Cross Section Area for Strength to Ultimate Limit State is given by;
A = Where F = Axial load carried, and σ = compression stress.
Given, F = NG + NQ
= 1000 kN + 650 kN
= 1650 kN and,
σ = 1050 MPa (N/mm2)
Adequate Cross Section Area = = 1571.4285 mm2
The member should be minimum 1572 mm square.
Proposed Cross-section = 450 x 450 = 202500 mm2
202500 mm2 > 1572 mm square OK. Proposed Section Adequate.
Factor of safety for no cracking under full service load;
Full Service Load = NG + NQ
= 1000kN + 650kN
= 1650 kN
Member under tension, therefore,
Limits are: fv = f d
Range = fv + f d
Factor of Safety for no Cracking under full service load =
Given, fc = 5000N/mm2, fi = 10000mm, and fd = 450 mm,
Factor of Safety =
The factor of safety for no cracking under the full load is 2.8. This value is adequate because it does not exceed the required limit as per section 6 AS3600.
The safety of people in any design project is the one most important aspect put under consideration. The prestressed concrete used in the member under analysis must be consider safe so as not to put any involved member in any danger.
At ultimate, the section is not ductile. This is because the section is characterized by a low ratio between the ultimate and yield strengths. There is also a reduced ultimate strain and the yield strength values are higher than the conventional values. Therefore, the use of the steels and concrete in this section increases local strengths, and ultimately leads to reduced local ductility. Also, the section is not subject to plastic deformation which spreads in the steel to produce brittle characteristics of the section.
For Serviceability Limit State, incremental extension under full imposed action, NQ;
Given NQ = 650 kN
Stress on the member section σ =
= 3.2 MPa
Incremental extension of the member is:
E = Stress/ Ec =
= 84.47 x 10-6
Incremental extension = (84.47 x 10-6) (10 x 10000)
= 8.44 mm
Under increasing applied load, the 8N20 reinforcement yields first. An additional loads assumes peak lateral strains and a loss of the ultimate capacity. When the highest/peak ultimate levels are reached, the prestressed strands will tend to be large at some short distance from the ends of the member under consideration. Most damage and cracking of the member tends to take place from the ends due to the combined high flexural and shear demand. With the continued damage, more cracks are formed and they intersect the reinforcement thus increasing the strain in the bars. Therefore, the 8N20 reinforcement will yield first before the 7/15.2mm prestressing strands.
Abeles, P. W., & Bardhan-Roy, B. K. (2014). Prestressed concrete designer's handbook. CRC Press.
STANDARDS Australia. (2010). Australian Standard Concerete Structures. AS 3600 - 2009 . Standards Australia Limited.