When designing any load-bearing structures, whether it is a carport or a production floor, it is critical to consider not only strength, but also rigidity. Farm deflection calculation This is a key step in ensuring that the building does not lose its functionality and appearance during operation. Ignoring this parameter can lead to the destruction of the roofing, the appearance of cracks in the finish or even to an emergency state of the entire system.
Deflection is the vertical movement of farm nodes under the influence of loads. If the design bends more than the construction mechanics allow, it will cause stress in the elements that are not designed for it. In this article, we will discuss in detail how to correctly determine deformations, what regulatory documents regulate limit values and what modern methods of computing exist for engineers and designers.
Regulatory requirements and limit states
The main document regulating the design of steel structures in the Russian Federation is SP 16.13330. "Steel structures." It is here that the limit values of relative deflections for various types of structures are prescribed. Exceeding these norms puts the structure in the second limiting state, which makes its operation impossible or limited.
Strict limits are set for coating beams and floors. For example, for crane beams, the deflection is limited to 1/400 of the span, and for elements that perceive the load from hanging cranes, the requirements are even stricter. SNIP II-23-81* It has also served as a base for many years, but now priority is given to updated codes of rules that take into account modern materials.
β οΈ Note: The full span of the structure must be taken into account when calculating the deflection, not just the distance between the supports if there are significant cantilever overhangs.
It is important to distinguish deflection from regulatory and design load. To check the rigidity, a regulatory load is used, which is not multiplied by reliability factors. This allows us to evaluate the actual behavior of the structure in standard conditions without the margin of safety laid down to prevent destruction.
Methods for determining deformations
There are several ways to calculate the movements of farm nodes. The classic method is the Mora method, which is often combined with the Vereshchagin rule. This approach allows accurate analytical values, but it is time-consuming for complex systems with a large number of rods.
For farms with parallel belts and identical cells, formulas derived from the Mora integral are often used. They allow you to quickly estimate the order of the deflection value without a detailed calculation of each node. However, if the geometry is complex, such as a triangular or trapezoidal farm, it is better to apply universal methods.
- π The Mora Method - a universal method based on the principle of virtual work of forces, requiring the construction of epics of effort.
- π» Matrix method It is ideal for computer computing and complex spatial systems.
- π Graphic-analytical It allows visual assessment of deformations, but gives less accuracy.
Modern design has almost completely switched to software systems using the finite element method (FEM). They allow to take into account the work of nodes, the rigidity of connections and nonlinearity of materials, which is not available with manual calculation using simplified formulas.
Formula More for farms
The deflection is calculated by the formula: Ξ = Ξ£ (N) n (l) / (E * A), where N is the load force, n is the unit force, l is the length of the rod, E is the elasticity module, A is the cross-sectional area.
Factors affecting structural rigidity
The hardness of the farm depends on many parameters, and deflection is the total result of their interaction. The first and most important factor is the modulus of the elasticity of the material. E. For steel, it is about 206,000 MPa, and this value cannot be changed, you can only choose a material with other characteristics, for example, aluminum, which has a modulus of elasticity three times less.
The second critical factor is the geometry of the cross-section of elements. Increase in the height of the farm significantly reduces the deflection, as the moment of inertia increases. It is also important to take into account the area of the cross-section of the rods: the larger it is, the less deformation, but the weight of the structure increases.
| Factor. | Effect on deflection | Regulatory method |
|---|---|---|
| Farm height | Inversely proportional | Increase in overall height |
| Elasticity module | Direct dependency | Material selection (steel, wood) |
| The load | Direct dependency | Reducing the weight of the coating |
| Type of nodes | Substantial | Hard knots reduce deflection |
Do not forget about the temperature effects. Although they are more likely to cause movement in the horizontal plane, in statically undetectable systems, temperature changes can cause additional internal forces that affect the overall deformation.
Use the building lift when installing farms. This is a preliminary bend of the structure in the direction opposite to the action of the load, which compensates for the future deflection.
Incorporation of load types in calculation
Correct. farm-deflection It is impossible without proper collection of loads. The main ones are constant loads (weight of the farm itself, roofing, communications) and temporary (snow, wind, payload). To determine the deflection, the full normative value of the snow load is taken.
Wind load often creates a suction, that is, acts in the opposite direction of snow. In some cases, this can be a favorable factor reducing the overall deflection, but when counting on stability, this can become critical. Different loading combinations should be considered.
- βοΈ Snow load The main factor for regions with heavy rainfall, requires accounting for snow bags.
- π¬οΈ Wind load It can both increase and decrease the deflection depending on the direction.
- ποΈ Installation loads The weight of machinery and people in installation, often ignored but important for lightweight constructions.
β οΈ Note: If there are hanging equipment (crane beams, ventilation), their weight should be added to the constant load at the point of application.
Dynamic loads, such as vibration from running equipment, can also affect the comfort of people in a building, even if the static deflection is normal. In such cases, a separate calculation for vibration resistance is required.
Calculation in software complexes
In the digital age, manual calculation is used mainly to verify results obtained in specialized software. Programmes of type LIRA-SAPR, SCAD Office or RFEM They allow you to create an accurate model of the farm, set all connections and loads.
When working in programs, it is important to correctly set the types of nodes. If in reality the farm is assembled on flanges or welding, providing rigidity, and the model is set hinges, the results may differ. Modern complexes allow you to simulate semi-rigid nodes, which increases accuracy.
Calculation algorithm in the software:1. Building a geometric model.
2. Purpose of sections and materials.
3. The setting of reference conditions (pinching, hinge).
4. Application of loads and combinations.
5. Start solver and analyze epiures.
Errors in the modeling stage, such as incorrect fixing of nodes or skipping loads, lead to incorrect results. Therefore, the engineer needs to have the skills of engineering intuition to understand whether the deflection figures obtained are realistic.
βοΈ Testing of the farm model
Practical recommendations for reducing deflection
If the calculation showed that the deflection exceeds the permissible values, it is not necessary to completely redo the project. There are a number of constructive measures to increase rigidity. The easiest way is to increase the height of the farm, as the stiffness increases proportionally to the square of the height.
You can also increase the cross sections of the most loaded elements, usually these are the belts in the span. The use of Sprengel systems (additional suspensions inside the panel) allows you to redistribute forces and reduce the length of the compressed elements, which also affects the overall deformation.
An important aspect is the quality of manufacturing and installation. Inaccuracies in the length of the elements, initial curvatures (initial camber), can lead to the fact that the real design will work differently than the calculated one. Geometry control is mandatory at all stages.
The optimal farm-to-span height ratio for minimizing deflection is 1/10 to 1/15, depending on the type of load.
Frequently Asked Questions (FAQ)
What is the maximum allowable deflection for a canopy farm?
For coatings without partitions based on the run, the limit deflection is usually taken to be 1/150 - 1/200 of the span. If fragile materials (glass, tiles) are based on the farm, the requirements are stricter - up to 1/400.
Should the farmβs own weight be taken into account when calculating the deflection?
Yes, the weight is a constant load and is always taken into account in the calculation. For light farms, its contribution may be negligible compared to snow, but for heavy structures it is a significant part of the deformation.
Can the deflection be reduced by installing additional supports?
Absolutely. Installing an additional support in the middle of the span reduces the estimated span by half, and the deflection is reduced by 16 times (since it depends on the span in the fourth degree for the distributed load). It's the most efficient way.
Does the steel grade affect the amount of deflection?
Practically not. Elasticity module E all grades of structural steel (St3, 09G2C, etc.) are almost the same and is about 2.06Γ105 MPa. Raising the steel class increases strength, but not rigidity.