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CHAPTER 7

TIMBER ELEMENTS DESIGNCOMPOSED CROSS-SECTION ELEMENTS

7.1. General design considerations

In wood construction, because of the few kinds of wood types, composed cross-section

elements are often used. Joints of wooden elements, excluding the glued ones, deform themselves

when are subjected to varios actions. Displacements are produced between joined elements,

allowing their deformation, somehow independently, and increasing the total deformation of the bar

and reduces its rigidity. This phenomenon decreases the strength capacity of the composed section

elements with respect to an equivalent simple section element. The deformation of flexible joint,

and the failing of splices are very important in computations where the beam stiffness is taken into

account, that means for bending and compression with buckling.

For centrically tensioned members, for which beam stiffness do not influence the unit

stresses, the strength capacity of the composed beam is the same as for a beam with equivalentsimple section.

The computation of bars with built-up section becomes in all cases the computation of

equivalent values of inertia moment, resistance modulus and slenderness coefficients, on the basis

of some approximate formulas (resulting from exact solutions after a number of simplifications);

making the computations available.

7.2. Elements subjected to axial tension

The tension capacity for every element i composing the cross-section is given by:

RTti,net

c

ti,rmmART = (7.1)

where: i,rT is tension capacity of the i element, in N;c

tR - design tension strength of massive wood function of wood species, wood quality class

and exploitation conditions of the structure, in N/mm2;

Anet,i the gross area of the designed cross-section i, in mm2;

mTt treatment coefficient for tension;

mR load repartition coefficient with value 0,90.

The capacity of composed elements subjected to tension is established through the

summation of the capacities of the component elements if they have the same elasticity modulus:

=

=n

1ii,rr

TT (7.2)

For the check of every element of the tensioned composed bar, the effective tension forceTef,i is established by dividing the total effective force Tef proportionally to the gross area of the

element i.e.:=

=n

1ii,gross

i,gross

efi,ef

A

ATT

. (7.3)

7.3. Elements subjected to centrically compression

Compressed elements with composed cross-section can be:

- package bars for which all elements are acted at their extremities (figure 7.1, a);

- bars with continuous interior plates (figure 7.1, b) and bars with continuous exteriorplates (figure 7.1, c) for which the principal elements are acted only at their extremity.

Continuous interior and exterior plates are secondary elements increasing element

stiffness.


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x x

y


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a b c d e f

Figure 7.1. Types of centrically compressed members

- bars with discontinuous interior plates (figure 7.1, d), principal elements are located at a

certain distance and assembled with discontinuous and isolated interior plates.;

- latticed members (figure 7.1, e);- raft bars (figure 7.1, f) for which elements are assembled through a plywood or plank

wall.

7.3.1. Package bars design

7.3.1.1. The compression capacity of package bars with respect to the axis normal to the

joints, Crx, in N, is established with the relationship:

Tcxdesign

c

crxmARC =

| | (7.4)

where:c

cR

| | is the design compression strength parallel to grains established function of wood

species characteristic strength to compression parallel to grains, quality class of wood andexploitation conditions, expressed in N/mm2 (see table 6.2)

Adesign design cross-section area of all elements (the weakenings area should be maximum

25% from the gross area, in mm2;

mT treatment coefficient of wood for compression parallel to grains.

cx buckling coefficient with respect to x-x axis.

7.3.1.2. The compression capacity of package bars with respect to axis parallel to the joints,

Cry, in N, is established with the relation:

Tcydesign

c

crymARC =

| | (7.5)

where:

c

c

R| | is the design compression strength parallel to grains established function of wood

species characteristic strength to compression parallel to grains, quality class of wood and

exploitation conditions, expressed in N/mm2 (see table 6.2)

Adesign design cross-section area of all elements (the weakenings area should be maximum

25% from the gross area, in mm2;

mT treatment coefficient of wood for compression parallel to grains.

cy buckling coefficient with respect to y-y axis.The buckling coefficient with respect to the y-y axis is determined function of the

transformed slenderness coefficienttr

y as follows:

y

tr

y= (7.6)

where is an increasing coefficient for the composed element slenderness with respect to the axisparallel to joints:

e

2

f

6

n

10rhbk1

+=

(7.7)

where: k is design coefficient function of joint type, joining means and efforts type (computing

formula is given in table 7.1);

b the cross-section dimension parallel to joints, in mm;

h the cross-section dimension normal to joints, in mm;

r number of sliding joints;

f - buckling length of the member, in mm;

ne the effective number of shear joints distributed along 1 m of the member length in eachjoint.

Values ofkcoefficient

Table 7.1

y


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Joint

types

kcoefficient for:

compression compression + bendind

Nails2d10

1

2d5

1

Screws2d3

1

2d5,1

1

7.3.2. The design of bars with continuous interior plates (figure 7.1, b) and bars with

continuous exterior plates (figure 7.1, c)

7.3.2.1. The design capacity to centrically compression with respect to x-x axis has the same

formula as for package bars (7.4), where Adesign = Ap (area of main elements of bar) and cx is

determined function of giration radius as follows:p

sxpx

xA

I5,0Ii

+= , where Ipx and Isx are inertia

moments of main elements respectively of secondary elements of the bar with respect to x-x axis.

7.3.2.2. The design capacity to centrically compression with respect to y-y axis has the sameformula as for package bars (7.5), where Adesign = Ap (area of main elements of bar) and cx is

determined function transformed slenderness coefficient (see relation 7.6) where y depends on

giration radius:p

sypy

yA

IIi

+= , where Ipy and Isy are inertia moments of main elements respectively

of secondary elements of the bar with respect to y-y axis.

7.4. Elements subjected to eccentrically compression

7.4.1. The verification (for the strength check in the bending moment plane) with respect to

y-y axis relation is:

00,1M

M

C

Cc

r

fef

r

ef (7.8)

where: Cefis effective compression effort, in N;

Cr compression capacity of the element in N;

Adesign Ap (principal elements area);f

efM - maximum final bending moment established function of the y-y axis normal on force

direction, in Nmm;c

rM - corrected bending capacity of the element, in Nmm, established with relation:

Ti

y

design

c

iw

c

rmWRkM = (7.9)

kw coefficient reducing the bending moment taking into account joint deformations,having the values 0,90 for bars with one sliding joint and 0,80 for bars with two or more sliding

joints;c

iR - bending design strength established function of the wood species characteristic

strength to bending, quality wood class and exploitation conditions, expressed in N/mm2 (table 6.2);y

designW - strength modulus with respect to y-y axis for the most acted cross-section of the

element, in mm3;

mTi treatment coefficient for bending.

7.4.2. The verification with respect to x-x axis, relation is:

00,1MM

CC

rx

f

x,ef

rx

ef (7.10)

where: Cefis effective compression effort, in N;

Cr compression capacity of the element, in N, taking Adesign = Ap (principal elements area);


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f

x,efM - maximum final bending moment established function of the x-x axis normal on force

and joints direction, in Nmm;

rxM - bending capacity of the element with respect to x-x axis, in Nmm.

7.5. Elements subjected to bending

Built-up members subjected to bending are made of two or more timber pieces, superposed,

joined longitudinally with wooden wedges or steel rings and bolts.

The computation of built-up members subjected to bending implies checking in bending

deflection and shear of joints.

7.2. Built-up beam made by two elements joined with prismatic wedges

Bearing capacity of timber composed cross-section elements subjected to bending Mr,

expressed in Nmm, is given by the following general relationship:

Ti

c

design

c

irmWRM = (7.11)

where:c

iR is the design bending strength established function of wood species characteristic

strength to bending, quality class of wood and exploitation conditions, expressed in N/mm2;c

designW is the corrected axial strength modulus in mm3 ( netw

c

designWkW = );

mT treatment coefficient of wood for bending;

kw coefficient reducing the bending moment taking into account joint deformations,

having the values 0,80 or 0,90 for bars made up with two or three elements with no interspace

between them and 0,80 or 0,60 for bars with two or three elements located with interspace between;Wnet the strength modulus of the net area of the cross-section, considered unitary and no

deformability of joints is taken into account.

The deflection check for composed cross-section elements subjected to bending is the same

as for simple cross-section elements but when determining the maximum final deflection, a

corrected moment of inertia is taken into account:

grossicIkI = (7.12)

where:

ki is a reduction coefficient of inertia moment taking into account the deformability of joints;

Igross gross cross-section moment of inertia.

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