Geometrical limits for Web openings in Non-composite beams (Eurocode)

Environment

Eurocode

Introduction

This article will look at the geometrical requirements when specifying web openings in non-composite beams to the Eurocode.

Web openings can only be defined within a beam once a section size has been specified. This is achieved by either specifying the section size to check, or by running an initial Automatic design and then adding the web openings to the proposed section via the Web openings page of the Edit member dialog (right click beam and Edit…) once the Automatic design option is unchecked.

It is worth noting that if you use the Quick layout option and Add openings then the geometrical limits are automatically satisfied.

This article is interested in reviewing the geometrical limits if we attempt to edit or manually input the individual web opening values in the screenshot above.

In order to achieve this we will look at defining rectangular and circular openings in a 686x254x125 UB rolled section. A few properties are highlighted as these are referenced later during verification.

The overall height, h of the section is 677.9mm
The flange thickness, t_f = 16.2 mm
Root radius, r = 15.2 mm

The design of web openings follow the guidance contained in the Steel Construction Institute (SCI) P355 document “Design of Composite beams with large web openings” which covers both composite and non-composite situations. Table 2.1 specifies the recommended Practical geometric limits for non-composite beams with large web openings for both rectangular and circular openings. This extract is shown below.

Extract from SCI P355 “Design of Composite beams with large web openings” Table 2.1 which specifies the Practical geometric limits for non-composite beams with large web openings.

There are a number of parameters within the table that affect the positioning of web openings and these can be broken down into separate groups for consideration - Openings, Tees, Posts and Loading. We will look at each of these groups by considering Rectangular and Circular openings separately.

The screenshot below shows the main web opening dialog with a number of issues being reported.

These include:

Arrows between openings or the end of a beam indicating an issue with the web or end post spacing
Shading of the parts above/below an opening indicating an issue with the Tee’s
A solid fill within an opening indicating an issue with the web opening size or aspect ratio

Rectangular

Openings

Max. depth of opening

The maximum depth of an opening, h₀, (denoted d₀ in TSD) is <= 0.7h , where h is the height of the section.

Thus, for our 686x254x125 section, h₀ = 0.7(677.9) = 474.53mm

A red warning cross is displayed along with a tooltip should any geometrical requirement not be met. The tooltip provides the value limits required to satisfy any constraints.

Max. Unstiffened opening length

The maximum unstiffened opening length, l₀ for a rectangular opening is dependant upon the shear condition of the beam:

High shear <= 1.5 h₀
Low shear <= 2.5 h₀

In Tekla Structural Designer the definition of the web openings are defined prior to any analysis or design taking place, hence it is not possible to position the web opening to satisfy point loads or to consider the high/low shear requirements. Tekla Structural Designer therefore conservatively determines the maximum unstiffened opening length limit on the more onerous condition for high shear of <= 1.5 h₀

Thus, the aspect ratio, l₀ / h₀ <= 1.5

Taking the depth of opening, h₀ = 470mm, the maximum unstiffened opening length, l₀ = 1.5(470) = 705mm

Note. As briefly mentioned, Tekla Structural Designer provides a red warning cross and a tooltip with value limits when you input invalid values within the web opening dialog. For a rectangular opening it works by allowing you to specify the opening length, l₀ you would like to consider and then checks the requirement for the opening depth against both the aspect ratio and maximum depth limit.

i.e. taking l₀ = 706mm, the allowable range for the opening height, h₀ can range between l₀ / 1.5 = 706/1.5 = 470.7mm and 0.7(h) = 474.53mm. This is provided to you in the tooltip for guidance.

Tees

SCI P355 Table 2.1 provides recommended limits for the minimum depth of tees and the maximum ratio of the depth between tees.

For a rectangular opening using a 705mm unstiffened opening length, l₀ and 470mm opening height, h₀ located within the web of our 686x254x125 section where:

Min depth of tees >= 0.1 h = 0.1(677.9) = 67.79mm
Min depth of top tee >= 0.1 l₀ = 0.1 (705) = 70.5mm
Max ratio of depth of tees 1 <= h_b / h_t <= 2

Therefore, taking the opening at the centre depth of the section, d_c = 677.9/2 = 338.9mm (from top of section) both tees are (677.9-338.9) / 2 = 169.5mm > min depth of top tee 70.5 mm so OK ✔️

Ratio = 169.5/169.5 = 1 so OK ✔️

As a further example, let us now adjust the centre position of the opening so that it is located at d_c = 300 mm from the top of the section. This will provide different depths for the top and bottom tees.

Tee bottom, h_b = 677.9 - 300 - 470/2 = 142.9mm > min depth of tees 67.79 mm so OK ✔️
Tee top, h_t = 677.9 - 142.9 - 470 = 65mm < min depth of top tee 70.5 mm so unsatisfactory ❌

Ratio 142.9 / 65 = 2.19 > max. ratio of 2 so unsatisfactory ❌

The tooltip above provides the required input for d_^c to ensure the maximum ratio of depth of tees is satisfied 1 <= h_b / h_t <= 2.

Web Posts

We will now utilise a rectangular web opening, length l₀ = 705mm and height, h₀ = 470mm located at the vertical centre of the section, d_c = 677.9/2 = 338.95 to move onto looking at web posts

If we add an additional rectangular opening by using the Copy… command then it inputs the required distance between centres of openings to satisfy the geometrical requirements for posts.

Table 2.1 of SCI P355 suggests that the minimum width of the web post is:

Low shear >= 0.5 l₀
High shear >= 1.0 l₀

Again, since loading conditions are unknown at the time of input the high shear condition is taken as the more conservative value.

According to Table 3.1 the distance taken between centres of web openings is 705 / 2 +1.0(705) + 705 / 2 = 1410mm. This does not match with the value displayed in the Web opening dialog above which recommends a value of 1645mm. If we input a value as Table 3.1 of 1410mm we can clearly see the web post opening is reported as being insufficient. The triangles overlap. As you increase the post spacing the triangle overlap reduces. Once they do not overlap the spacing is satisfactory.

Why is this so? SCI P355 Table 2.1 suggests a value of 1410mm is satisfactory by ensuring that the spacing between openings equals or exceeds the length of the opening. However, taking this at face value highlights two simplifications:

It assumes the lengths of both openings are the same (this is not always the case)
It has no consideration of the depth of the openings. In theory, if you took this check at face value, then you could have two openings that have very short lengths and high depths, and have them very closely spaced. This would satisfy the SCI P355 check, but wouldn’t necessarily be an appropriate approach to take.

Therefore, in Tekla Structural Designer we have implemented the following geometric limit, which effectively averages out any potential difference in web opening lengths, and takes account of the aspect ratios of the openings by also considering their depths.

S > Max [2 x (d_a + d_b) / 2 , (l_a + l_b) / 2]

Where:

S = Spacing between openings
d_a = Depth of opening a
d_b = Depth of opening b
l_a = Length of opening a
l_b = Length of opening b

So for the example above.

S > Max [ 2 x (470 + 470) / 2 , (705 + 705) /2] = Max [ 940, 705 ] = 940 mm

Therefore, the centre to centre spacing should be 705 / 2 + 940 + 705 / 2 = 1645 mm (as stated in the Copy… command).

Checking the difference in L_c values the centre to centre spacing = 4645 - 3000 = 1645mm. You will note that no issues are reported in the dialog.

End Posts

The minimum recommended width of end post in accordance with Table 2.1 is >= l₀, the length of the opening and >= h, the height of the section

Tekla Structural Designer takes the minimum value as Max[ l₀, 2(h₀)].

The reasoning is the same as the web posts discussed earlier. Table 2.1 makes no allowance for the depth of the openings. If we consider the aspect ratio for high/low shear as ranging between 1.5 and 2.5 taking the average value of 2, we could say that l₀ is equivalent to 2(h₀) if the opening height was greater than the length.

Thus, the distance from beam end to centre of opening is taken as = Max [ (l0, 2(h₀) ] + l0 /2 = 2(470) + 705 / 2 = 1292.5 mm

If the end post spacing is not sufficient then a triangle is displayed where the point overlaps the end of the beam. As you increase the spacing the overlap reduces until you have provided the required spacing. The tooltip provides the end post value required.

Circular

Openings

Max. depth of opening

The maximum depth of an opening, h0, (denoted d₀ in TSD):

circular <= 0.8h = 0.8(677.9) = 542.32mm

Max. opening length

The max. opening length is the same as the depth of opening <= 0.8h. Tekla Structural Designer does not require this value.

Tees

SCI P355 Table 2.1 provides recommended limits for the min depth of tees and the max. ratio of the depth between tees.

For a circular opening:

Min depth of tees >= t_f + 30 = 16.2 + 30 = 46.2 mm
Min depth of top tee >= t_f + 30 = 16.2 + 30 = 46.2 mm
Max ratio of depth of tees 0.5 <= h_b / h_t <= 3

Therefore, taking the opening at the centre depth of the section, d_c = 677.9/2 = 338.9mm (from top of section)

Both tees are (677.9-338.9)/2 = 169.5mm > min depth of tee 46.2 mm so OK ✔️

Ratio = 169.5/169.5 = 1 so OK ✔️

Let us now adjust the centre position of the opening so that it is located at d_c = 310 mm from the top of the section. This will provide different depths for the top and bottom tees.

Tee bottom, h_b = 677.9 - 310 - 542/2 = 96.9 mm > min depth of tees 46.2 mm so OK ✔️

Tee top, h_t = 677.9 - 96.9 - 543 = 38 mm < min depth of top tee 70.5 mm so Unsatisfactory ❌

Ratio 96.9 / 38 = 2.55 < 3 so Ok. ✔️

The tooltip above provides the required input for dc to ensure the maximum ratio of depth of tees is satisfied 0.5 <= h_b / h_t <= 3.

Web Posts

We will now utilise a circular web opening, d_c = 542mm located at the centre dc = 677.9/2 = 338.95 to move onto looking at web posts. The opening is located 3m along the beam length from the left hand edge.

If we add an additional circular opening by using the Copy… command it inputs the required distance between centres of openings to satisfy the geometrical requirements for posts.

For a circular web opening, Table 2.1 of SCI P355 specifies that the minimum width of the web post is = 0.4 h₀

Thus centre to centre spacing = 542/2 + 0.4(542) + 542/2 = 758.8mm

If we were to reduce the centre to centre spacing to something less than the value calculated above then warning triangles are displayed since they overlap. As you increase the post spacing the triangle overlap reduces. Once they do not overlap the spacing is satisfactory.

End Posts

The minimum width of end post in accordance with Table 2.1 is >= 0.5 h₀.

Tekla Structural Designer takes the minimum value as >= h₀

The reasoning is that since l₀ and 2(h₀) are equivalent for a rectangular opening (see the Rectangular opening end post section), for a circular opening this equates to h₀ and h₀ (since there is no l₀). The difference between Table 1 values between rectangular and circular web openings is 0.5, hence we take half of the 2(h₀) value = h₀. To put this into perspective, the Table 3.1 value of 0.5(h₀) is very small, since Tekla Structural Designer is a centre wire model. i.e. the limit is measured from the centre line of the column. If the beam was connected to the flange of the column then half the column depth has already been truncated.

Note. In all of this, when red crosses are displayed it is to highlight that recommended values have been exceeded. If you ignore and click OK to confirm the layout of the openings, the design still runs. You as the engineer can make a judgement.

Therefore the end distance to centre of opening in Tekla Structural Designer is taken as = h₀ + h₀ / 2 = 813mm

If the end post spacing is not sufficient then a triangle is displayed, where the point overlaps the end of the beam. As you increase the spacing the overlap reduces until you have provided the required spacing. The tooltip provides the end post value required.

Web Posts between rectangular and circular openings

Using the same rectangular and circular opening sizes used earlier. The required centre to centre spacing is 1365 mm (see screenshots below)

No guidance is provided in SCI P355 for the Minimum width of web post between openings of different types. Therefore, Tekla Structural Designer assumes the following formulae for calculating the web post spacing

= 0.5(dia)+Max[0.5(L₀),h₀]

where:

circular opening, dia = 542mm
rectangular, l₀ = 705mm
rectangular, h₀ = 470mm

= 0.5(542)+ Max[0.5x705,470] = 271+Max[352.5,470] = 741mm

Thus, the centre to centre spacing is 542 / 2 + 741 + 705 / 2 = 1364.5mm

Summary

The above article has been written to explain the geometric limits imposed by Tekla Structural Designer when manually editing or defining web openings. If you use the Quick layout command then these limits are automatically catered for. These are recommended limits and you are able to ignore the red crosses within the input dialog and proceed with a design. An example of this is where you know the opening is located within the low shear region and hence the aspect ratio could be greater. It should be borne in mind that you are the engineer and hence are ultimately responsible for any input values assumed for the design.