Short Notes: Analysis of a Truss | Short Notes for Civil Engineering - Civil Engineering (CE) PDF Download

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ANALYSIS OF A TRUSS 
Definition: A truss is an assembly of beams or other elements that creates a rigid structure. In 
engineering, a truss is a structure that consists of two force members only, where the members are 
organized so that the whole assembly should behave as a single object. 
1. ASSUMPTIONS USED IN TRUSS ANALYSIS 
(i) Members of the truss will be subjected to axial force only. 
(ii) Members are initially straight and load is acting only on joints 
(iii) All joints can be assumed as frictionless hinges. 
(iv) All the members of truss are assumed in the same plane called the middle plane of truss. 
2. ANALYSIS OF STATICALLY DETERMINATE AND STABLE TRUSSES 
There are two methods of analysis for statically determinate and stable trusses. 
(i) Method of Section 
(ii) Method of Joints 
 Methods of section 
The advantage of this method is that, force in an intermediate member can be found directly 
without finding force in any other members. Equilibrium of sections of truss is considered in 
method of section. The procedure of this method comprises of following steps. 
(i) Determine the value of support reaction. 
(ii) Cut the member under consideration by a section (1)-(1) and consider equilibrium of either 
left hand side of (1)-(1) or R.H.S. of (1)-(1) and use SFx = 0, SFy = 0 and SM = 0 to find 
unknown forces in members. 
(iii) Cut the member such that entire truss is divided into two separate parts. 
 
(iv) Preferably, don’t cut more than 3 members (because, in method of section, we have 3 
equilibrium equation which are SFx = 0, SFy = 0 SM = 0 with 3 equilibrium equation we can 
easily find 3 unknown values. 
(v) Cut the member such that all the cut members do not meet at one joint. If they meet at 
one joint, SM = 0 becomes useless equation and it becomes method of joints problem. 
Methods of Joints 
The free body diagram of any joint is a concurrent force system in which the summation of 
moment will be no help. Recall that only two equilibrium equations can be written as SFx = 0 
and SFy = 0. This means that to solve completely for the forces acting on a joint, we must 
select a joint with not more than two unknown forces involved. This can be started by selecting 
a joint acted on by only two members. We can assume any unknown member to be either 
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ANALYSIS OF A TRUSS 
Definition: A truss is an assembly of beams or other elements that creates a rigid structure. In 
engineering, a truss is a structure that consists of two force members only, where the members are 
organized so that the whole assembly should behave as a single object. 
1. ASSUMPTIONS USED IN TRUSS ANALYSIS 
(i) Members of the truss will be subjected to axial force only. 
(ii) Members are initially straight and load is acting only on joints 
(iii) All joints can be assumed as frictionless hinges. 
(iv) All the members of truss are assumed in the same plane called the middle plane of truss. 
2. ANALYSIS OF STATICALLY DETERMINATE AND STABLE TRUSSES 
There are two methods of analysis for statically determinate and stable trusses. 
(i) Method of Section 
(ii) Method of Joints 
 Methods of section 
The advantage of this method is that, force in an intermediate member can be found directly 
without finding force in any other members. Equilibrium of sections of truss is considered in 
method of section. The procedure of this method comprises of following steps. 
(i) Determine the value of support reaction. 
(ii) Cut the member under consideration by a section (1)-(1) and consider equilibrium of either 
left hand side of (1)-(1) or R.H.S. of (1)-(1) and use SFx = 0, SFy = 0 and SM = 0 to find 
unknown forces in members. 
(iii) Cut the member such that entire truss is divided into two separate parts. 
 
(iv) Preferably, don’t cut more than 3 members (because, in method of section, we have 3 
equilibrium equation which are SFx = 0, SFy = 0 SM = 0 with 3 equilibrium equation we can 
easily find 3 unknown values. 
(v) Cut the member such that all the cut members do not meet at one joint. If they meet at 
one joint, SM = 0 becomes useless equation and it becomes method of joints problem. 
Methods of Joints 
The free body diagram of any joint is a concurrent force system in which the summation of 
moment will be no help. Recall that only two equilibrium equations can be written as SFx = 0 
and SFy = 0. This means that to solve completely for the forces acting on a joint, we must 
select a joint with not more than two unknown forces involved. This can be started by selecting 
a joint acted on by only two members. We can assume any unknown member to be either 
 
 
tension or compression. If negative value is obtained, this means that the force is opposite in 
action to that of assumed direction. One the forces in on joint are determined their effect on 
adjacent joints are known. We then continue solving on successive joints until all members 
have been found. 
3. ZERO FORCE MEMBERS 
Zero force members in a truss are members which do not have any force in them. There are 
two rules that may be used to find zero force members in a truss. They are as follows. 
Case 1: At a two-member joint which are not parallel and there are no other external loads or 
reaction at the joint then both members are zero force members. 
Case 2: At a three-member joint, if two of those members are parallel and there are no other 
external loads (or reaction) at the joint then the member that is not parallel is a zero-force 
member.