Prestressed Design
You are requested to design a continuous simply supported prestressed concrete beam over 2 spans as shown in Figure 2. This beam carries a 120 mm thick concrete slab together with a nominal live load of w. Concrete slab should be considered with an effective width of a for the calculation. You may need to use the parameters as given in Table 1.
Figure 2. Configuration of the beam
Table1: Design parameters
|
Last digit of your student number
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
|
L(m)
|
7.0
|
10.0
|
12.0
|
9.0
|
11.0
|
14.0
|
14.0
|
15.0
|
15.0
|
16.0
|
|
w(kN/m)
|
8.0
|
6.5
|
6.0
|
7.0
|
6.5
|
6.0
|
6.5
|
6.0
|
6.5
|
5.0
|
|
a(mm)
|
620
|
780
|
875
|
600
|
800
|
850
|
820
|
860
|
780
|
860
|
Standard I-Girder Sections
|
Girder
Type
|
A
(mm2)
|
Zt
(mm3)
|
Zb
(mm3)
|
Ixx
(mm4)
|
Yb
(mm)
|
|
2
|
218x103
|
41.1x106
|
48.1x106
|
19950x106
|
415
|
|
3
|
317x103
|
82.9x106
|
91.1x106
|
49900x106
|
548
|
|
4
|
443x103
|
135.9x106
|
168.6x106
|
105330x106
|
625
|
Other Data:
Density of the concrete 24 kN/m3
Concrete strength f'c = 60 MPa (at transfer the strength will be 70% of the f'c)
Minimum cover should be 40 mm
Friction loss can be assumed as 3.0% of the applied force
Your tasks:
Your submission must have following components:
1. Selection of suitable beam section from Standard 1-Girder sections given above
2. Estimating prestressing force and eccentricity
3. Tendon details (use 12.7 mm strand tendons) - size of the tendons, required number and arrangement at the mid-span section
4. Ultimate moment capacity of the beam
5. Losses in the beam (long term loss)
Hints:
At transfer: Cross section will be same as given above.
At service: Composite beam (given section + slab)
It is recommended to develop a excel worksheet, so that you can able to determine the dimension and prestressing force easily (still you must show the equations and all necessary steps in the calculation).
Strand Properties (AS1311) of 12.7 mm strand
Nominal diameter = 12.7 mm
Nominal area = 100.1 mm2
Minimum Breaking load = 184 kN
Minimum Proof load (0.2% offset) = 156.4 kN (0.85% of the breaking load)
| Tendon unit |
No of Strands |
Minimum Breaking
Load (kN)
|
Steel Duct internal
diameter (mm)
|
|
| 5-3 |
2 |
368
|
39 |
|
| 3 |
552 |
|
| 5-7 |
4 |
736 |
51 |
|
| 5 |
920 |
|
| 6 |
1100
|
|
| 7 |
1290
|
|
| 5-12 |
8 |
1470
|
69 |
|
| 9 |
1660
|
|
|
10
|
1840
|
|
| 11 |
2020
|
|
|
|
120
|
2210
|
|
|
| 5-19 |
13 |
2390
|
84 |
|
| 14 |
2580
|
|
|
| 15 |
2760
|
|
| 16 |
2940
|
|
| 17 |
3130
|
|
| 18 |
3310
|
|
| 19 |
3500
|
|
90
|
|
| 5-22 |
20
|
3680
|
|
| 21 |
3860
|
|
|
| 22 |
4050
|
|