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.

How you should cater for each of the requirements will depend on the design code you are working to. The approach for steel can be different to that for concrete.

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.

*The terminology: "Non-sway" and "Sway sensitive" can vary between codes.

For an overview of how you should cater for P-∆ according to the design code you are working to, see Allowing for global 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.

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

*The terminology: "Short" , "Stocky" and "Non-slender" can vary between codes.

Steel structures

These effects are intrinsically allowed for in the design equations.

Global imperfections

Note: Global Imperfections apply regardless of whether the structure is "Non-sway" or "Sway sensitive."

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.

Tekla Structural Designer uses the second option.

For an overview of how this varies according to the design code you are working to, see Allowing for global imperfections

Member imperfections

Member Imperfections apply regardless of whether members are slender or not. They are normally dealt with as part of the member design.

For an overview of how this varies according to the design code you are working to, see Allowing for member imperfections

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:


Member Effects	Global Effects
	Non-sway	Sway Sensitive
Short Member	A	C
Slender Member	B	D

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

Remember: Every structure and every member has 2 directions!