structural analysis

1. CEE-311
Structural Analysis-I
(3.0 credit)
Lecture:11
Bijit Kumar Banik
Assistant Professor, CEE, SUST
Room No.: 115 (“C” building)
bijit_sustbd@yahoo.com
Department of Civil and Environmental Engineering

2. Reactions due to moving concentrated loads (S&V; pp-112)
Condition-1: (No wheels comes on the span during movement)
1
1.
P
L
dP
R −=∆
∑
Where, R = change of reactions due to moving from one load
over the reaction to the next
P1 = the wheel which was over the reaction & is moved
off the span
d1 = the distance between P1 and the following wheel
∑P = the summation of all loads which are on the span
& stay during movement

3. Reactions due to moving concentrated loads (S&V; pp-112)
Condition-2: (Wheels comes on the span during movement)
Where, Pʹ = load which comes on during movement
e = distance which Pʹ moves on the span
1
1 ..
P
L
eP
L
dP
R −
′
+=∆
∑
If ∆R,
Positive → continue movement
Negative → stop movement

4. Reactions due to moving concentrated loads (S&V; pp-112)
Find maximum reaction at ‘A’ when wheels
move right to left.
RA
1
A B
60ʹ
1 2 3 4 5 6 7 8 9 10 11 12 13 14
5ʹ 8ʹ 6ʹ 6ʹ 6ʹ 8ʹ 4ʹ 9ʹ 4ʹ 4ʹ 12ʹ 4ʹ 4ʹ
10k 10k 36k 36k 36k 36k
10k 10k 20k 20k 20k
20k 20k 20k

5. Reactions due to moving concentrated loads (S&V; pp-112)
A B
60ʹ
Position-1: wheel 1 at ‘A’
1 2 3 4 5 6 7 8 9 10 11 12 13 14
5ʹ 8ʹ 6ʹ 6ʹ 6ʹ 8ʹ 4ʹ 9ʹ 4ʹ 4ʹ 12ʹ 4ʹ 4ʹ
10k 10k 36k 36k 36k 36k
10k 10k 20k 20k 20k
20k 20k 20k

6. Reactions due to moving concentrated loads (S&V; pp-112)
A B
60ʹ
Position-2: wheel 2 at ‘A’
5ʹ
1 2 3 4 5 6 7 8 9 10 11 12 13 14
5ʹ 8ʹ 6ʹ 6ʹ 6ʹ 8ʹ 4ʹ 9ʹ 4ʹ 4ʹ 12ʹ 4ʹ 4ʹ
10k 10k 36k 36k 36k 36k
10k 10k 20k 20k 20k
20k 20k 20k
P = 234 k [No.2 to no.11]
kR 5.910
60
5*234
+=−=∆ continue
Condition-1

7. Reactions due to moving concentrated loads (S&V; pp-112)
A B
60ʹ
1 2 3 4 5 6 7 8 9 10 11 12 13 14
5ʹ 8ʹ 6ʹ 6ʹ 6ʹ 8ʹ 4ʹ 9ʹ 4ʹ 4ʹ 12ʹ 4ʹ 4ʹ
10k 10k 36k 36k 36k 36k
10k 10k 20k 20k 20k
20k 20k 20k
Position-3: wheel 3 at ‘A’
1ʹ
P = 224 k [No.3 to no.11]
continue
Condition-2
kR 2.2010
60
1*20
60
8*224
+=−+=∆

8. Reactions due to moving concentrated loads (S&V; pp-112)
A B
60ʹ
1 2 3 4 5 6 7 8 9 10 11 12 13 14
5ʹ 8ʹ 6ʹ 6ʹ 6ʹ 8ʹ 4ʹ 9ʹ 4ʹ 4ʹ 12ʹ 4ʹ 4ʹ
10k 10k 36k 36k 36k 36k
10k 10k 20k 20k 20k
20k 20k 20k
Position-4: wheel 4 at ‘A’
3ʹ
P = 208 k [No.4 to no.12]
Stop
Condition-2
kR 2.1436
60
3*20
60
6*208
−=−+=∆

9. Reactions due to moving concentrated loads (S&V; pp-112)
So, wheel 3 at A will produce maximum reaction
RA
1
A B
60ʹ
1 2 3 4 5 6 7 8 9 10 11 12 13 14
5ʹ 8ʹ 6ʹ 6ʹ 6ʹ 8ʹ 4ʹ 9ʹ 4ʹ 4ʹ 12ʹ 4ʹ 4ʹ
10k 10k 36k 36k 36k 36k
10k 10k 20k 20k 20k
20k 20k 20k
( )
60
1
*20
60
13
*20
60
17
*20
60
21
*20
60
30
*10
60
34
*10
60
42
*36
60
48
*36
60
54
*361*36max
+++++++++=AR
= 150.4 k