Beams

Background

The EU timber beam calculator can be used to calculate both the demands as well as the resistance of a straight beam.

The analysis capabilities include:

• Point transverse forces and point uni-axial moments (excluding torsion)
• Line Loads (including linearly varying)
• Distributed Loads (including varying tributary width). For details on tributary widths, refer to the article, What is tributary width?

The design capabilities include:

• ULS: Moment Resistance (EN 1995-1-1:2004 Cl 6.1.6)
• ULS: Shear Resistance (EN 1995-1-1:2004 Cl 6.1.7)
• ULS: Lateral Torsional Buckling (EN 1995-1-1:2004 Cl 6.3.3)
• ULS: Bearing at Supports (EN 1995-1-1:2004 Cl 6.1.5)
• SLS: Deflection analysis

The members that are supported include:

• Softwood and Hardwood Timber
• Laminated Veneer Lumber (LVL)
• Glue Laminated Lumber

Tutorial

In this worked design example, we will go through the design process of a single-span LVL floor bearer. It will be holding 5 equally spaced beam floor joists and a residential live load. Joist spacing is at every 1500mm, and the beam is laterally restrained at every joist. It is for a residential ground floor hotel room in the United Kingdom (Category A3). This satisfies Service Class 1 for LVLs.

1. Create a Calculation

When adding a new timber beam calculation, you can select between various types of residential timber beam. The sheet and calculations for each are the same, however, some default values and criteria, such as deflection limits and centre to centre spacing, have been made specific to each beam type. For this example, we will select a floor joist.

2. Entering our key properties

Quick Tip - If you're ever unsure what something means in ClearCalcs,simply click the field label for references, checks, conditionals, and descriptions.

First, we enter the key properties of our beam:

• Member Type - Clicking "Select" will open a list of all properties and allow you to select timber sizes from a database, or custom dimensioned timber. Refer to related article Quickly finding the best section with the member selector. We want to use a Kerto-S Laminated Veneer Lumber and initially select a member based on past experience:

• Total Beam Length - The length between start and end of the beam, irrespective of the support conditions. We select 6000 m.
  • Length between lateral restraints - We are confident that the beam has adequate lateral bracing at each joist, so the length between lateral restraints is equal to our spacing of 1500 mm.

• Member Orientation - All timber beams can be analysed bending about either Y or Z-axis. Where it is bending about the minor axis, some checks are not required (e.g. lateral torsional buckling). In our case we select "Loaded from Top"

• Position of Supports from Left - The support conditions may be at any position along the beam. A cantilever can be created on either end by moving the support condition away from "0" or the "Total Beam Length". In our case, the default simply supported position is adequate. The bearing length is used for bearing calculations l_contact to determine the effective bearing contact area and capacity.

3. Load Details

ClearCalcs offers a number of ways to enter loads, to suit a range of uses. These include:

• Distributed Loads (kPa)
• Line Loads (kN/m)
• Point & Moment Loads (kN or kNm)

It also shows a diagram of all "unfactored" load, which auto-converted distributed area loads into equivalent line loads.

Because we selected the "Floor Joist" type of timber beam, ClearCalcs autofills expected loading in accordance with EN 1995, which can be reviewed in the "Project Defaults" tab on the sidebar. Note this may be manually set in the individual calculations, so don't worry if you haven't yet explored the "Project Defaults" tab. Snapshot from Project Defaults:

Distributed Loads: Our 5 joists are entered in as a distributed load, as the difference in actions is minimal relative to placing concentrated loads at regular intervals. You do have the flexibility to do this however in the "Point & Moment Load" table below. We see the Permanent Load qk and wG have been transferred from the Project Defaults. All that is needed is to set the tributary width for the floor load to 2000mm to reflect the imposed load on half the length of the joists. Refer to the article, What is tributary width? for further details.

• Dead load - leave as 0.9 kPa to reflect the weight of the joists and flooring materials.
• Live Load - leave as 2 kPa to reflect the British National Annex Table NA.3,.

Quick Tip: If the floor joists are designed within ClearCalcs, you can load link the reactions directly into the Roof Bearer either as an effective "Line Load" (for regularly spaced joists), or as individual concentrated loads.

Refer to the article here on load linking / load path tracking. This prevents having to re-type the loading, and avoids errors.

Point & Moment Loads:

• Live Load - EN1991-1-1:2004 Cl 6.3.1.2 (3) requires that a concentrated load Qk acting alone should be taken into account. Using the British National Annex Table NA.3, we confirm Qk = 2 kN live load should be checked. ClearCalcs "alternate" imposed loads _QI, _ QI2 and QI3 are applied separately from each other, however are combined with other dead, snow, wind load types. In this case, it’s pretty clear that it won’t govern, but we will still apply for the example. Since the concentrated load doesn’t apply at the same time as the UDL, we’ll apply it in the “Point & Moment Loads” section.

Self-weight may be automatically calculated using the self-weight toggle.

4. Informational and National Annexes

EN1995-1-1 identifies a number of clauses that may be specifically overridden by national annexes, which are summarised in the Foreword under Section "National Annex for EN 1995-1-1". ClearCalcs offers a handy section "Information and National Annexes" that gives access to review or alter these parameters quickly.

Service Class - The service class dropdown affects the duration factors k_mod and the deformation factor k_def. We will set this to Service Class 2 in accordance with British National Annex Table NA.2 (Ground Floors). You will see a quick overview of of the selected factors:

Default Load Duration Assignments per Load Combination: ClearCalcs shows also what modification factor has been assigned to each load combination. Example duration factors are pulled from Table 2.2, and may be altered in the Project Default tab in the sidebar. Note that all accompanying variables are applied at the same time e.g. G + QI + all a comp. factors ( S + W + T).

Partial Factor / Influence of crack width: These factors will infrequently require amending based on National Annex requirements. In our case, the British annex is consistent with EN1995 and we can leave as it is.

Deflection limits: These pending upon the national annex and depending upon the use of the structure. In our case, we shall assume the structure is designed according to Table NA.5 BS EN1995-1-1:2004 (UK annex) and carries a plaster ceiling. Therefore, the final net load combination due to variable load only is span / 250. Instant limits may be chosen based on national requirements.

The absolute criterion can be adjusted that set a hard limit on any deflections. This may be set project-wide in your Project Defaults or can be manually set for this structure.

5. Section selection

At this point, we can see that our beam passes, with the highest utilisation of 90% for deflection. However, we want to make sure we're getting the most out of our member, so go back to the member selector and review the various options available. We note we can achieve a fully utilised beam by reducing the thickness to a 81 thick LVL beam, instead of 90mm.

6. Summary of results and internal force diagrams

Once we’ve got our beam design, we can quickly glance at relevant values to make sure everything corresponds to what we’d expect. On the right panel is the summary section, where we find things such as the critical moment demand and capacity, shear, moment and deflections. Where a calculation for lateral torsional buckling was required based on Eurocode criteria, totals will also be shown.

We can also look at the shear, bending and deflection diagrams to make sure they correspond to what we anticipate.

For deflections, the graph will always show the instantaneous deflection for the governing instantaneous deflection case (characteristic or frequent. We can scroll down the graph to see exact deflection values at different points.

We can also see the "factored" loads applied for each load combination. We can see that the QI2 = 2kN load was factored by 1.5x. Also the distributed load was converted to a line load and factored. QI and QI2 are not applied concurrently as discussed previously.

7. Printing and Member Schedule

Printing: We can now print our fully designed. Before finishing, let's write a Comment to ourselves. This will appear in the printout.

And here is the printout ready for submission!

Member Schedule: ClearCalcs provides a handy Member Schedule that can be viewed from the sidebar and/or printed.

A more in-depth look

Detailed Mode:

While the previous steps are all that is required to design our beam, it may be desirable to see more information about the beam. ClearCalcs fully exposes all code calculations to see every step of the process employed to design the beam. For instance, we can go look at how the lateral-torsional buckling strength is calculated. Some calculations are hidden for clarity, however, they can be made visible by selecting "Detailed" mode. See article on how to view all detailed calculation steps. For example, see the equation for the elastic critical buckling moment

Multiple Laminations

Users may design custom sections, where the database doesn't have the exact size and grade you need. In addition, a database or custom section can be laminated, with all laminations working in composite.

This concludes our short tutorial on designing a timber beam per EN1995-1-1:2004 with ClearCalcs.