Estimating prestressing force and eccentricity

Reference no: EM131522023

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
5-3	3	552	39
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
	19	3500	90
5-22	20	3680	90
	21	3860
	22	4050

Reference no: EM131522023

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