BFC (Mechanics of Materials) Chapter 7: Statically Determinate Plane Trusses Shahrul Niza Mokhatar

Chapter Learning Outcome 1.Determine the type of trusses and its application in construction 2.Analyse the trusses members using related methods. BFC (Mechanics of Materials) Shahrul Niza Mokhatar

Introduction A truss is defined as a structure composed of slender elements joined together at their end points. The members commonly used in construction consist of wooden struts, metal bars, angles or channels. If all the members of a truss and the applied loads lie in a single plane, the truss is called a plane truss. Plane or planar truss composed of members that lie in the same plane and frequently used for bridge and roof support. Loads that cause the entire truss to bend are converted into tensile and compressive forces in the members. Loading causes bending of truss, which is develops compression in top members, tension in bottom members.

Application Two or more trusses are connected at their joints by beams, termed as purlins, to form a 3-D framework. The roof is attached to the purlins, which transmit the roof load (weight of the roof plus any other load) as well as their own weight to the supporting trusses at the joints. Because of this applied loading acts on each truss in its own plane, the trusses can be treated as plane trusses. The roof truss along with its supporting columns called as a bent. To keep the bent rigid and capable of resisting horizontal wind forces, knee braces are sometimes used at the supporting columns. The space between adjacent bents is called a bay. Bays are often tied together using diagonal bracing to maintain rigidity of the structure. The gusset plate is the connections which formed by bolting or welding at the ends of the members to a common plate.

Type of roof truss

Assumptions in analysis The assumptions are necessary to determine the force developed in each member when the truss is subjected to a given loading. The assumptions are; – All members are connected at both ends by smooth frictionless pins. – All loads are applied at joints (member weight is negligible). Because of these two assumptions, each truss acts as an axial force member and the forces acting at the ends of the member must be directed along axis of the member. If the force tends to elongate the member, it is tensile force (T) If the force tends to shorten the member, it is compressive force (C).

Stability and Determinacy Stability of truss is depend on the support condition and number of internal member. To determine whether the truss is determinate or indeterminate To determine whether the truss is internally indeterminate or externally indeterminate m+r = 2j ……just stiff (statically determinate) m+r < 2j ……under stiff (form a mechanism)…unstable (it will collapse since there will be an insufficient number of reactions to constraint all the joints). m+r > 2j ……over stiff (statically indeterminate) m > 2j -3……statically internal indeterminate, r = 3 m > 2j -3……statically external indeterminate, r > 3 m = total number of members j = total number of joints r = number of reaction forces

Example 1

Method of to analyze member forces Method of joint – Method of Joints-the axial forces in the members of a statically determinate truss are determined by considering the equilibrium of its joints. – Tensile(T) axial member forceis indicated on the joint by an arrow pulling away from the joint. – Compressive(C) axial member forceis indicated by an arrow pushing toward the joint. – When analyzing plane trusses by the method of joints, only two of the three equilibrium equations are needed due to the procedures involve concurrent forces at each joint.

Method of to analyze member forces Method of Sections – This method involves cutting the truss into two portions (free body diagrams, FBD) by passing an imaginary section through the members whose forces are desired. – Desired member forces are determined by considering equilibrium of one of the two FBD of the truss. – This method can be used to determine three unknown member forces per FBD since all three equilibrium equations can be used.

Method of to analyze member forces Alternative Computation using Joint Equilibrium Method – An alternative method can be applied to determine the member forces. – The purpose is to reduce the time for calculation. Zero Force Members – If only two non collinear members are connected to a joint that has no external loads or reactions applied to it, then the force in both members is zero. – If three members, two of which are collinear, are connected to a joint that has no external loads or reactions applied to it, then the force in the member that is not collinear is zero.

Example 2 Calculate all member forces by using method of joints.

Example 2: Solution

Example 3 Calculate all member forces by using method of joints.