nExample 1

10 9

Trusses2j = b + r (just stiff / statically determinate)2j > b + r (under stiff / forms a mechanism)2j < b +r (over stiff / statically indeterminate)orCheck the number of redundancyNumber of redundancy = b + r 2jUnknown b + r = 17Equation 2(J) = 16 1the structure is over stiff ( statically determinate) to 1st degreeb = 14j = 8r = 3Example FOR MORE EXAMPLE SEE PAGE 48, 49, 52, 53, 67, 123

Smooth pin connected collarCO1 : An ability to identify the stability and determinacy of structures Covered..StabilityDeterminacy and stability of structuresPART 3 ARIFSULAIAMN53ObjectivesAt the end of this lesson, students should be able to:Defined the term of stabilityIdentified the stability of the structureCalculated the determinacy criteria of structure and check the stability of structure.54SULAIAMNARIFWhat is stability ??

Which one is better??

Figure aFigure bFigure a will change their shape without change their member lengthWhich one is stable??

To ensure the equilibrium of a structure or its member, it is not only necessary to satisfy the equation of equilibrium, but the member must also be properly held or constrained by their support. Two situations may occur where the conditions for proper constraint have not been met. There are:STABILITYPartial ConstraintsImproper ConstraintsPartial ConstraintIn some cases a structure or one of its members may have fewer (less) reactive forces than equations of equilibrium that must be satisfied. The structure then becomes only partially constrained therefore the structure unstable as shown in Figure

Note:Not fulfill equation of equilibriumFx=0 will not be satisfiedMember will be unstable

Improper constraints

In some cases there may be as many unknown forces as there are equations of equilibrium; however, instability or movement of its members can develop because of improper constraining by the support. This can occur if ALL the support reactions are concurrent (intersect at a same point) at a point as shown in Figure. Another way, in which improper constraining leads to instability occurs when the reactive forces are all parallel as shown in FigureWhen support reaction concurrent at joint reaction force are all parallelEXAMPLE

Figure AFigure BFigure CABABCABC

Figure DFigure E

ABThe structure is not stable because the reaction at support A and B are parallel.Figure A

ABCThe structure is not stable because the reaction at A and B is concurrent at joint CFigure B

ABCThe structure is not stable because the reaction at support A, B and C are parallelFigure C

The structure externally unstable because all the reactions at A and B are concurrent at one point AB

The structure is internally unstable because it can be seen that no restraint or fixity is provided between joint C and F or B and E. ABFGECDHDETERMINACY AND STABILITY

r = 3n = 1 r = 3n 3 = 3The structure is statically determinate but unstable because all reactions are parallel. Example 1Check the determinacy criteria for structure and classified it as stable or unstable.

Figure 1

Figure 3The structure is statically determinateStable since the reactions are not concurrent and non parallel

Figure 2ABCC is hingeThe compound beam is stable. It is also indeterminate to second degree.ABThe member is unstable since the three reaction is concurrent at B.

Figure 4Hinge at point B and CThe structure is unstable. Also, this can be seen by inspection, since AB can move horizontally without restraint.ABFOOD OF MINDClassify each of the structure as statically determinate, statically indeterminate or unstable. If indeterminate, specify the degree of indeterminacy.

CO1 : An ability to identify the stability and determinacy of structures Covered..Discussion 8060kN

A

B

C

10m

5m

P kN

P kN

P

A

A is fixed connected roller

O

P

A

C

B

P kN

A

B

A

D

B

C

Figure 1

Figure 2