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6/7/2013 Dr. Nasrellah H A 6 Analysis of Statically Determinate Trusses
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Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

May 15, 2018

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Page 1: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

6/7/2013 Dr. Nasrellah H A 6

Analysis of Statically Determinate Trusses

Page 2: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

1. Common types of Trusses:

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Page 3: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

1.1 Roof Trusses:

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Page 4: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Page 5: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Page 6: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

1.2 Bridge Trusses:

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Page 7: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Page 8: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Page 9: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

Assumptions for design: 1. The members are joined together by smooth pins. 2. All loadings are applied at the joints Because of these two assumptions, each truss member acts as an axial force member

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Page 10: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

Classification of coplanar trusses:

A simple truss is constructed by starting with a basic triangular element, such as ABC in Fig. below, and connecting two members (AD and BD) to form an additional element

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Page 11: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Page 12: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

A compound truss is formed by connecting two or more simple trusses together. Quite often this type of truss is used to support loads acting over a large span

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Page 13: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

A complex truss is one that cannot be classified as being either simple or compound

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Page 14: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

Method of Joints: If a truss is in equilibrium, then each of its joints must also be in equilibrium. Hence, the method of joints consists of satisfying the equilibrium conditions

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Page 15: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Page 16: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Example 1:

Page 17: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

Joint A:

Joint G:

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Solution:

Page 18: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

Joint B:

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Page 19: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

Zero force members:

zero-force members may be necessary for the stability of the truss during construction and to provide support if the applied loading is changed. The zero-force members of a truss can generally be determined by inspection of the joints, and they occur in two cases.

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Page 20: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

Case 1: If there are any two members are connected together at and there is no external load or support reaction on the joint, These two members become a zero-force members.

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Page 21: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

Case 2: if three members form a truss joint for which two of the members are collinear, the third member is a zero-force member, provided no external force or support reaction is applied to the joint

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Page 22: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Example 2: Using the method of joints, indicate all the members of the truss shown in Fig. below that have zero force.

Page 23: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Solution:

Page 24: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Page 25: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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If the forces in only a few members of a truss are to be found, the method of sections generally provides the most direct means of obtaining these forces. The method of sections consists of passing an imaginary section through the truss, thus cutting it into two parts. Provided the entire truss is in equilibrium, each of the two parts must also be in equilibrium; and as a result, the three equations of equilibrium may be applied to either one of these two parts to determine the member forces at the “cut section.”

Method of Sections:

Page 26: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Page 27: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Example 3: The Howe bridge truss is subjected to the loading shown. Determine the force in members HD, CD, and GD, and state if the members are in tension or compression.

Page 28: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Solution:

Page 29: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Page 30: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Analysis of compound trusses: It was stated that compound trusses are formed by connecting two or more simple trusses together either by bars or by joints. Occasionally this type of truss is best analyzed by applying both the method of joints and the method of sections. Example 4: Indicate how to analyze the compound truss shown in below. The reactions at the supports have been calculated.

Page 31: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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The truss is a compound truss since the simple trusses ACH and CEG are connected by the pin at C and the bar HG. Section aa in Fig. above cuts through bar HG and two other members having unknown forces. Force in HG is determined as follows:

Solution:

Page 32: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Page 33: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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We can now proceed to determine the force in each member of the simple trusses using the method of joints. For example, the free-body diagram of ACH is shown in Fig. Above .The joints of this truss can be analyzed in the following sequence: Joint A: Determine the force in AB and AI. Joint H: Determine the force in HI and HJ. Joint I: Determine the force in IJ and IB. Joint B: Determine the force in BC and BJ. Joint J: Determine the force in JC.

Page 34: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Analysis of Complex Trusses: The member forces in a complex truss can be determined using the method of joints; however, the solution will require writing the two equilibrium equations for each of the (j) joints of the truss and then solving the complete set of (2j) equations simultaneously. This approach may be impractical for hand calculations, especially in the case of large trusses. Therefore, a more direct method for analyzing a complex truss, referred to as the method of substitute members, will be resented here.

Page 35: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Procedure for Analysis:

Page 36: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Step 1: Reduction to stable simple truss:

Determine the reactions at the supports and begin by imagining how to analyze the truss by the method of joints, i.e., progressing from joint to joint and solving for each member force. If a joint is reached where there are three unknowns, remove one of the members at the joint and replace it by an imaginary member elsewhere in the truss. By doing this, reconstruct the truss to be a stable simple truss.

Page 37: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Step (2): External Loading on Simple Truss: Load the simple truss with the actual loading P, then determine the force in each member . In Fig. below.

S

Page 38: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Step (3) :Remove External Loading from Simple Truss: Consider the simple truss without the external load P. Place equal but opposite collinear unit loads on the truss at the two joints from which the member was removed. If these forces develop a force in the truss member.

Page 39: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Step (4): Superposition:- If the effects of the above two loadings are combined, the force in the member of the truss can be determine as following:

Or for member EC:

Since member EC does not exist:

Once the value of (x) has been determined, the force in the other members (i) of the complex truss can be determined from Eq. (1).

Page 40: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Determine the force in each member of the complex truss shown in Fig. below. Assume joints B, F, and D are on the same horizontal line. State whether the members are in tension or compression

Example 5:

Page 41: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Solution:

Page 42: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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Page 43: Analysis of Statically Determinate Trusses Dr. Nasrellah H A 6/7/2013 We can now proceed to determine the force in each member of the simple trusses using the method of joints. For

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