Prestressed Concrete Design: Ultimate Limit State and Serviceability

This document presents a detailed solution to a prestressed concrete design assignment. The solution addresses key aspects such as determining the required cross-sectional area for strength under the ultimate limit state, calculating the factor of safety for no cracking under full service load, and evaluating incremental extension under full imposed action for serviceability. The analysis includes calculations based on given parameters like axial loads, stresses, and material properties, adhering to relevant standards like AS3600. The solution also discusses the behavior of reinforcement under increasing loads, explaining which reinforcement yields first and the implications on the structural integrity. The assignment covers various aspects of prestressed concrete design, providing a comprehensive understanding of structural behavior and safety considerations. The assignment is well-structured, includes all necessary calculations, and follows structural engineering principles.

Prestressed Concrete Design 1
PRESTRESSED CONCRETE DESIGN
by [Name]
Course
Professor’s Name
Institution
Location of institution
Date

Prestressed Concrete Design 2
Prestressed Concrete Design
Question 1a.
Cross Section Area for Strength to Ultimate Limit State is given by;
A = F
σ 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 = 1650000
1050 N /mm2 = 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.
Question 1b.
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 = fc+fi
fd+ fc

Prestressed Concrete Design 3
Given, fc = 5000N/mm2, fi = 10000mm, and fd = 450 mm,
Factor of Safety = 5000+10000
450+5000
= 2.8
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.
Question 1c.
For Serviceability Limit State, incremental extension under full imposed action, NQ;
Given NQ = 650 kN
Stress on the member section σ = P
Area
= 650000
450 x 450
= 3.2 MPa
Incremental extension of the member is:

Prestressed Concrete Design 4
E = Stress/ Ec = 3.2 x 1000000
38000
= 84.47 x 10-6
Incremental extension = (84.47 x 10-6) (10 x 10000)
= 8.44 mm
Question 1d.
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.

Prestressed Concrete Design 5
References
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.