For both steel and concrete, first-order analysis is only acceptable providing second order effects are small enough to be ignored - see: A practical approach to setting the analysis type below.

Both steel and concrete can use the amplified forces method to determine second-order effects although for steel this does have restrictions on use (regular frameworks with λ_cr > 4).

If the amplified forces method is selected you must also indicate which formula to use for determining the amplification factor,

If the structure is clad and if the stiffening effect of cladding is not taken into account explicitly:

k_amp = λ_cr/(1.15λ_cr - 1.5)

If the structure is unclad or clad with a direct allowance made for the stiffening effect:

k_amp = λ_cr/(λ_cr - 1)

During the design process for both steel and concrete members, the member end forces from the analysis of the lateral loadcases are amplified by the 'appropriate' value of k_amp. Since the analysis is first-order this is carried out as part of summing the load effects from each loadcase (multiplied by their appropriate load factor given in the design combination). The 'appropriate' value is the worse of k_amp,Dir1 and k_amp,Dir2 based on the worst value of λ_cr for all stacks in the building.

The k_amp results are summarized for each column in both directions. These can be viewed as follows:

1. Open a Review View, and select Tabular Data from the Review tab.
2. Select 'k_amp' from the View Type drop list on the Review tab.
3. The k_amp results in both directions are tabulated for each column in the building.

Full second-order analysis is not restricted to regular frameworks, but requires λ_cr > 2.

The accuracy of determination of the second-order effects for concrete structures is dependent upon a reasonable estimation of the concrete long term properties. This is a significant issue for both the amplified forces method and second-order analysis. It is therefore important that appropriate member type specific modification factors have been specified - see Use of modification factors.

Unless λ_cr is greater than 10 (in which case second-order effects can be ignored), it is essential that your final design utilizes one of the second-order analysis approaches. During the initial sizing process you may however choose to run a first-order analysis. Proceeding in this way you can obtain sections and an overall building performance with which you are satisfied, before switching to P-∆ analysis.

Note: If the rigorous second-order (P-∆) analysis approach is used during the initial sizing process, you may find that it can be more sensitive to parts of your model that lack stiffness.

The following approach to setting the analysis type is suggested:

1. On the Analysis page of the Design Settings dialog, initially set the analysis type to First-order analysis.
2. Perform Design All (Gravity) using first-order analysis in order to size members for the gravity loads.
3. Once the members are adequately sized for the gravity combinations obtain a figure for the building's elastic critical load factor, λ_cr. See: How do I assess the worst elastic critical load factor for the building? section below.
4. If the λ_cr that has been determined is greater than 10 you can continue to perform Design All (Static) with the analysis type set to First-order analysis.
5. If λ_cr is less than 10 you will need to proceed with one of the second-order approaches - and if it is very low (i.e. less than 2.0) some remodelling is required:
   • Either, refine the design until λ_cr is greater than 2.0 to make the structure suitable for a final design using the full second-order approach, (which is the only method permitted if the structure contains non-linear members such as tension only braces - see below),
   • Or, in order to use the amplified forces (k_amp) approach, refine the design further until λ_cr is greater than 4.0.
6. When a suitable λ_cr has been achieved change the analysis type to the full second-order, or the amplified forces method as appropriate. (If the k_amp approach is selected you must also indicate which formula to use for determining the amplification factor, This will depend on whether the structure is clad or not and if the cladding is taken into account explicitly or not.)
7. With the analysis type still set to the full second-order, or the k_amp approach perform Design All (Static).

If you use the k_amp approach be aware that BS5950-1:2000 classes certain structures outside the scope of this method. e.g. tied portals, or structures containing tension only braces. For such structures, you would need to ensure that λ_cr is greater than 2.0, and use the full second-order analysis approach for the static design.

To determine the sway sensitivity for the building as a whole, the worst stack (storey) in the worst column throughout the building in both directions has to be identified - this can be done as follows:

1. On completion of the analysis, open a Review View and select Tabular Data from the Review tab.
2. Select 'Sway' from the View Type drop list on the Review tab.
3. The elastic critical load factor in both directions ( (λ_Dir1 & (λ_Dir2) is tabulated for each column in the building.
4. Make a note of the smallest λ value from all of the columns in either direction.

In BS 5950-1:2000 a building can be considered as 'non-sway' when λ_cr ≥ 10 else it is 'sway sensitive' and (global) second-order effects must be taken into account.

Note however that you are not restricted in your choice of analysis type irrespective of the value of λ_cr (it is your call, although we will warn you about it).

In order to determine whether a building is 'non-sway' or 'sway sensitive', Tekla Structural Designer calculates the elastic critical buckling load factor, λ_cr. It is calculated in the same manner for steel and concrete. The approach adopted is that for each loadcase containing gravity loads (Dead, Imposed, Roof Imposed, Snow) a set of Notional Horizontal Forces (NHF) are determined. It uses 0.5% of the vertical load at the column node applied horizontally in two orthogonal directions separately (Direction 1 and Direction 2). From a first order analysis of the NHF loadcases the deflection at each storey node in every column is determined for both Direction 1 and Direction 2. The difference in deflection between the top and bottom of a given storey (storey drift) for all the loadcases in a particular combination along with the height of that storey provides a value of λ_cr for that combination as follows,

λ_cr =h/(200 * δ_s)

Where

h= the storey height

δ_s =the storey drift in the appropriate direction (1 or 2) for the particular column under the current combination of loads.

A ‘measure’ of twist is also tabulated for each column - this indicates the degree to which if you push the column one way, how much it moves orthogonally as well. If you have a building where the 'lateral load resisting system' is not well dispersed then pushing one way can cause significant movement in the other direction.

The twist is reported as a ratio of: distance moved in the direction of loading/absolute distance moved.

Example:

When a column node moves in X and Y then the 'total' deflection is √(δ_x² + δ_y²)) in other words the diagonal of the triangle and not either of the sides.

So if a node moves say 10mm in X and 2mm in Y, its diagonal i.e. absolute deflection in this plane is √(100 + 4) = 10.198.

Hence its twist is what it should have been with just X loading i.e. 10mm divided into what it actually moved i.e. 10.198.

So Twist = 1.0198.