## Info

i/75

Note: i is the beam span or the length of the cantilever.

Note: i is the beam span or the length of the cantilever.

wcreep is the creep deformation; i.e. the deformation that is permitted to arise with time under the combination of loading causing the creep behaviour. wfin is the final deformation; i.e. the combination of the instantaneous and the creep deformation.

wnet,fin is the net final deformation; i.e. the deformation below the straight line joining the supports.

The net final deformation can be written as

To prevent the occurrence of unacceptable damage arising due to excessive deflections as well as to meet functional and visual requirements, deflections have to be specified for the project and agreed with the client. Recommended ranges of limiting values for the deflection of simply supported beams and cantilevers are given in 7.2(2) of EC5 and specific values are given in NA.2.5 of the UKNA to EC5 [6] for wnet fin. A summary of these requirements is given in Table 4.6.

In EC5, the design loading used to determine displacements at the SLS is based on the characteristic combination of actions and is discussed in 2.2.25.2. With the characteristic combination of actions, the design is based on an irreversible SLS, which means that no consequences of actions exceeding the specified SLS requirements can remain when the actions are removed.

The terminology used in EC5 to describe the actual displacement in a structure is the same as that used in Figure 4.17 for the limiting displacement but with the letter w replaced by u. The components of deformation are described in 2.3.2, and adopting the EC5 approach the instantaneous deflection (uinst) and the final deflection (ufin) of a structural member will be obtained as follows:

(i) The instantaneous deflection uinst of a solid member acting alone should be calculated using the characteristic combination of actions (equation (2.24)), the appropriate mean value modulus of elasticity parallel to the grain, £0,mean and/or the mean value shear modulus, Gmean. The relationship between Gmean and £0,mean is taken to be Gmean = £0,mean/16 for timber and values of these properties for timber and other wood-based structural products are given in Chapter 1.

(ii) The final deformation ufin is obtained by combining the instantaneous deflection derived from (i) and the creep deflection and the method used will be in accordance with the requirements of 2.3.4.1(b) where the structure has a linear elastic behaviour and consists of members, components and connections having the same creep behaviour or 2.3.4.1(c) where this is not the case. For the case where 2.3.4.1(b) applies, and assuming that a pre-camber is not used, as stated in 2.3.2, the final displacement will be as follows.

For permanent actions, G:

u fin, G = u inst, G + u creep, G = uinst,G (1 + kdef) (4.41)

For the leading variable action Q1:

u fin, Q, 1 = uinst, Q, 1 + uCTeep,Q,1 = uinst,Q,1(1 + ^kdef) (4.42)

For the accompanying variable actions, Qi, where / > 1:

u fin,Q,i = u inst, Q, / + ucreep,Q,i = u inst,Q,i (^0,i + ^2,/kdef) (4.43)

And the final condition will be:

where the functions and symbols are as described in 2.2.14, 2.2.24 and 2.3.2.

Creep in wood arises due to the combined effects of load duration, moisture content, temperature and stress level. Provided the temperature does not exceed 50°C the influence of temperature on creep can be ignored and when the stress level in the wood is at the SLS condition it has also been found that the rate of creep due to this effect will stabilise. For these reasons, the creep deformation caused by moisture content and load duration effects derived using the factors in EC5 is only relevant to the SLS loading condition.

As the duration of the load extends and also as the moisture content rises, the creep deformation of structural elements will increase and from the results of creep tests, values of a deformation factor, kdef (which is a factor that is used in the determination of creep deformation), have been derived for timber and wood-based materials under service class 1, 2 and 3 conditions. Values of the factor are given for timber and some wood-based products in Table 2.10 and the methodology used for the calculation of the final deformation of a structure (or a structural element) is explained in 2.3.2.

When a member is subjected to bending by shear forces, in addition to deformation due to the effect of the bending moment it will also deform due to the effect of the shear forces, and the significance of the shear deformation will primarily be a function of the ratio of the modulus of elasticity £0,mean of the member to its shear modulus Gmean. Consider, for example, a simply supported rectangular beam of depth h and design span £ carrying a point load at mid-span. The ratio of the instantaneous deflection at mid-span caused by the shear forces, uinst v, to the instantaneous deflection at mid-span caused by the bending moment, uinst m, will be:

For structural steel, the ratio £0,mean/Gmean is approximately 2 and consequently in steel design when using normal sections, the shear deformation effect is generally ignored. With timber, however, E0,mean/Gmean is approximately 16 and for practical beam design, h/£ will range between 0.1 and 0.05 resulting in a shear deformation between 5 and 20% of the flexural value. As this is a significant percentage, the effect of shear deformation must be taken into account when designing timber structures.

Shear deformation can be expressed in terms of the flexural deflection multiplied by a shear amplification factor, and the value of the factor associated with a simply supported rectangular beam of width b, depth h and design span £ for some standard load cases is given in Table 4.7. The combined shear and flexural deflection in the beam for the selected load case is obtained by multiplying the bending deflection by the accompanying shear amplification factor. Approximate values for shear amplification factors for other beam configurations are also given in NA.2.6.2 of the UKNA to EC5.

4.6.1.2 Deformation due to compression over supports

When the bearing stress factor, kc 90, referred to in 4.5.3, is unity at a support in a member the bearing strain will be approximately 2-3% and deflection due to compression of the member at its supports at the SLS condition can be ignored. If, however, at the ULS a high value of kc,90 is required to achieve the required bearing strength, the strain could be as high as 10% and the additional deformation caused by compression at the bearing locations in such situations at the SLS must be taken into account in the design.

In the proposed draft amendment to EC5, summarised in Appendix C, 6.1.5, the effect of the proposed change will mean that high compressive strains perpendicular to the grain will not arise and there will be no need to consider compression deformation at supports for normal design conditions.

Table 4.7 Bending deflection and shear amplification factors for standard load cases on simply supported or cantilevered beams of rectangular cross-section

Load case

Uniformly distributed load (udl) equal to a total load Q (kN) along the length of a simply supported beam

Point load P (kN) at mid span of a simply supported beam

Point load P (kN) at the end of a cantilever

Bending deflection (mm) At mid-span = ..._ 5Q! ,,.,3

At the end of the cantilever

= E0,meanb

PomUoad P (kN) at the quarter and Atmkl-span = 32^ ( !f (l + 0-873 (fe) ( h )2)

three quarter points of a simply supported beam

Point load P (kN) at the quarter, mid span and three quarter points of a simply supported beam

Note: £o,mean is the mean modulus of the beam material parallel to the grain (in kN/mm2); Gojmean is the mean shear modulus (in kN/mm2); b is the member breadth (in mm); h is the member depth (in mm); I is the design span (in mm).

### 4.6.2 Vibration

The human body is extremely sensitive to vibration, and compliance with the criteria given in EC5, which relates to the design requirements of wood-based structural floors in residential property, will ensure that the vibration behaviour of the structure is kept within an acceptable zone when subjected to the SLS loading condition.

Human sensitivity to vibration is a complex subject and from research into human discomfort it has been concluded that the major factors influencing a person's view on the acceptability, or otherwise, of vibration are as follows:

• Discomfort due to machine-enforced vibrations

• Discomfort due to footstep-enforced vibrations

• Proximity to and transfer of the vibration.

The effect of these factors can be reduced to acceptable levels by design and by appropriate detailing of the structure as well as non-structural elements. In regard to the specific design requirements, design criteria are given in EC5, and in particular, in the UKNA to EC5, and these are discussed in the following sub-sections.

### 4.6.2.1 Machine-enforced vibrations

Structural vibrations arising from machinery can affect human sensitivity, and acceptable levels of continuous vibration due to vibrating machinery will be obtained from ISO 2631:2 [7]. Where the machine vibration exceeds the acceptable level, the most common way to deal with the problem is to either isolate the machine foundations from the structure or to install anti-vibration mountings between the machine and the structure, detuning the structural response. This will normally involve an analysis of the dynamic behaviour of the structure, and because of the specialist nature of the problem, it is not addressed in EC5.

4.6.2.2 Footstep (footfall) induced vibrations

This is a matter that has been the subject of investigation for some considerable time and over this period the criteria set for the boundaries of the problem have tended to change. The design requirements in EC5 relate solely to residential floors having a fundamental frequency greater than 8 Hz. Floors with a fundamental frequency less than 8 Hz require special investigation, and are not covered in the code.

EC5 requires that the fundamental frequency of the residential floor be greater than 8 Hz and for a rectangular floor with overall dimensions l x b, simply supported along four sides and with timber beams spanning in the l direction, the approximate value of the fundamental frequency, f1, can be calculated from equation (4.46):

• l is the design span of the floor beams (in metres).

• (EI)l is the equivalent flexural rigidity of the floor supporting structure about an axis perpendicular to the direction of the beam span, in N m2/m. Unless the floor decking is designed to act with the floor beams as a composite structure in the direction of the beam span (e.g. in the case of thin flanged composite beams), (EI)l should only be based on the flexural rigidity of the floor beams. Composite action between the floor decking and the timber joists can only be assumed to occur where the floor decking is glued to the joists and designed in accordance with 9.1.2, EC5 and noting that the adhesives must comply with the requirements of 3.6 and 10.3 in EC5.

• m is the mass per unit area of the floor, in kg/m2, and is based on permanent actions only without including partition loads.

For residential floors having a fundamental frequency greater than 8 Hz, human sensitivity relates to the effects of vibration amplitude and velocity caused by dynamic footfall forces. To ensure compliance with the SLS criteria set for these issues, design criteria for residential wood-based plate type floors are given in EC5 and the UK requirements are given in the UKNA to EC5. The UKNA guidance is based on the use of joist-type floors, which is the most common type of floor structure used in the United Kingdom, and it is this category of floor that is considered in the following sub-sections. Where the modulus of elasticity is used in equations, unless otherwise stated, Emean will apply. The requirements to be satisfied in EC5 are as follows:

(a) Low-frequency effects (step frequency effect).

The enforcing frequency on the floor from this action will be less than 8 Hz and consequently the effect of the step action can be considered to be the same as that caused by a static load. The static load simulating the foot force effect is 1 kN applied

Where:

at the centre of the floor and the deflection of the floor at this point, a, must be no greater than the limit given in Table NA.5 in the UKNA to EC5, i.e.

a < 1.8 (mm) for floor spans < 4000 mm (4.47)

## Post a comment