Bmb

Le= 2L3 for p2

L-j /4 L1 /2 Lj /4 L?/4 L2/2 k->\<-'---—:—>\<-

Po i

Figure 5.6: Simplified assumptions for continuous beams

5.5 Combined tension and bending

(1)P Cross-sections subject to combined axial tension A^ and bending moments My Sd and Mz Sd shall satisfy the criterion:

fyAghu fy Weff,y,ten 7^M /y Weff,z,ten 77M where:

^eff,y,ten the effective section modulus for maximum tensile stress if subject only to moment about the y - y axis;

Weff z ten is the effective section modulus for maximum tensile stress if subject only to moment about the z - z axis;

and 7m = 'Ymo ^eff = ^ef f°r eac^ ^^ ab°ut which a bending moment acts, otherwise ym = Tmi •

(2)P If Weff y ten > Wcff y com or Weff z ten > WQff z>com (where Weff y com and Weff z com are the effective section moduli for the maximum compressive stress in a effective cross-section that is subject only to moment about the relevant axis), the following criterion shall also be satisfied:

in which 0vec is the factor for vectorial effects defined in ENV 1993-1-1.

5.6 Combined compression and bending

(1)P Cross-sections subject to combined axial compression A^ and bending moments My sd and Mz Sd shall satisfy the criterion:

in which Acff is as defined in 5.3, Weff y com and Weff z com are as defined in 5.5 and 7M = 7M0 if Atff = Ag, otherwise yM = ym .

(2)P The additional moments AMy Sd and AA/Z Sd due to shifts of the centroidal axes shall be taken as:

A^y.Sd = NSdeUy = NSdeUz in which eNy and ¿Nz are the shifts of the centroidal axes in the y and z directions, see 5.3(3)P.

(3)P If Weff y com > Weff y ten or Weff z com > Weff z ten the following criterion shall also be satisfied:

My,Sd + AMy,Sd + Mz,Sd + AMz,Sd _ ^vec^Sd < { (5 1Qb)

in which Wgff y len, Weff z ten and i/^ec are as defined in 5.5.

5.7 Torsional moment

(1)P Where loads are applied eccentric to the shear centre of the cross-section, the effects of torsion shall be taken into account.

NOTE: As far as practicable, torsional moments are best avoided or reduced by restraints, because they substantially reduce the load bearing capacity, especially with open sections.

(2) The centroidal axis and shear centre to be used in determining the effects of the torsional moment, should be taken as those of the effective cross-section for the bending moment due to the relevant load.

(3) The direct stresses due to the axial force N^ and the bending moments My Sd and Afz ^ should be based on the respective effective cross-sections used in 5.2 to 5.4. The shear stresses due to transverse shear forces, the shear stress due to uniform (St. Venant) torsion and the direct stresses and shear stresses due to warping, should all be based on the properties of the gross cross-section.

(4) In cross-sections subject to torsion, the following conditions should be satisfied:

where:

ortot Ed is the total direct stress, calculated on the relevant effective cross-section; rtot Ed tota' shear stress, calculated on the gross cross-section, and 7M = 7M0 if Weff = Wef for each axis about which a bending moment acts, otherwise 7M = 7M1 .

(5) The total direct stress atot Ed and the total shear stress rtot Ed should by obtained from:

atot,Ed = aN,Ed + aMy,Ed + *Mz,Ed + (7w,Ed ••• (5.12a)

rtot,Ed = rVy,Ed + rVz,Ed + rt,Ed + rw,Ed ••• (5.12b)

where:

aMy Ed is the direct stress due to the bending moment My ^ ;

aMz Ed is the direct stress due to the bending moment Mz Sd ;

crN ^ is the direct stress due to the axial force AfSd ;

aw ^ is the direct stress due to warping;

rVy,Ed *s shear stress due to the transverse shear force Vy ^ ;

rVz ^ is the shear stress due to the transverse shear force Vz Sd ;

rt,Ed s^ear stress due to uniform (St. Venant) torsion;

rw ^ is the shear stress due to warping.

5.8 Shear force

(1)P The shear resistance of the web Vw Rd shall be taken as the lesser of the shear buckling resistance Vb Rd and the plastic shear resistance Vp( Rd.

(2) The plastic shear resistance V]?( Rd should be checked in the case of a web without longitudinal stiffeners if j*w It < 72£(/yb//y)(7Mo/7Mi) or generally if Xw < 0,83(/yb//y)(TM0/7mi) •

(3)P The shear buckling resistance Vb Rd shall be determined from:

where:

/bv is the shear buckling strength;

/iw is the web height between the midlines of the flanges, see figure 3.3(c);

<f> is the slope of the web relative to the flanges.

(4)P The plastic shear resistance V?i Rd shall be determined from:

(5)P The shear buckling strength /bv for the appropriate value of the relative web slenderness Xw shall be obtained from table 5.2.

Table 5.2: Shear buckling strength fb

Relative web slenderness

Web without stiffening at the support

Web with stiffening at the support "

Xw < 1,40

0,48/yb/Xw

0,48/yb/Xw

Xw > 1,40

0,67/yb/Xw2

0,48/yb/Xw

Stiffening at the support, such as cleats, arranged to prevent distortion of the web and designed to resist the support reaction.

(6)P The relative web slenderness Xw shall be obtained from the following:

fyjfi

- for webs without longitudinal stiffeners: X,

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