# D11.A.4 Member Resistance

The member resistance is calculated in STAAD according to the procedures outlined in NZS 3404-1997. Calculated design capacities are compared to corresponding axial, bending moment, and shear forces determined from the STAAD.Pro analysis. These are used to report the fail or pass status for the members designed.

## D11.A.4.1 Slenderness

For calculating member slenderness, the length of unbraced segment for compression is considered.

For analytical member design, the `MAIN` and `TMAIN` parameters are used.

## D11.A.4.2 Bending

Bending capacities are calculated per NZS3404 Section 5. The allowable bending moment of members is determined as the lesser of nominal section capacity and nominal member capacity (ref. Cl.5.1).

### D11.A.4.2.1 Bending Section Strength

The nominal section moment capacity, ϕM_{s}
,
is calculated about both principal x and y axes and is the capacity to resist
cross-section yielding or local buckling and is expressed as the product of the
yield stress of the material and the effective section modulus (ref. Cl.5.2.1).
The effective section modulus is a function of section type (i.e., compact,
non-compact, or slender) and minimum plate yield stress fy.
The nominal member capacity depends on overall flexural-torsional buckling of
the member (ref.Cl.5.3).

### D11.A.4.2.2 Bending Member Strength

For sections where the web and flange yield stresses
(f_{y,web}
and f_{y.flange}
respectively) are different, the lower of the two yield stresses is applied to
both the web and flange to determine the slenderness of these elements.

For sections where the web and flange yield stresses (fy,web and
fy.flange respectively) are different, the lower of the two yield stresses is
applied to both the web and flange to determine the slenderness of these
elements. Member moment capacity, φM_{b}
, is
calculated about the principal x axis only (ref. Cl.5.6). Critical flange
effective cross-section restraints and corresponding design segment and
sub-segments are used as the basis for calculating capacities.

The
`ALM` design parameter is used to specify
α_{m}
(refer cl. 5.6.1.1).

The
`SKR`,
`SKT`,
`SKL`,
`UNT`,
`UNB`, and
`PBRACE` design parameters are also used for bending
checks.

## D11.A.4.3 Shear

Section web shear capacity, φV_{v}
, is
calculated per Cl.5.11, including both shear yield and shear buckling
capacities. Once the capacity is obtained, the ratio of the shear force acting
on the cross section to the shear capacity of the section is calculated. If any
of the ratios (for both local Y & Z-axes) exceed 1.0 or the allowable value
provided using the
`RATIO` parameter, the section is considered to have failed
under shear.

The following table highlights which shear capacities are calculated for different profile types.

General Profile Type | New Zealand Section | Shear Checks |
---|---|---|

I-Section (i.e., parallel to minor principal axis) | WB, WC, UB, UC | Calculated for web only |

T-Section | BT, CT | |

Channel | PFC | |

Angle | EA, UA | No checks performed |

Tube | SHS, RHS | Calculated parallel to both z & y principal axes |

Pipe | CHS | Per NZS3404 5.11.4 |

Only unstiffened web capacities are calculated. Stiffened webs are not considered. Bearing capacities are not considered.

The
`TSP` design parameter is used in shear capacity
calculations.

## D11.A.4.4 Compression

The compressive strength of members is based on limit states per NZS3404 Section 6. It is taken as the lesser of nominal section capacity and nominal member capacity.

### D11.A.4.4.1 Compression Section Strength

Nominal section capacity, φN_{s}
, is a function of form factor (Cl.6.2.2), net area of the cross section, and yield stress of the material. Through the use of the NSC parameter, you may specify the net section area. Note that this parameter is different from that corresponding to tension. The program automatically calculates the form factor. The

k_{f}

_{y}yield stress is based on the minimum plate yield stress.

The `NSC` (net section factor for compression) design parameter is used for compression sectoin strength checks.

### D11.A.4.4.2 Compression Bending Strength

Nominal member capacity, φN_{c}
, is a function of nominal section capacity and member slenderness reduction factor (Cl.6.3.3). This value is calculated about both principal x and y axes. Here, you are required to supply the value of α_{b}
(Cl.6.3.3) through the `ALB` parameter. The effective length for the calculation of compressive strength may be provided through the use of the parameters `KY`, `KZ`, `LY`, and `LZ`.

The `PBCRES` and `LHT` design parameters are also used for this check.

## D11.A.4.5 Tension

The criteria governing the capacity of tension members are based on two limit states per NZS3404 Section 7.

The limit state of yielding of the gross section is intended to prevent excessive elongation of the member.

The second limit state involves fracture at the section with the minimum effective net area φN_{t}
section axial tension capacities are calculated (Cl.7.2). Through the use of the `NSF` parameter, you may specify the net section area. STAAD.Pro calculates the tension capacity of a member based on these two limit states per Cl.7.1 and Cl.7.2 respectively of NSZ3404. Eccentric end connections can be taken into account using the `KT` correction factor, per Cl.7.3. The f_{y}
yield stress is based on the minimum plate yield stress. Parameters `FYLD`, `FU`, and `NSF` are applicable for these calculations.

## D11.A.4.6 Combined Forces

### D11.A.4.6.1 Combined Section Strength

Combined section bending and shear capacities are calculated using the shear and bending interaction method as per Cl.5.12.3. This check is only carried out where φV_{v}
section web shear capacities are calculated.

### D11.A.4.6.2 Combined Member Strength

The member strength for sections subjected to axial compression and uniaxial or biaxial bending is obtained through the use of interaction equations. Here, the adequacy of a member is also examined against both section (ref. Cl.8.3.4) and member capacity (ref.Cl.8.4.5). These account for both in-plane and out-of-plane failures. If the summation of the left hand side of the equations, addressed by the above clauses, exceeds 1.0 or the allowable value provided using the `RATIO` parameter, the member is considered to have failed under the loading condition.

## D11.A.4.8 Seismic Provisions

The program performs the following checks per the seismic provisions in section 12 of the code.

- Minimum specified yield stress (table 12.4)
- Maximum ratio of (fy
/ fu) (table 12.4)
The member seismic category is specified using the

`DUCT`design parameter. - Fabrication requirement (Sec.12.4.1.2) - Category 1 or 2 members shall be hot-rolled or fabricated by welding from hot-rolled plate, except that category 2 members may be cold-formed, provided that adequate ductility capacity of the member and its connections is established by experimental testing or rational design.
- Element slenderness (sec.12.5.1.1) - The elements of category 1, 2, 3 and 4 shall comply with the plate-element slenderness limitations presented in Table 12.5.
- Section symmetry requirement (sec.12.5.2) – The yielding regions of category 1 or 2 members shall be doubly symmetric sections. The yielding regions of category 3 members shall be doubly or singly symmetric sections.
- Web slenderness of beam (sec.12.7.2.1) - The web thickness within the yielding region of a beam shall be not less than (d1/82) (fy / 250) for a category 1 or 2 member or less than (d1/101) (fy / 250) for a category 3 member.
- Limit on axial force
(sec.12.8.3.1) - The ratio of design axial force, N*, to
design section capacity, ϕN
_{s}, (refer to 6.2) shall not exceed the values given in (a) through (c) below:- The general limit given in table 12.8.1.
- In addition to (a), for
category 1, 2 and 3 column members, excluding brace members of concentrically
and eccentrically braced frames, the following limitation on design axial
compression shall apply, unless waived according to 12.8.3.2
${N}^{*}\le \varphi {N}_{s}\left(\frac{1+{\beta}_{m}-\sqrt{{N}_{s}/{N}_{oL}}}{1+{\beta}_{m}+\sqrt{{N}_{s}/{N}_{oL}}}\right)$ Eq. 12.8.3.1 - When the slenderness ratio for the member web exceeds that given in table 12.8.2 for the appropriate member category, the design axial force generated by gravity loading alone, Ng*, shall comply with the axial force limitation equation given therein.

- Shear-bending interaction
(12.10.3.1) - When a capacity design procedure is not used, at yielding regions
in category 1 or 2 beams forming part of a seismic-resisting system, when
designing for load combinations including earthquake loads the nominal web
shear capacity of the beams shall be taken as 80% of that calculated from
5.11.4.1 and the interaction of shear and bending moment shall satisfy:

whereM* ≤ ϕM _{sv}- M
_{sv}= - $\begin{array}{cc}{M}_{s}& \text{for}{V}^{*}\le 0.6\varphi {V}_{w}\\ {M}_{s}(1.38-\frac{{V}^{*}}{1.6{V}_{w}})& \text{for}0.6\varphi {V}_{w}\le {V}^{*}\le 0.8\varphi {V}_{w}\end{array}$
The ratio will be calculated as – M* / ϕM

_{sv} - M