### Activity Duration Predecessor ES EF LS LF TF FF INTF INDF A 5

```Week 4 - Floats , Two span bridge
1. The critical path activities has ___ float
a. Negative
b. Zero
c. Non zero
d. Positive
2. The critical path is the _____ path in the project and delaying the critical path will delay the
______.
a. Shortest, Activity duration
b. Longest, Project
c. Earliest, Early start of the activity
d. Latest, Slack of an activity
Question #3 to 6: The details of the project are given below in the table. 1.
Table 1
Activity
A
B
C
D
E
F
G
Duration
5
9
3
6
4
4
4
Predecessors
A
A
A
B, C
C, D
E, F
Activity Duration Predecessor ES EF LS LF TF FF INTF INDF
A
5
0 5 0 5 0 0 0
0
B
9
A
5 14 5 14 0 0 0
0
C
3
A
5 8 11 14 6 3 3
3
D
6
A
5 11 8 14 3 0 3
0
E
4
B, C
14 18 14 18 0 0 0
0
F
4
C, D
11 15 14 18 3 3 0
0
G
4
E, F
18 22 18 22 0 0 0
0
3. What is (ES, EF) of activities B,D,F,G?.
a) (5,14); (5, 11); (11,15); (18,22)
b) (5,14); (5, 8); (11,15); (18,22)
c) (5,14); (5,11); (14,18); (18,22)
d) (0,5); (5,11); (11,15); (18,22)
4. What is (LS, LF) of activities C,E,F,G?.
a.
b.
c.
d.
(11, 14); (14,18); (11,15); (18,22)
(2,14); (14,18); (11,15); (18,22)
(11,14); (14,18); (14,18); (18,22)
(11,14); (5,11); (11,15); (18,22)
5. What is (Total Float, Free Float) of activities C,D,E,F?.
a. (6,3); (3,0); (11,15); (3,3)
b. (6,3); (3,0); (0,0); (3,3)
c. (6,3); (3,3); (0,0); (3,3)
d. (3,0); (3,0); (0,0); (3,3)
6. What is (Interfering Float, Independent Float) of activities B,C,D,F?.
a. (0,0); (3,3); (3,0); (3,0)
b. (0,0); (0,3); (3,0); (0,0)
c. (0,0); (3,3); (0,3); (0,0)
d. (0,0); (3,3); (3,0); (0,0)
Question #7-10: The table.2 below shows the activities and duration for a prefabricated suspension
type pipeline crossing structure carrying steel pipes (Fig. 1).
Fig 1
(Source: ASCE manual reports on Engineering Practice no.89)
Table 2
Activity
1
Start
Predecessor
Duration
---
0
2
Excavate
1
1
3
Anchor 1
2
2
4
Footing 1
2
3
5
Tower 1
4
2
6
Footing 2
4
3
7
Tower 2
5, 6
2
8
Anchor 2
3
2
9
Braces and guys
7, 8
2
10
String cables
7, 8
4
11
Hangers and pipe racks
10
4
12
Lay pipes
9, 11
3
13
Paint
12
2
14
Finish
13
0
Activity
Predecessor
Duration ES EF LS LF T.F F.F INT.F IND.F
Start
---
0
Excavate
Start
1
Anchor 1
Excavate
2
Footing 1
Excavate
3
Tower 1
Footing `1
2
Footing 2
Footing 1
Tower 2
0 0 0 0
0 1 0 1
0
0
0
0
0
0
0
0
1 3 5 7
1 4 1 4
4
0
4
0
0
0
0
0
1
1
0
1
3
4 6 5 7
4 7 4 7
0
0
0
0
Tower 1, Footing 2
2
7 9
7 9
0
0
0
0
Anchor 2
Anchor 1
2
4
4
0
0
Braces and guys
Tower 2, Anchor 2
2
3 5 7 9
15 17
9 11
6
6
0
6
0
0
0
0
0
0
0
0
String cables
Tower 2, Anchor 2
4
9 13
9 13
Hangers and pipe
racks
String cables
4
13 17
13 17
Place pipes
Braces and guys, hangers and pipe
racks
3
Paint
Place pipes
2
Finish
Paint
0
17 20
17 20
0
0
0
0
20 22 20 22
22 22 22 22
0
0
0
0
0
0
0
0
7. By how much can the bracing subcontractor delay his activity from early start without delaying
the 22 day duration (without delaying the project)?.
a. 5 days
b. 4 days
c. 6 days
d. 3 days
8. The bracing subcontractor decides to start his activity at the latest date, Should the pipe laying
subcontractor worry about his activity getting delayed because of bracing activity starting late?
Why?.
a. Should be worried, because it will affect the start of the project
b. Need not be worried, because bracing activity has free float (of 6days) (which will not
affect the early start of succeeding activity i.e. pipe laying activity)
c. Should be worried, because it will ultimately delay the project.
d. Need not be worried, because the bracing activity has a total float of zero.
9. If Anchor 2 activity start at the latest date possible, it will cause delays to the early start of
______ activity without delaying the _____?
a. Tower 1, project
b. Braces and guys, project
c. Anchor 2, Critical path
d. String cables, project
10. The activity “Tower 1” has an independent float of ___ days
a. 1 day
b. 2 days
c. 3 days
d. 4 days
Question #11-15: Two span bridge with resource constraints (Table. 3).
Table 3
Activity no
1
2
Activity
Order and deliver piles
Cast beams
Duration
15
20
Predecessors
Start
Start
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Activity no
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Drive piles east
Construct east pile cap
Construct east abutment
Drive piles center
Construct center pile cap
Construct center pier
Drive piles west
Construct west pile cap
Construct west abutment
Place beams on east span
Place beams on west span
Deck slab east
Deck slab west
12
8
36
6
7
27
12
8
36
7
7
15
15
25
1
3
4
3
4, 6
5, 7
6
7, 9
8, 10
2, 8
11, 12
12
13, 14
15
Activity
Duration Predecessors ES EF LS LF TF FF INTF INDF
Order and deliver piles
15
Start
0 15 0 15 0 0
0
0
Cast beams
20
Start
0 20 99 119 99 78 21 78
Drive piles east
12
1
15 27 15 27 0 0
0
0
Construct east pile cap
8
3
27 35 27 35 0 0
0
0
Construct east abutment
36
4
35 71 35 71 0 0
0
0
Drive piles centre
6
3
27 33 58 64 31 0 31
0
Construct center pile cap
7
4,6
35 42 64 71 29 3 26
0
Construct center pier
27
5,7
71 98 71 98 0 0
0
0
Drive piles west
12
6
33 45 78 90 45 0 45
0
Construct west pile cap
8
7,9
45 53 90 98 45 45
0
0
Construct west abutment
36
8,10
98 134 98 134 0 0
0
0
Place beams on east span
7
2,8
98 105 119 126 21 0 21
0
Place beams on west span
7
11,12
134 141 134 141 0 0
0
0
Deck slab east
15
12
105 120 126 141 21 21
0
0
Deck slab west
15
13,14
141 156 141 156 0 0
0
0
25
15
156 181 156 181 0 0
0
0
11. Find the critical path for the project?.
I.
Start,1,3,4,5,8,11,13,15,16,Finish
II.
Start,2,3,4,5,12,14,15,16,Finish
III.
Start,1,3,6,7,8,11,13,15,16,Finish
IV.
Start,2,3,6,9,10,11,13,15,16,Finish
12. What is (ES, EF) of activities 2,3,15,16?.
a. (0,20); (20,42); (146,161); (161,181)
b. (0,20); (20,32); (141,155); (155,180)
c. (0,20); (15,27); (141,156); (156,181)
d. (0,20); (20,32); (141,161); (161,181)
13. What is (LS, LF) of activities 6,7,8,9?.
a. (62,68); (68,75); (75,102); (83,95)
b. (58,64); (64,71); (71,98); (78,90)
c. (63,69); (69,76); (76,103); (84,96)
d. (63,69); (69,76); (76,102); (83,95)
14. What is (Total Float, Free Float) of activities 1,6,9,14?.
a. (5,0); (31,0); (45,0); (48,48)
b. (5,5); (31,31); (45,0); (48,48)
c. (5,5); (31,0); (45,0); (48,0)
d. (0,0); (31,0); (45,0); (21,21)
15. What is (Interfering Float, Independent Float) of activities 5,7,11,12?.
a. (0,0); (26,0); (0,0); (21,0)
b. (0,5); (26,0); (0,0); (48,0)
c. (0,0); (0,26); (0,0); (48,0)
d. (0,0); (26,0); (0,0); (48,48)
```