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

1. Common types of Trusses:


1.1 Roof Trusses:




1.2 Bridge Trusses:




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


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



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


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


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




Example 1:

Joint A:

Joint G:


Solution:

Joint B:


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.


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.


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



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


Solution:



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:



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.


Solution:



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.


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:



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.


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.


Procedure for Analysis:


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.


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


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.


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).


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:


Solution:



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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