Effective length calculations (column and wall:ACI 318)

Tekla Structural Designer
2021
Tekla Structural Designer

Effective length calculations (column and wall:ACI 318)

Unsupported Length

The unsupported length, lu, of a column is the clear distance between lateral supports.

If, at an end of the compression member (stack), no effective beams, flat slab or slab on beams to include is found, then the clear height includes the (compression member) stack beyond this restraint, and the same rules apply for finding the end of the clear height at the end of the next stack (and so on). If there is no stack beyond this restraint (i.e. this is the end of the column), the clear height ends at the end of the column.

Effective Length

The effective length, le is calculated automatically from ACI 318. You have the ability to override the calculated value.

Tekla Structural Designer will impose the following limits for stacks that are designated as braced:

0.5 ≤ le / lu ≤ 1

When both ends of an unbraced compression member are hinged (pinned), a “Beyond Scope” warning is displayed.

The effective length of the stack (compression member) is given by:

le = k * lu

The program uses the bottom end of the stack (compression member) as end 1 and the top as end 2.

Any beams framing into the end of the compression member (stack) within 45 degrees of the axis being considered are said to be restraining beams for the stack in that direction. No adjustment is made to the restraint provided by the beam for the angle (i.e. the full value of “E * I / l” is used for all beams within 45 degrees of the axis).

A beam is to be considered as a restraining beam in the direction considered if:

-45° < β ≤ 45°

where

β is the angle from the axis in the direction considered to the beam, measured anti-clockwise when viewed from above (i.e. back along the length of the stack from the end towards the start).

Fixed Column Base

Since in practical structures there is no such thing as a truly fixed end, Tekla Structural Designer limits ψ ≥ 0.20. This being the practical lower limit suggested in “RC Mechanics” by McGregor and Wright.

Pinned Column End

In any situation where the end of a column anywhere in the structure is pinned, ψ = 1000. (This being the upper limit on ψ that is imposed by Tekla Structural Designer.)

No Effective Beams Found

If no effective beams are found to restrain the end of the stack in the direction in question, then the program will consider whether there is a flat slab restraining the stack at this end. If a flat slab is found it will either be considered as a restraint, or not, in each direction at each end of the stack - this is controlled by checking the option Use slab for calculation... located as a Stiffness setting in the column properties.

If there are no effective beams and there is no flat slab (or any flat slab is not to be considered), then the program will look for a slab on beams. If a slab on beams is found, this acts as a restraint at the position. Slabs on beams will only be considered if the “Use slab for calculation...” option is selected, as is the case for flat slabs.

If no beams and no flat slab or slab on beams is found, then the program will look for the far end of the stack on the other side of the joint, and look at the restraints there, and so on until a restraint with an effective beam, flat slab or slab on beams to be considered is found.

If the stack is restrained by a flat slab, then the slab will be considered to act as a beam in this direction - note that it is one beam in the direction and NOT a beam on each side of the column. The beam's length is taken as four times its width.

If the stack is restrained by a slab on beams, this will have a zero contribution to the stiffness. This thoretically has the effect of setting ψ = infinity, though it is limited to 1000 in Tekla Structural Designer before being used in the calculations.

If the stack is an end stack and there are no supports, beams, flat slabs or slabs on beams considered to restrain the stack at this end in the direction, the end is therefore free in this direction and ψ = 1000.

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