BS Example _ Steel1

International Codes

British Codes - Design Per British Cold Formed Steel Code 2E.4 Design Equations

Tensile Strength

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

The tensile strength,

Pt of the member should be determined from clause 7.2.1

Where

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

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

And

and

1

Where

Ft is the applies tensile strength Pt is the tensile capacity determined in accordance with clause 7.2.1 of the subject

code Mz,My,Mcz,Mcy are as defined in clause 6.4.2 of the subject code

Compressive Strength

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

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is described below.

For sections symmetrical about both principal axes orclosed cross-sections which are not subjected to torsionalflexural 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, Pc, 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.

Torsional flexural buckling

Design of the memberswhich 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 aLE/r in place of actual slenderness ratio while reading Table 10 for the value of Compressive strength(pc).

Where

= 1 , otherwise

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

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

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

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

The Mcz, Mcy and Mb are calculated from clause numbers 5.2.2 and 5.6 in the manner described hereinbelow.

Calculation of moment capacities

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

Mcz = SzzX po Mcy = Syy X po

Where Mcz is the Moment resistance of the section in z axis Mcz is the Moment resistance of the section in z axis po is 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 , Mc , and the buckling resistance moment of the beam, Mb

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

MY is 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 is the elastic lateral buckling resistance as per clause 5.6.2.2

is 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 abovementioned equations.

Shear Strength

The maximum shear stress should not be greater then 0.7 pyas per clause 5.4.2

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

The parameters are calculated as follows :-

pv = 0.6 X py

Pv= A*Min(pv,qcr)

Where

Pv is the shear capacity in N/mm^2 py is the design strength in N/mm^2 t is the web thickness in mm D is the web depth in mm

Combined bending and Shear

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



Where

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

The next table contains the input parameters for specifying values of design variables and selection of design options.

BRITISH COLD FORMED STEEL DESIGN PARAMETERS

Parameter Name Default Value Description

BEAM

1.0 When this parameter is set

to 1.0 (default), the adequacy of the member is determined by checking a total of 13 equally spaced locations along the length of the member. If the BEAM value is 0.0, the 13 location check is not conducted, and instead, checking is done only at the locations specified by the SECTION command (See STAAD manual for details. For TRUSS members only start and end locations are designed.

CMZ 1.0

Coefficient of equivalent uniform bending Cb. See BS:5950-5:1998,5.6. Used for Combined axial load and bending design.

CMY 1.0

Coefficient of equivalent uniform bending Cb. See BS:5950-5:1998,5.6. Used for Combined axial load



and bending design.

CWY 1.0

Specifies whether the cold work of forming strengthening effect should be included in resistance computation. See BS:5950-5:1998,3.4

Values: 0 effect should not be included 1 effect should be included

FLX

1 Specifies whether

torsional-flexural buckling restraint is provided or is not necessary for the member. See BS:5950-5:1998, 5.6

Values:

0 Section not subject to torsional flexural buckling

1 Section subject to torsional flexural buckling

FU

430 MPa

Ultimate tensile strength of steel in current units.

FYLD

250 MPa

Yield strength of steel in current units.

KX

1.0 Effective length factor for torsional buckling. It is a fraction and is unit-less. Values can range from 0.01 (for a column completely prevented from buckling) to any user specified large value. It is used to compute the KL/R ratio for twisting for determining the capacity in axial compression.

KY

1.0 Effective length factor for overall buckling about the local Y-

axis. It is a fraction and is unit-less. Values can range from 0.01 (for a column completely prevented from buckling) to any user specified large value. It is used to compute the KL/R ratio for determining the capacity in axial compression.

KZ

1.0 Effective length factor for overall buckling in the local Z-axis. It

is a fraction and is unit-less. Values can range from 0.01 (for a member completely prevented from buckling) to any user specified large value. It is used to compute the KL/R ratio for determining the capacity in axial compression.

LX

Member Unbraced length for twisting. It is input in the current units of



length

length. Values can range from 0.01 (for a member completely prevented from torsional buckling) to any user specified large value. It is used to compute the KL/R ratio for twisting for determining the capacity in axial compression.

LY

Member length

Effective length for overall buckling in the local Y-axis. It is input in the current units of length. Values can range from 0.01 (for a member completely prevented from buckling) to any user specified large value. It is used to compute the KL/R ratio for determining the capacity in axial compression.

LZ

Member length

Effective length for overall buckling in the local Z-axis. It is input in the current units of length. Values can range from 0.01 (for a member completely prevented from buckling) to any user specified large value. It is used to compute the KL/R ratio for determining the capacity in axial compression.

MAIN

0 0 Check slenderness ratio

0 Do not check slenderness ratio

NSF

1.0 Net section factor for tension members

DMAX

2540.0 cm. Maximum allowable depth. It is input in the current units of

length.

RATIO

1.0 Permissible ratio of actual to allowable stresses

TRACK

0

This parameter is used to control the level of detail in which the design output is reported in the output file. The allowable values are:

0 - Prints only the member number, section name, ratio, and PASS/FAIL status.

1 - Prints the design summary in addition to that printed by TRACK 1

2 - Prints member and material properties in addition to that printed by TRACK 2.



BS Example _ Steel1

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