D3.E.3.1 Tensile Strength

The allowable tensile strength, as calculated in STAAD as per BS5950-5, section 7 is described below.

The tensile strength, P_t of the member should be determined from clause 7.2.1

P_t = A_ep_y

where

Ae	=	the net area An determined in accordance with cl.3.5.4
py	=	the design strength

D3.E.3.2 Combined bending and tension

As per clause 7.3 of BS 5950-5:1998 members subjected to both axial tension and bending should be proportioned such that the following relationships are satisfied at the ultimate limit state

F_t/P^t + M_z/M_cz + M_y/M_cy ≤ 1

M_z/M_cz ≤ 1

and

M_y/M_cy ≤ 1

where

Ft	=	the applies tensile strength
Pt	=	the tensile capacity determined in accordance with clause 7.2.1 of the subject code
Mz,My,Mcz,Mcy	=	as defined in clause 6.4.2 of the subject code

D3.E.3.3 Compressive Strength

The allowable Compressive strength, as calculated in STAAD as per BS5950-5, section 6 is described below

For sections symmetrical about both principal axes or closed cross-sections which are not subjected to torsional flexural buckling, the buckling resistance under axial load, Pc, may be obtained from the following equation as per clause 6.2.3 of the subject code

For sections symmetrical about a single axis and which are not subject to torsional flexural buckling, the buckling resistance under axial load, P_c, may be obtained from the following equation as per clause 6.2.4 of the subject code

Where the meanings of the symbols used are indicated in the subject clauses.

D3.E.3.4 Torsional flexural buckling

Design of the members which have at least one axis of symmetry, and which are subject to torsional flexural buckling  should be done according to the stipulations of the clause 6.3.2 using factored slenderness ratio αL_E/r in place of actual slenderness ratio while reading Table 10 for  the value of Compressive strength(p_c).

where

α	=	(PE/PTF) when PE > PTF
α	=	1, otherwise

Where the meanings of the symbols used are indicated in the subject clause.

D3.E.3.5 Combined bending and compression

Members subjected to both axial compression and bending should be checked for local capacity and overall buckling

Local capacity check as per clause 6.4.2 of the subject code

F_c/P^cs + M_z/M_cz + M_y/M_cy ≤ 1

D3.E.3.6 Overall buckling check as per clause 6.4.3 of the subject code

For beams not subjected to lateral buckling, the following relationship should be satisfied

For beams subjected to lateral buckling, the following relationship should be satisfied:

where

Fc	=	the applied axial load
Pcs	=	the short strut capacity as per clause 6.2.3
Mz	=	the applied bending moment about z axis
My	=	the applied bending moment about y axis
Mcz	=	the moment capacity in bending about the local Z axis in the absence of Fc and My, as per clause 5.2.2 and 5.6
Mcy	=	the moment capacity in bending about the local Y axis, in the absence of Fc and Mz,as per clause 5.2.2 and 5.6
M­b	=	the lateral buckling resistance moment as per clause 5.6.2
PEz	=	the flexural buckling load in compression for bending about the local Z axis
PEy	=	the flexural buckling load in compression for bending about the local Y axis
Cbz,Cby	=	taken as unity unless their values are specified by the user

M_cz, M_cy, and M_b are calculated from clause numbers 5.2.2 and 5.6 in the manner described herein below.

For restrained beams, the applied moment based on factored loads should not be greater then the bending moment resistance of the section, M_c

M_cz = S_zz x p_o

M_cy = S_yyx p_o

Where

where

Mcz	=	the Moment resistance of the section in z axis
Mcz	=	the Moment resistance of the section in z axis
po	=	the limiting stress for bending elements under stress gradient and should not greater then design strength py

For unrestrained beams the applied moment based on factored loads should not be greater than the smaller of the bending moment resistance of the section , M_c , and the buckling resistance moment of the beam, M_b

Then buckling resistance moment, M_b, may be calculated as follows

$M_b=\frac{M_E{M}_y}{{\varphi }_B+\sqrt{{\varphi }_B^2-M_E{M}_y}}\le M_c$

φB = [My + (1 + η)ME]/2

where

MY	=	the yield moment of the section , product of design strength py and elastic modules of the gross section with respect to the compression flange Zc
ME	=	the elastic lateral buckling resistance as per clause 5.6.2.2
η	=	the Perry coefficient

Please refer clause numbers 5.2.2 and 5.6 of the subject code for a detailed discussion regarding the parameters used in the above mentioned equations.

The maximum shear stress should not be greater then 0.7 ´ p_y as per clause 5.4.2

The average shear stress should not exceed the lesser of the shear yield strength, p_v or the shear buckling strength, q_cr as stipulated in clause 5.4.3 of the subject code.

The parameters are calculated as follows:

pv = 0.6·py

qcr = (1000·t/D)2 N/mm2

Pv = A·min(pv, qcr)

where

Pv	=	the shear capacity in N/mm2
py	=	the design strength in N/mm2
t	=	the web thickness in mm
D	=	the web depth in mm

For beam webs subjected to both bending and shear stresses the member should be designed to satisfy the following relationship as per the stipulations of clause 5.5.2 of the subject code

(F_v/P_v)² + (M/M_c)² ≤ 1

where

Fv	=	the shear force
M	=	the bending moment acting at the same section as Fv
Mc	=	the moment capacity determined in accordance with 5.2.2