Analysis of Statically Determinate Trusses 12/3/2018 Analysis of Statically Determinate Trusses 12/3/2018 Dr. Nasrellah H A

1. Common types of Trusses: Dr. Nasrellah H A 12/3/2018

1.1 Roof Trusses: Dr. Nasrellah H A 12/3/2018

Dr. Nasrellah H A 12/3/2018

Dr. Nasrellah H A 12/3/2018

1.2 Bridge Trusses: Dr. Nasrellah H A 12/3/2018

Dr. Nasrellah H A 12/3/2018

Dr. Nasrellah H A 12/3/2018

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 Dr. Nasrellah H A 12/3/2018

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 Dr. Nasrellah H A 12/3/2018

Dr. Nasrellah H A 12/3/2018

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 Dr. Nasrellah H A 12/3/2018

A complex truss is one that cannot be classified as being either simple or compound Dr. Nasrellah H A 12/3/2018

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 Dr. Nasrellah H A 12/3/2018

Dr. Nasrellah H A 12/3/2018

Dr. Nasrellah H A 12/3/2018

Dr. Nasrellah H A 12/3/2018

Dr. Nasrellah H A 12/3/2018

Example 1: Dr. Nasrellah H A 12/3/2018

Solution: Joint A: Joint G: Dr. Nasrellah H A 12/3/2018

Joint B: Dr. Nasrellah H A 12/3/2018

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. Dr. Nasrellah H A 12/3/2018

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. Dr. Nasrellah H A 12/3/2018

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 Dr. Nasrellah H A 12/3/2018

Example 2: Using the method of joints, indicate all the members of the truss shown in Fig. below that have zero force. Dr. Nasrellah H A 12/3/2018

Solution: Dr. Nasrellah H A 12/3/2018

Dr. Nasrellah H A 12/3/2018

Method of Sections: 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.” Dr. Nasrellah H A 12/3/2018

Dr. Nasrellah H A 12/3/2018

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. Dr. Nasrellah H A 12/3/2018

Solution: Dr. Nasrellah H A 12/3/2018

Dr. Nasrellah H A 12/3/2018

Dr. Nasrellah H A 12/3/2018

Dr. Nasrellah H A 12/3/2018