Short Notes: Trusses and Frames | Short Notes for Mechanical Engineering PDF Download

 Page 1


Trusses and Frames  
Trusses are used commonly in Steel buildings and bridges.The article contains 
fundamental notes on "Analysis of Trusses" topic of "Engineering Mechanics" 
subject. Also useful for the preparation of various upcoming exams like Mechanical 
Engineering(ME) examinations
Analysis of Trusses
Trusses are used commonly in Steel buildings and bridges.
Page 2


Trusses and Frames  
Trusses are used commonly in Steel buildings and bridges.The article contains 
fundamental notes on "Analysis of Trusses" topic of "Engineering Mechanics" 
subject. Also useful for the preparation of various upcoming exams like Mechanical 
Engineering(ME) examinations
Analysis of Trusses
Trusses are used commonly in Steel buildings and bridges.
transverse
Definition: A truss is a structure that consists of
• All straight members
• Connected together with pin joints
• Connected only at the ends of the members
• All external forces (loads & reactions) must be applied only at the joints.
• Trusses are assumed to be of negligible weight (compared to the loads they 
carry)
Types of Trusses
Typical R oof T r u s t s
/w m
Pratt
mk W arm ]
Baltimore*
K truss
Typical Bridge Trusses
Degree of Static Indeterminacy
• Ds = m+re - 2j where, D§ = Degree of static indeterminacy m = Number of 
members, re = Total external reactions, j = Total number of joints
• Ds = 0 = > Truss is determinate
If Ds e = + 1 & DS j = -1 then Ds = 0 at specified point.
Page 3


Trusses and Frames  
Trusses are used commonly in Steel buildings and bridges.The article contains 
fundamental notes on "Analysis of Trusses" topic of "Engineering Mechanics" 
subject. Also useful for the preparation of various upcoming exams like Mechanical 
Engineering(ME) examinations
Analysis of Trusses
Trusses are used commonly in Steel buildings and bridges.
transverse
Definition: A truss is a structure that consists of
• All straight members
• Connected together with pin joints
• Connected only at the ends of the members
• All external forces (loads & reactions) must be applied only at the joints.
• Trusses are assumed to be of negligible weight (compared to the loads they 
carry)
Types of Trusses
Typical R oof T r u s t s
/w m
Pratt
mk W arm ]
Baltimore*
K truss
Typical Bridge Trusses
Degree of Static Indeterminacy
• Ds = m+re - 2j where, D§ = Degree of static indeterminacy m = Number of 
members, re = Total external reactions, j = Total number of joints
• Ds = 0 = > Truss is determinate
If Ds e = + 1 & DS j = -1 then Ds = 0 at specified point.
Ds > 0 = > Truss is indeterminate or dedundant.
Truss Analysis: Method of Joints
• Conditions of equilibrium are satisfied for the forces at each joint
• Equilibrium of concurrent forces at each joint
• Only two independent equilibrium equations are involved
Steps of Analysis
1. Draw Free Body Diagram of Truss
2. Determine external reactions by applying equilibrium equations to the whole 
truss
3. Perform the force analysis of the remainder of the truss by Method of Joints 
Example 1
Determine the force in each member of the loaded truss by Method of Joints
Solution
lIF y = 0] 0.866AB - 30 = 0 AB = 34.6 kN T
[IF , » 0] AC - 0.5(34.6) = 0 AC = 17.32 kN C
= 0) 0.866BC - 0.866(34.6) = 0 BC = 34.6 kN C
[IF , = 0] BD - 2(0.51(34.6) = 0 BD “ 34.6 kN T
Jo in t A Joint B
Page 4


Trusses and Frames  
Trusses are used commonly in Steel buildings and bridges.The article contains 
fundamental notes on "Analysis of Trusses" topic of "Engineering Mechanics" 
subject. Also useful for the preparation of various upcoming exams like Mechanical 
Engineering(ME) examinations
Analysis of Trusses
Trusses are used commonly in Steel buildings and bridges.
transverse
Definition: A truss is a structure that consists of
• All straight members
• Connected together with pin joints
• Connected only at the ends of the members
• All external forces (loads & reactions) must be applied only at the joints.
• Trusses are assumed to be of negligible weight (compared to the loads they 
carry)
Types of Trusses
Typical R oof T r u s t s
/w m
Pratt
mk W arm ]
Baltimore*
K truss
Typical Bridge Trusses
Degree of Static Indeterminacy
• Ds = m+re - 2j where, D§ = Degree of static indeterminacy m = Number of 
members, re = Total external reactions, j = Total number of joints
• Ds = 0 = > Truss is determinate
If Ds e = + 1 & DS j = -1 then Ds = 0 at specified point.
Ds > 0 = > Truss is indeterminate or dedundant.
Truss Analysis: Method of Joints
• Conditions of equilibrium are satisfied for the forces at each joint
• Equilibrium of concurrent forces at each joint
• Only two independent equilibrium equations are involved
Steps of Analysis
1. Draw Free Body Diagram of Truss
2. Determine external reactions by applying equilibrium equations to the whole 
truss
3. Perform the force analysis of the remainder of the truss by Method of Joints 
Example 1
Determine the force in each member of the loaded truss by Method of Joints
Solution
lIF y = 0] 0.866AB - 30 = 0 AB = 34.6 kN T
[IF , » 0] AC - 0.5(34.6) = 0 AC = 17.32 kN C
= 0) 0.866BC - 0.866(34.6) = 0 BC = 34.6 kN C
[IF , = 0] BD - 2(0.51(34.6) = 0 BD “ 34.6 kN T
Jo in t A Joint B
F2Fy = 0) 
[IF , = 0]
BC =
34.6 kN
\ / C ° 
60 X /60 ’
-------H
AC =
y *-------
CE
17.32 kN
1
20 kN
\D E
6 0 '\ 69.3 kN
-------
CE = i
--------
3.5 kN
10 kN
Joint C Joint E
0.866CD - 0.866(34.6) - 20 = 0 
CD = 57.7 kN T
CE - 17.32 - 0.5(34.6) - 0.5(57.7} = 0 
CE = 63.5 kN C
[lFy = 0] 0.866DE = 10 DE = 11.55 kN C
and the equation X/'j = 0 checks.
Truss Member Carrying Zero forces
(i) Mf, M2, M3 meet at a joint M1 & M2 are collinear = > M3 carries zero force where 
M-i, M% M3 represents member.
(ii) M1 & M2 are non collinear and Fe x t = 0 = > M1 & M2 carries zero force.
Page 5


Trusses and Frames  
Trusses are used commonly in Steel buildings and bridges.The article contains 
fundamental notes on "Analysis of Trusses" topic of "Engineering Mechanics" 
subject. Also useful for the preparation of various upcoming exams like Mechanical 
Engineering(ME) examinations
Analysis of Trusses
Trusses are used commonly in Steel buildings and bridges.
transverse
Definition: A truss is a structure that consists of
• All straight members
• Connected together with pin joints
• Connected only at the ends of the members
• All external forces (loads & reactions) must be applied only at the joints.
• Trusses are assumed to be of negligible weight (compared to the loads they 
carry)
Types of Trusses
Typical R oof T r u s t s
/w m
Pratt
mk W arm ]
Baltimore*
K truss
Typical Bridge Trusses
Degree of Static Indeterminacy
• Ds = m+re - 2j where, D§ = Degree of static indeterminacy m = Number of 
members, re = Total external reactions, j = Total number of joints
• Ds = 0 = > Truss is determinate
If Ds e = + 1 & DS j = -1 then Ds = 0 at specified point.
Ds > 0 = > Truss is indeterminate or dedundant.
Truss Analysis: Method of Joints
• Conditions of equilibrium are satisfied for the forces at each joint
• Equilibrium of concurrent forces at each joint
• Only two independent equilibrium equations are involved
Steps of Analysis
1. Draw Free Body Diagram of Truss
2. Determine external reactions by applying equilibrium equations to the whole 
truss
3. Perform the force analysis of the remainder of the truss by Method of Joints 
Example 1
Determine the force in each member of the loaded truss by Method of Joints
Solution
lIF y = 0] 0.866AB - 30 = 0 AB = 34.6 kN T
[IF , » 0] AC - 0.5(34.6) = 0 AC = 17.32 kN C
= 0) 0.866BC - 0.866(34.6) = 0 BC = 34.6 kN C
[IF , = 0] BD - 2(0.51(34.6) = 0 BD “ 34.6 kN T
Jo in t A Joint B
F2Fy = 0) 
[IF , = 0]
BC =
34.6 kN
\ / C ° 
60 X /60 ’
-------H
AC =
y *-------
CE
17.32 kN
1
20 kN
\D E
6 0 '\ 69.3 kN
-------
CE = i
--------
3.5 kN
10 kN
Joint C Joint E
0.866CD - 0.866(34.6) - 20 = 0 
CD = 57.7 kN T
CE - 17.32 - 0.5(34.6) - 0.5(57.7} = 0 
CE = 63.5 kN C
[lFy = 0] 0.866DE = 10 DE = 11.55 kN C
and the equation X/'j = 0 checks.
Truss Member Carrying Zero forces
(i) Mf, M2, M3 meet at a joint M1 & M2 are collinear = > M3 carries zero force where 
M-i, M% M3 represents member.
(ii) M1 & M2 are non collinear and Fe x t = 0 = > M1 & M2 carries zero force.
• If only two non-collinear members form a truss joint and no external load or 
support reaction is applied to the joint, the two members must be zero force 
members
• 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.
Method of Section
• It can be used to determine three unknown member forces per FBD since all 
three equilibrium equations can be used
• Equilibrium under non-concurrent force system
• Not more than 3 members whose forces are unknown should be cut in a 
single section since we have only 3 independent equilibrium equations