# D3.B.13 Design of Tapered Beams

Sections will be checked as tapered members provided that are defined either as a Tapered I section or from a USER table.

Example using a Tapered I section:

UNIT CM
MEMBER PROPERTY
1 TO 5 TAPERED 100 2.5  75 25 4 25 4

Example using a USER table:

START USER TABLE
TABLE 1
UNIT CM
ISECTION
1000mm_TAPER
100 2.5 75 25 4 25 4 0  0 0
750mm_TAPER
75 2.5 50 25 4 25 4 0  0 0
END

You must specify the effective length of unrestrained compression flange using the parameter UNL.

The program compares the resistance of members with the applied load effects, in accordance with BS 5950-1:2000. Code checking is carried out for locations specified by the user via the SECTION command or the BEAM parameter. The results are presented in a form of a PASS/FAIL identifier and a RATIO of load effect to resistance for each member checked. The user may choose the degree of detail in the output data by setting the TRACK parameter.

The beam is designed as other wide flange beams apart from the Lateral Torsional Buckling check which is replaced by the Annex G.2.2. check.

## D3.B.13.1 Design Equations

A beam defined with tapered properties as defined above will be checked as a regular wide flange (e.g., UB or UC), except that the following is used in place of clause 4.3.6, the lateral torsional buckling check.

## D3.B.13.2 Check Moment for Taper Members as per clause G.2.2

The following criterion is checked at each defined check position in the length of the member defined by the BEAM parameter.

 Mxi ≤ Mbi (1 - Fc/Pc)

where
 Fc = the longitudinal compression at the check location Mbi = the buckling resistance moment Mb from 4.3.6 for an equivalent slenderness λTB, see G.2.4.2, based on the appropriate modulus S, Seff, Z or Zeff of the cross-section at the point i considered Mxi = the moment about the major axis acting at the point i considered Pc = the compression resistance from 4.7.4 for a slenderness λTC .y, see G.2.3, based on the properties of the minimum depth of cross-section within the segment length L

## D3.B.13.2 G.2.3 Slenderness lTC

 λTC = yλ

where
 y = $[ 1 + ( 2 a / h s ) 2 1 + ( 2 a / h s ) 2 + 0.05 ( λ / x ) 2 ] 0.5$ λ = Ly/ry a = the distance between the reference axis and the axis of restraint, hs = the distance between the shear centers of the flanges Ly = the length of the segment ry = the radius of gyration for buckling about the minor axis x = is the torsional index

## D3.B.13.4 G.2.4.2 Equivalent slenderness ITB for tapered members

λTB = cntνtλ

Where, for a two-flange haunch:
$v t = [ 4 a / h s 1 + ( 2 a / h s ) 2 + 0.05 ( λ / x ) 2 ] 0.5$
where
 C = the taper factor, see G.2.5

## D3.B.13.5 G.2.5 Taper factor

For an I-section with D ≥ 1.2B and x ≥ 20, the taper factor, c, is as follows:
$c = 1 + 3 x − 9 ( D max D min − 1 ) 2 / 3$
where
 Dmax = the maximum depth of cross-section within the length Ly, see Figure G.3 Dmin = the minimum depth of cross-section within the length Ly, see Figure G.3 x = the torsional index of the minimum depth cross-section, see 4.3.6.8

Otherwise, c is taken as 1.0 (unity).