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ZURAIDAH BINTI AHMADPEJABAT B, JKA, PUOhttp://mindasarjana.blogspot.com

CC601- STRUCTURAL ANALYSIS 2

CHAPTER 1: ANALYSIS OF STATICALLY DETERMINATE 2D PIN JOINTED TRUSSESLECTURE: 6 HOURSTUTORIAL: 3 HOURS1.0 ANALYSIS OF STATICALLY DETERMINATE 2D PIN-JOINTED TRUSSES.1.1 Understand the application of method of joints and method of sections in determining the forces in trusses1.1.1 Explain types of trusses.1.1.2 Differentiate between determinate and indeterminate trusses.1.1.3 Explain tension members and compression members.1.1.4 State the symbol for tension and compression members.1.1.5 Explain the method of joints.1.1.6 Explain zero-force members.1.1.7 Evaluate the truss members forces using the method of joints.1.1.8 Explain the method of sections.1.1.9 Estimate the truss members forces using the method ofSections.Definition:A truss is a structure that consists ofAll straight membersConnected together with pin jointsConnected only at ends of the membersAnd all external forces (loads & reactions) must be applied only at the jointsNote:Every member of a truss is a 2 force member.Trusses are assumed to be of negligible weight (compared to the loads they carry)1.1.1 Types of trussesa truss is a structure comprising one or more triangular units constructed with straight members whose ends are connected at joints referred to as nodes. External forces and reactions to those forces are considered to act only at the nodes and result in forces in the members which are either tensile or compressive forces. Moments (torques) are explicitly excluded because, and only because, all the joints in a truss are treated as revolutes.A planar truss lies in a single plane. Planar trusses are typically used in parallel to form roofs and bridges.A planar truss lies in a single plane. Planar trusses are typically used in parallel to form roofs and bridges.A space frame truss is a three-dimensional framework of members pinned at their ends. A tetrahedron shape is the simplest space truss, consisting of six members which meet at four joints.Differentiate between determinate and indeterminate trusses.

This is a necessary conditions for statically determinacy.This is not sufficient condition. So even if a truss satisfies the above relation it may not be determinate. But if it is determinate than it satisfies the above relation.M=2n-r : statically determinateM 2n-r: statically indeterminateexample2n = m+rm=5r=3n=42n =2x4 = 8m+r =5 +3 =8

example

2n = m+rm =15r=3n=92n =2x 9 = 18m+r =15 +3 = 18m = memberr = reactionsn = joints

External forces: "Loads" acting on your structure. Note: this includes "reaction" forces from the supports as well.Internal forces: Forces that develop within every structure that keep the different parts of the structure together.

Explain tension members and compression members.State the symbol for tension and compression members.Type of internal forces Symbols Tension +ve (T)

Compression -ve (C)Truss Analysis Method of Joints :

Method of joint is astructural analysis method todetermine the internal forces of members in atruss. This method is derived based on the equilibrium conditions at joints.It is basically, a special case of equilibrium of concurrent (intersecting)forces. In this case rotational or moment equilibrium is readily satisfied at the joint. Therefore in the method of joint for plane truss there are only two equilibrium equations required:Procedure for method of joints:Select a joint having at least one known force and at most two unknown forces (because we have only two equilibrium equations). If the joint is located at the support, we may need to first determine external reactions at the truss supports. Draw the free-body diagram (FBD) for the selected joint. Make sure that all known and unknown forces are accounted for. For the unknown forces, thedirection of the forces need to be assumed. My recommendation is to always assume that the unknown forces are in tension. Negative value from the analysis means that the actual force direction is reverse and the member is in compression. Orient the x and y axes so that the forces can be easily resolved into their x and y components. Apply the equilibrium equations and solve for the unknown member forces and check their directions. Continue the same process to another joint until all internal memberforces in a trussstructureare solved. As you can see, the method of joint is straight forward and not difficult. You just need to be smart in selecting the sequence of joints ,need to be solved because the maximum unknown forces that can be solved using this method is two. Thus sometimes method of joints cannot be applied for a particular joint because it has more than two unknown forces. In this case ,normally we solve it by first solving its neighborhood joints.Thus the methods of joint is basically a method to determine the internal forces in the members of truss structure by satisfying the equilibrium conditions of forces at each joint of the truss.

Explain the method of joints.If a truss is in equilibrium, then each of its joints must be in equilibrium. The method of joints consists of satisfying the equilibrium equations for forces acting on each joint.

Fx =0; Fy=0

Method of jointsConsider the truss shown. Truss analysis involves:(i) Determining the EXTERNAL reactions.

(ii) Determining the INTERNAL forces in each of the members (tension or compression).Recall:External forces: "Loads" acting on your structure. Note: this includes "reaction" forces from the supports as well.Internal forces: Forces that develop within every structure that keep the different parts of the structure together.

(i) External reaction

(ii) Internal Forces

Joint B

fy=0; CD + 20 = 0 CD = -20kN [Compression] Joint C

Fx = 0; -BC AC Cos 450 + 10 = 0AC = 10/Cos 450 = 14.14N

9 December 2013: Method of JointRecallWhere: m = no. of member r = no. of reactions j = no. of joint m=2j-r : statically determinatem 2j-r: statically indeterminateNo. of redundancy = m + r -2j= Degree of indeterminate= Degree of Freedom

Example 2. Determine the degree of freedom of the structure. By using the method of joints, determine the force in each member of the truss.25kNDCBA50kN4m4m4m(1) Degree of Freedom= m- 2j + r m=5r=3j=4DoF=m-2j +r DoF = 5-(2x4)+3 DoF= 0- No redundancy- Statically determinateExample 3. By using the method of joints, determine the force in each member of the truss.25kNDCBA50kN4m4m4m(2) External Reactions Fx=0Bx = 0Mb=0Ay(4)+50(4)=0Ay = -50kNFy=0Ay +By-25-50 =0-50 +By -75 =0By =125kN

AyByBx(2) Internal forcesFy=0AD Cos450 50 =0AD = 70.71kN (tension)Fx=0AB + AD Cos450 = 0AB = -50kN (compression)50kNABADJoint AFree body DiagramJoint BFree body DiagramFx=0BC Cos450 - AB = 0BC Cos450 (-50) = 0BC = -70.71kN (compression)Fy=0BD +BC Cos450 + 125 =0BD + (-70.71) Cos450 +125= 0BD = -75kN (compression)125 kNABBCBD(2) Internal forcesFx=0CD + CB Cos450 = 0CD + (-70.71) Cos450 = 0CD = 50kN (tension)50kNCBCDJoint CFree body DiagramInternal forces

Example 3. Determine the degree of freedom of the structure. By using the method of joints, determine the force in each member of the truss.(1) Degree of Freedom= m- 2j + r m=13r=3j=8DoF=m-2j +r DoF = 13-(2x8)+3 DoF= 0- No redundancy- Statically determinate

Example 3. Reaction forces at supportsFx=0Gx +5(3) +15(3) = 0Gx + 60 =0Gx= -60kNMg=0Hy(4)-15(3+6+9)-5(3+6+9)=0Hy= 90kNFy=0Gy+ Hy =0Gy + 90 =0Gy =-90kN

GyGxHy

Example 3. Internal forcesGyGxHy

Example 4. Determine the degree of freedom of the structure. By using the method of joints, determine the force in member AB, AE, CD, DG.Degree of Freedom= m- 2j + r m=11r=3j=7DoF=m-2j +r = 11-2x7+3 DoF= 0- No redundancy- Statically determinate

(1) External reactionFy=0Ay- 4 (12.5) =0Ay =50kNMa=0Ex(2.5)-12.5(2+4+6)=0Ex = 60kNFx=0Ax +Ex = 0Ax + 60 =0Ax= -60kN

AyAxEx(2) Internal forcesFy=050 -12.5 AE =0AE = 37.5kN (tension)Fx=0AB -60 = 0AB =60kN (tension)50kN60kN12.5kNAEABJoint AFree body DiagramJoint DFree body DiagramFy=0-DGSin -12.5 =0-DG(2.5/6.5)-12.5 = 0DG= -32.5kN (Compression)

Fx=0DC + DGCos = 0DC + (-32.5)(6/6.5) =0DC= 30kN (Tension)12.5kNDGDCDE=(62+2.52)1/2DE = 6.5mExample 5: Determine the degree of freedom of the structure. By using the method of joints, determine the force in each member of the truss.

10kN A BC

4m D E F G 20kN 30kN 2m 2m 2m

Example 6: Determine the degree of freedom of the structure. By using the method of joints, determine the force in each member of the truss.

Example 7: Determine the degree of freedom of the structure. By using the method of joints, determine the force in each member of the truss.

Example 8: Determine the degree of freedom of the structure. By using the method of joints, determine the force in each member of the truss.

Example 9: Determine the degree of freedom of the structure. By using the method of joints, determine the force in each member of the truss.

2m10kN5kN4m4mExample 9. (1) Degree of Freedom= m- 2j + r m=5r=3j=4DoF=m-2j +r DoF = 5-(2x4)+3 DoF= 0- No redundancy- Statically determinate

10kN5kN4m4m2mExample 9. (2) External ReactionsFy=0Ay -5-10 =0Ay = 15kNMa=0Bx(2)= 5(4) + 10(8)Bx = 50kNFx=0Ax + Bx = 0Ax + 50 =0Ax = -50kN

10kN5kN4m4m2mAxAyBxJoint DDADC10kNFy=0DA Sin 10 =0DA(2/68)-10 =0DA = 41.23kN (tension)Fx=0DC + DA Cos = 0DC+DA(8/68)=0DC = -40kN (compression)AD=(22+82)1/2= 68 (2) Internal forcesFy=0AB =0Fx=0BC + 50 = 0BC = -50kN (compression)50kNBCABJoint BFree body DiagramJoint CFree body DiagramFy=0CA Sin = 5CA( 2/20) =5CA = 11.18 kN (tension)Fx=0CB+CA Cos =CDCB+11.18 (4/20) = -40BC = -50kN (compression) - proven

5 kNCBCDCAAC=(22+42)1/2= 20

Explain zero-force members50kNBCABFy=0AB =0 zero force memberFx=0BC + 50 = 0BC = -50kN (compression)Fx=0BC = 0

BC is a zero force memberIn the field of engineering mechanics, a zero force member refers to a member (a single truss segment) in a truss which, given a specific load, is at rest: neither in tension, nor in compression. In a truss a zero force member is often found at pins (any connections within the truss) where no external load is applied and three or fewer truss members meet. Recognizing basic zero force members can be accomplished by analyzing the forces acting on an individual pin in a physical system.NOTE: If the pin has an external force or moment applied to it, then all of the members attached to that pin are not zero force members UNLESS the external force acts in a manner that fulfills one of the rules below:If only two members meet in an unloaded joint, both are zero-force members. If three members meet in an unloaded joint of which two are in a direct line with one another, then the third member is a zero-force member. If two members meet in a loaded joint and the line of action of the load coincides with one of the members, the other member is a zero-force member. Reasons for Zero-force members in a truss systemThese members contribute to the stability of the structure, by providing buckling prevention for long slender members under compressive forces These members can carry loads in the event that variations are introduced in the normal external loading configuration

Identify the zero force member from the truss below.GyGxHyMember ACMember GHThe zero force member carry no internal force.Member ADMember BC

Identify the zero force member from the truss below.

2m10kN5kN4m4mIdentify the zero force member from the truss below.Member AB

Identify the zero force member from the truss below.Member ABMember BGMember DIMember DE