structural analysis

1. CEE-311
Structural Analysis-I
(3.0 credit)
Lecture: 2
Bijit Kumar Banik
Assistant Professor, CEE, SUST
Room No.: 115 (“C” building)
bijit_sustbd@yahoo.com
Department of Civil and Environmental Engineering

2. Frame
No. of unknown = 4
Known equation = 3
DOI = 4-3 = 1
1˚ ID
Internal hinge
No. of unknown (UK) = 4
Known equation (K) = 3
Condition of construction (c) = m-1
m = no. of joining member at hinge
DOI = 4-3-(2-1) = 0
Determinate

3. Frame
No. of unknown (UK) = 5
Known equation (K) = 3
Condition of construction (c) = m-1
m = no. of joining member at hinge
DOI = 5-3-(3-1) = 0
Determinate

4. Trusses
In structural engineering, a truss is a structure
comprising one or more triangular units constructed
with straight members whose ends are connected
at joints referred to as nodes (hinge or pin).
Assumptions
1.Members are connected at their end by
frictionless pins
2. Loads and reactions applied only at joints
3. Two force members

5. Trusses
If j > 2n-3 Indeterminate truss
If j < 2n-3 Unstable truss
Here the assumption was, truss is simply supported.
But a more robust expression is:
If j+r < 2n
Where,
‘n’ = no of joints
‘j’ = number of members
Where, ‘r’ = reaction
Statically Unstable truss
(internal instability)
A truss is externally unstable if it’s reaction are all
concurrent (act through same point) or parallel

6. Trusses
If j+r > 2n Statically indeterminate
DOI = j+r-2n
L0
L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
j = 21; r = 5 and n = 12
DOI = j+r-2n = 21+5-12*2 = 2˚ ID

7. Trusses
L0
L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
j = 21; r = 3 and n = 12
DOI = j+r-2n = 21+3-12*2 = 0˚
Unstable

8. Trusses
L0
L1 L2 L3 L4 L5
L6
U1
U2
U3
U4
U5
j = 21; r = 3 and n = 12
DOI = j+r-2n = 21+3-12*2 = 0˚
Unstable

9. Trusses
Internally Unstable
j = 4; r = 3 and n = 4
DOI = j+r-2n = 4+3-4*2 = -1
Unstable
If j+r < 2n