Why reduce stiffness?
💎Reasonable load-bearing structure when spending just enough money 💶 to ensure durability and stiffness for the house
💎Enough typical stiffness in the house does not shake, shift too much when exposed to wind, earthquakes…
💎Concrete always cracks, reducing stiffness, increasing displacement. But it is too complicated in construction design, which requires immediate results
💎How to simplify and take advantage of the elastic diagram for quick calculation?
Stiffness reduction factor in high-rise building design
Elasticity means that the force increases, the deformation increases in the same proportion, according to a straight line relationship. Therefore, it is also called linear analysis. Some materials are elastic, such as steel, aluminum, etc. But the most common type of structure in construction design is concrete. The appearance of cracks leads to concrete working non-elastically, also known as nonlinear.
The nonlinear diagram as mentioned is not a convenient way to design structures. It is more practical to make some adjustments to the linear diagram, but still reflect the nonlinearity of concrete. Especially when designing ideas, it is necessary to quickly evaluate and choose different options.
One way to adjust is to use the stiffness reduction factor (hsgđc). In practice, it is simply necessary to multiply it to reduce the stiffness of the components in the Linear diagram. Obtain effective stiffness.
Speaking of speed, putting the design engineer under pressure, therefore, further simplification is needed. This leads to only one hsgđc for each type of structure. Europeans and Americans have been doing this for a long time. Design consultants should learn and apply based on understanding the principle of this simple method.
SRF in codes
Designing codes also tend to suggest a general Srf value for each type of structure: column, wall, beam, floor. And don’t forget to add the sentence: Unless there is a specific calculation. Of course, almost no one wants to do this “unless” 🤣.
🔲ACI:
This is the most familiar and popular way of design engineers. Section 6.6.3 of ACI 318-14 stipulates 2 ways to calculate Srf:
1/ one of two tables:
Stiffness reduction factor in concrete structure design according to ACI
or more simply
2/ equal to 0.5 for all components
That is for calculations according to the first limit state (TTGH1), in terms of strength.
When calculating according to TTGH2 such as calculating horizontal displacement due to wind, section 6.6.3.2.2 of ACI 318-14 allows an increase of 1.4 times, that is:
– Column, wall: 0.7*1.4 = 1.0 (no reduction)
– Beam: 0.35.1.4 = 0.5
– Floor: 0.25.1.4 = 0.35
or equal to 0.5.1.4 = 0.7 for all components if calculated according to the second method.
Horizontal displacement due to earthquake, according to section R18.2.2 of ACI 318-14, considers the behavior of concrete structures during earthquakes to be in the nonlinear region and at the design load level. R18.2.2 specifies the Srf for earthquakes according to case 2/, equal to 0.5.
🔲Eurocode:
Since the design standard for earthquake-resistant construction, TCVN 9386:2012, was originally translated from Eurocode 8. Design engineers often take item 4.3.1.(7) to reduce 50% of stiffness (Srf=0.5) for all load-bearing structures: columns, walls, beams, floors in the calculation diagram of horizontal displacement caused by earthquake load combinations. This is similar to ACI.
🔲Other standards:
[1] statistics of Srf according to many standards, similar and different, as shown in the table below:
Stiffness reduction factor in concrete structure design in international codes
🔲TCVN: regulations in TCVN 9386:2012 on earthquakes, similar to Eurocode 8.
Load combination when calculating horizontal displacement
According to TTGH2, the displacement load is the standard load, not multiplied by the overload factor.
🔲Wind:
The eternally controversial issue between many schools of thought:
– School 1: the combination is taken as when calculating according to TTGH1 according to TCVN 2737:1995, meaning:
Standard dead load + Standard live load.0.9 + Wind.0.9
– School 2: only includes wind load
This sounds more logical, because considering the feeling caused by wind is of the user. At that time, the construction has been completed, dead load + live load are considered as initial conditions. The horizontal displacement caused by them is considered equal to 0.
Recommendation: TCVN should specifically regulate this issue.
🔲Earthquake:
Load combination according to TCVN 9386:2012 regulations.
Types of horizontal displacement design criteria
– Peak displacement: the absolute value of the horizontal displacement at the top of the structure (Diaphragm Center of Mass Displacements) corresponding to each direction of wind and earthquake loads.
Its limit is specified in the standard, for reinforced concrete frame houses according to TCVN 5574:2018, is H/500. H is the height of the house from the foundation surface.
– Diaphragm Average Drift: the ratio of the horizontal displacement difference of 2 consecutive floors divided by the floor height.
Meaning: 2 consecutive floors do not differ too much in horizontal displacement so that the enclosing structures (such as the exterior glass wall system) are not damaged. TCVN 5574: 2018 stipulates the limit value of the horizontal displacement of 1/500 for concrete houses, which is allowed to increase by 30% for multi-storey buildings (but not exceeding 1/150).
Limit displacement due to earthquake: according to TCVN 9386:2012 section 4.4.3.2,
equal to 0.005/n, in which n=0.4 is common for high-rise buildings. That is, it is 6 times larger than the limit due to wind.
Experience shows that a sufficiently stiff building meets the condition of displacement due to earthquake, which is more difficult than the top displacement.
How to calculate the stiffness reduction factor according to TCVN
A problem that many people wonder about when applying ACI, Eurocode as mentioned above is: It is too simple. As a design engineer, it is our duty to answer the question Why for each job we do (and the world has been used to doing it for generations). Why is it 0.35 and not another number? Why and so on…
If you have read [2], you can understand a little bit why. Because of cracking.
Can topic [2] be developed to calculate the reduced hsgđc? The answer is yes. You can do the “unless” above:
– Beams, floors: the spreadsheet attached to that topic calculates the reduced hsgđc
– Columns, walls: can also be used, by entering additional compressive longitudinal force N into the spreadsheet.
So you can get the internal force of the largest structural members, caused by the standard load combination causing the displacement that needs to be calculated.
Practical example
2 buildings with 30 and 40 floors as attached file.
On each diagram, calculate the horizontal displacement caused by wind load with 3 calculation diagrams:
– Original diagram: to get the internal force caused by the wind load combination
– Stiffness reduction diagram according to TCVN: calculate with the structure bearing the largest internal force from the diagram above for each type: column, wall, beam, floor. The results from the 2 examples are quite similar: HSGĐC according to TCVN for beam is nearly 0.8, floor 0.15, column and wall do not reduce stiffness
– Stiffness reduction diagram according to ACI
Comparing the results of horizontal displacement (top displacement, offset displacement) on the stiffness reduction diagram, according to ACI and TCVN, the difference is insignificant.
Up to this point, it is possible to see vaguely why it is possible to take the same HSGĐC for each type of structure, even though the internal forces can be very different. Reason: the structure has greater internal force, according to TTGH1, more reinforcement is needed. Therefore, there are fewer cracks, and vice versa. The more calculations are done on a large set of structures, the more likely it is that the HSGDC converges to a value.
Horizontal displacement due to wind in the design of 30-storey and 40-storey buildings
Conclusion
– It is possible to confidently apply ACI’s simple and practical method when calculating displacement due to wind
– Displacement due to Earthquake: according to TCVN 9386:2012
– In construction design situations, caution is required and state agencies must be explained, and the Srf can be calculated according to TCVN 5574 to compare displacement results between different methods
References:
1. Effective Stiffness for Modeling Reinforced Concrete Structures – structuremag.org
🎁Attached are the calculation files for 2 projects.
