Overview of stability requirements
The analysis and design process has to allow for the differences between a theoretical mathematical model of a building and a more realistic representation. For example, buildings are not truly vertical when first built nor do they remain so when subject to load. These are called stability requirements and are from four sources:
- Global second-order (P-∆) effects to allow for deformation of the structure under load,
- Member second-order (P-δ) effects to allow for deformation of the members under load,
- Global imperfections due to the structure not being built plumb and square,
- Member imperfections due to initial lack of straightness of the member.
There are various methods of allowing for each of these and they can be different for steel and concrete. There is also some variation based on country code.
Global second-order (P-∆) effects
If gravity loads are applied to the deflected shape of a structure the load P applied at eccentricity ∆ generates additional forces.
Provided the deflection is small:
- Structure is 'Non-sway'
- Second order effects can be ignored.
At some level these effects are no longer ignorable:
- Structure is 'Sway sensitive'
- And you have to do something to account for the second order effects.
Member second-order (P-δ) effects
Under load members will deform between their ends:
- Member curvature introduces a displacement δ between the member ends.
- The member axial loads applied at eccentricity δ generates additional forces.
In concrete structures:
- Where deflections are small :
- Member is 'Short' or 'Stocky' or 'Non-Slender'
- member second order effects are considered ignorable
- At some level they are no longer ignorable:
- Member is 'Slender'
- effects must be catered for in the design calculations
In steel structures: these effects are intrinsically allowed for in the design equations.
When must global and member second order effects be considered?
Depending on the building's overall sway classification and each member's slenderness, global and member effects must be considered as follows:
A - All second order effects can be ignored
B - Global effects can be ignored - member effects must be considered
C - Global effects must be considered - member effects can be ignored
D - Global effects must be considered - member effects must be considered
When the design code requires it you need to account for some degree of inclination (slope); typically in the range 0.2 to 0.5%
The codes allow you to cater for this in different ways:
- You could build multiple analysis models that are inclined
- You could have a single analysis model where you apply Equivalent Horizontal Forces [Eurocodes] / Notional Loads [AISC/ACI] / Notional Horizontal Forces [AUS/BS/IS] that will induce the same effect. Basically this means applying horizontal forces = 0.2 to 0.5% of the vertical forces in any combination.
In Tekla Structural Designer we use the second option.
Member Imperfections apply regardless of whether members are slender or not. They are normally dealt with as part of the member design.