Deflection and displacement limits under DSTU B V.1.2-3:2006: tables and how to use them

What the deflection limits restrict

The standard applies to load-bearing and enclosing structures of new and reconstructed buildings and facilities, whatever the material: steel, reinforced concrete, timber. It sets limit deflections and displacements, and the structure is checked under the second limit state group, that is, for serviceability and not for failure.

The condition is one: the calculated deflection f must not exceed the limit fu. f is found taking into account everything that affects it: elastic and inelastic deformation, cracking in concrete, the deformed scheme, the work of adjacent members, flexibility of joints and foundations. If justified, some factors can be ignored or taken approximately. For processes that develop over time (creep, settlement of foundations) the deflection grows, and this is allowed for too.

The calculation of deflection itself for a steel beam is covered in the article steel beam calculation; this one is about what counts as the limit and where to take it from.

Four groups of requirements

Deflection is limited not in general but for a particular reason, and everything depends on the reason: which load is taken, from which line deflection is measured and what value fu has. The standard names four groups of requirements, and each is checked separately from the others.

What deflection is measured from

For technological, structural and physiological requirements on roof and floor elements, deflection is measured from the bent axis corresponding to the state of the element at the moment the load causing the deflection is applied. For aesthetic and psychological requirements it is measured from the straight line joining the supports. If the structure is designed with camber and deflection is limited by appearance, the deflection is reduced by the camber.

Creep also depends on the group. For physiological requirements only short-term creep, which appears straight after loading, is taken. For technological, structural (except wind checks) and aesthetic requirements, full creep is taken.

In some cases the aesthetic requirement is not applied: the deflection does not spoil the appearance (membrane roofs, inclined canopies, structures with a sagging or raised bottom chord), the elements are hidden from view, or the room is occupied only briefly, such as a transformer substation or an attic.

Vertical deflection limits: table

Below are the main rows of the vertical deflection table. l is the design span of the element, a is the spacing of the beams or trusses that carry suspended crane tracks. For a cantilever, twice the overhang is taken in place of l. For intermediate l in the row for roofs open to view the values are interpolated linearly. The figures in brackets are used when the room height is up to 6 m inclusive.

Examples: what it looks like in millimetres

A purlin or roof beam with a 6 m span in a room where the structure is visible: l/200, that is 30 mm. A 12 m beam in a shop up to 6 m high: the row for 24 m (12 m) gives l/250, so 48 mm. These are the same values as in our calculation examples.

A 12 m crane runway beam, crane controlled from the floor: l/250, that is 48 mm under one crane. If the crane is cab-controlled and the duty group is 7K, it is already l/500, or 24 mm. The crane duty group sets the stiffness you will have to pay for in steel: at 8K the limit is twice as strict as for a floor-controlled crane.

A cantilever with a 1.5 m overhang visible from the room: l = 2 · 1.5 = 3 m, which in the table is l/150, so 20 mm at the tip. A lintel over a 2 m opening under masonry: l/200, that is 10 mm.

For elements whose limits are not set in this or other standards there is a general bound: no more than 1/150 of the span or 1/75 of the cantilever overhang under permanent, long-term and short-term loads.

Gaps, roof slope and crane restrictions

Deflection limited by structural requirements must not exceed the gap between the underside of the roof or floor element and the top of the partitions, glazing, window and door frames beneath it. As a rule this gap is not more than 40 mm. If meeting this would mean increasing the stiffness of the load-bearing elements, it is better to solve it by design: put the partitions beside the beam rather than under it, or make a flexible fixing.

The distance from the top of an overhead crane trolley to the lowest point of the deflected load-bearing roof structure (or objects attached to it) must be at least 100 mm. Roofs must deflect in such a way that a roof slope of at least 1/200 is kept in one direction.

For underhung crane tracks the deflection of the rafter structure is taken as the difference between the deflections of adjacent structures: the track beam sags unevenly between trusses, and it is the difference that troubles the crane. The integrity of the roofing membrane is as a rule ensured by design, with expansion joints or continuity of roof elements, and not by making the load-bearing elements stiffer.

Horizontal deflection under crane loads

For columns of buildings with overhead cranes, crane trestles, crane runway beams and braking structures (beams or trusses) the horizontal deflection limits are taken from the table, but not less than 6 mm. They are checked at the level of the crane rail head under braking forces of one crane trolley acting across the crane track, without allowing for foundation tilt.

h in the table is the height from the top of the foundation to the crane rail head (for single-storey buildings and trestles) or the distance from the axis of the floor girder to the rail head (for the upper storeys of multi-storey buildings). l is the design span of the beam.

Horizontal displacement of frames, wind posts and temperature effects

Horizontal displacement of framed buildings is limited first of all for structural reasons: so that the walls, partitions, windows and doors held by the frame are not damaged. It is found in the plane of the walls and partitions and, as a rule, with foundation tilt included. For buildings up to 40 m high, and for conveyor gallery supports of any height, tilt due to wind can be ignored. Frameless buildings are not limited for wind if the walls, partitions and their connections are checked for strength and crack resistance.

Here h is the height of a multi-storey building from the top of the foundation to the axis of the roof girder, and hs is the storey height: for a single-storey building from the top of the foundation to the underside of the rafter structures, for a multi-storey one between the axes of adjacent girders. Horizontal deflections from temperature and shrinkage effects are not added to deflections from wind and tilt. Temperature effects are taken without daily swings or the difference due to solar radiation.

Vibration and comfort

For floors, stairs, balconies and loggias of residential and public buildings, and for staff rooms of industrial buildings, deflection is limited on physiological grounds by a separate formula. It includes the weight of a person, the walking frequency (1.5 Hz, 2 Hz for dance halls), the weight of the element itself and the load on it. We do not reproduce the formula here, because the figures mean nothing without it; use the text of the standard.

Where equipment that excites vibration operates in the building, the limit values of vibration displacement, velocity and acceleration are taken from occupational safety and sanitary requirements, and for high-precision equipment and sensitive instruments from special technical conditions.

What the standard does not cover: line poles and switchyard gantries

For structures that differ from traditional buildings, the standard refers deflections and displacements to special technical conditions and standards. The list names bridges, hydraulic structures, nuclear power plants, poles of high-voltage overhead lines and switchyard gantries, greenhouses and glasshouses.

For us this is not abstract: we make poles and portals. So the tables in this article are not carried over to them automatically. The stiffness of a pole or portal is set by the standards and technical conditions for lines and switchgear and by the project brief; values from the building-frame table may prove too soft or needlessly strict.

Order of checking

First decide which requirements apply to the element: technological (there is a crane or equipment), structural (there are partitions, floors, window fillings), physiological (a floor for people), aesthetic (the structure is on view). One element often has several, and each is checked separately. Then pick the row in the table and the limit value fu.

Next take the matching loads: for technology, the action of the equipment; for structural requirements, what could damage adjacent elements; for appearance, permanent and long-term loads. Calculate f including creep and compare it with fu. If the condition fails, the section is most often increased for stiffness rather than strength; sometimes it is cheaper to change the scheme or the fixing.

How to calculate f for a steel beam is in beam calculation, for a column in column calculation, for a truss in truss calculation. We prepare KM and KMD drawings with the required stiffness and camber: KM and KMD design, fabrication.

Standards and validity

The tables and rules in this article follow DSTU B V.1.2-3:2006 «System of reliability and safety assurance in building projects. Deflections and displacements. Design rules» (in force from 01.01.2007; the standard itself requires it to be used together with DBN V.1.2-2:2006 «Loads and actions»). Steel structures are designed to DBN V.2.6-198:2014 «Steel structures. Design standards», which refers to this DSTU for deflection limits.

The validity and current edition of these documents must be checked before use in a project. The values in the tables are given as a guide and the text of the standards is not reproduced word for word: the final decision is the designer’s, based on the current text.