How to analyse prestressed RC beam Flashcards
What are the steps to analysing a prestressed RC beam?
- Consider the loads
- Calculate moments @ critical section (or stated position)
- Calculate the no. of strands
- Distribute strands in section
- Calculate A* and I* of transformed section
- Calculate stresses @ top and bottom fibres
- Calculate reinforcement index
What must be remembered when considering loads?
- Loads may be in SDL form
- Don’t forget SW
- Break down into variable and permanent
What are the equations for calculating moments @ critical section for both UDLs and PLs?
(UDL*L^2) / 8 = BMmax
(PL * L) / 4 = BMmax
What are the partial factors of safety for permanent and variable loads?
- For permanent: 1.35
- For variable: 1.50
When calculating moment @ critical section right after transfer, what loads and safety factors do you include?
- SW load only
- Therefore just 1.35 as a safety factor
When calculating moment @ critical section in service, what loads and safety factors do you include?
- ALL loads
- 1.35 for permanent, 1.5 for variable
- Variable load UDL must also be multiplied by 0.7 to convert characteristic variable action into representative one
How would you calculate the number of strands required in the section?
When distributing strands, what are the min spacing checks?
Cover must be >1.5 * diameter of strand where if <30mm, 30mm should be used.
Clear spacing >3 * diameter of strand where if <20mm, 20mm should be used
How do you calculate the max bars in bottom of section?
Clue: Equations
How do you calculate average eccentricity and therefore distribute strands?
- Work from the equation and perform trial and error until average achieved
- Average eccentricity < Target eccentricity
- Make sure all minimum spacing checks are satisfied!!
During the process of calculating A* and I*, the first stage is to calculate the area of concrete. What is the equation to calculate Ac?
Ac = A - N*Ap(1)
Where:
A = Cross sectional area from Design Table
Ap(1) = Area of one prestressing steel strand
During the process of calculating A* and I*, the second stage is to calculate the elastic moduli ratios Emod. What is the equation to calculate np and what must we remember?
np = Ep / Ec
Ep = Youngs modulus of prestressing steel
Ec = Youngs modulus of concrete
- Remember to do @ transfer and in service!
During the process of calculating A* and I, the third and final stage is to calculate the values of A and I*. What are the equations to do so and what must we remember?
When calculating the stresses @ top and bottom fibres, what do we need to remember?
- Remember signs!!
- If @ critical section, it will be on span therefore equation signs will be normal
- If working @ supports, signs will change!
What are the equations for calculating the stresses @ top and bottom fibres @ critical sections @ TRANSFER?
What are the equations for calculating the stresses @ top and bottom fibres @ critical sections IN SERVICE?
What are the checks when calculating the stresses @ top and bottom fibres @ critical sections IN SERVICE and @ TRANSFER?
In terms of Magnel’s diagram, what should our average eccentricity ideally be for optimal sustainability both in terms of resource efficiency and economics?
- Close to the emax but not equal to it
How can we adjust designs to improve them?
- Reduce or increase prestressing force
- Change section size parameters
- You can use Magnel’s diagram to see the feasibility region and therefore make adjustments accordingly
What state are we considering when calculating the reinforcement index?
- In service
What is the equation to calculate Mcr, the first step of the reinforcement index process.
What is the equation for the ultimate moment Mu in the reinforcement index calculation. Please also list the equations to calculate fpd, fcd, d.
What is the reinforcement index check to determine whether the section fails by cracking (satisfactory and safe)?
Mu > 1.2 * Mcr
What is the equation to determine the type of failure @ ULS and the associated check?
