D11.A.5.2 Physical Member Design

In case of analytical member design, all the design inputs are controlled by user input which is one-time for a whole analytical member. Specially the different unbraced lengths (UNT, UNB, LZ, LY), unbraced length factors (Kz, Ky) are considered constant throughout the length of the analytical member. But in case of a physical member, these values tend not to be constant throughout the length. The real essence of physical member design in NZS3404:1997 is the consideration of different values of unbraced lengths and unbraced length factors in different locations of same physical member to replicate the actual condition. This is achieved by auto calculation of these values from the user-provided physical bracings

In case of Physical member design in NZS3404:1997, the program does not divide the physical member into analytical member segments of equal length. Instead, each consisting analytical member is divided into 13 sections. Hence the physical member is considered as a member as a whole with "13n" sections for design checks, where n = number of component analytical members in the physical member under consideration. Clearly, in most of the cases, the distance between two sections will not be constant throughout the length of the member. In order to prevent overlapping design sections at the ends of adjoining componenet analytical members, a small gap of 0.001x the member length is used from the common joint to the design section at these locations. Doing so allows the program to capture changes in internal forces, particularly shear, at these joints within the physical member.

Additionally, PMEMBER automates:

steel grades based on section type, and
tensile stress, f_u , and yield stress, f_y , values based on plate thicknesses

Therefore it is recommend that PMEMBER design be used, even when a physical member consists of only one component analytical member.

D11.A.5.2.1 Modeling with Physical Members

You can use the physical modeling tools available in the user interface Analytical Modeling and Steel Design workflows to form physical members.

You can also define physical members using the DEFINE PMEMBER command. Refer to TR.16.2 Physical Members for details.

D11.A.5.2.2 Section Profiles

When a physical member is checked against the code (CODE CHECK) in NZS3404-1997, all the component analytical members within a single physical member must have the same section assigned. If not, a code check will not be made and an error is displayed in the output.

When a physical member profile is selected (SELECT) in NZS3404-1997, all the component analytical members within a single physical member must be assigned from the same profile table. For example, if one analytical member is assigned an Australian UB150X18.0, then the other analytical members must be assigned any profile from the Austrialin UB table.

D11.A.5.2.3 Calculation for Compression Buckling

For calculation of member compression buckling capacities about the principal axis, the PMEMBER Design uses the concept of unbraced segments against compression (Lz, Ly). The unbraced segments against compression buckling are evaluated using the user defined compression bracings (PBCRES) separately for ZZ and YY axis. The types of restraints that can be provided at any location of the PMEMBER using PBCRES are: U(unbraced), T(translational), R(rotational), and TR(translational-rotational). Compression buckling restraints automate following design calculations for each segment for buckling against both the principle axis:

Unbraced length of a segment for compression buckling – the distance between two consecutive T/R/TR type restraint. The program calculates it only when LZ or LY are not assigned.
Effective length factor, k_e – according to figure 4.8.3.2 of NZS3404:1997 specification using type of restraint (T/R/TR) at the ends of a segment/sub-segment. The program calculates it only when KZ and KY are not assigned.

If you do not assign any compression buckling restraint to the physical member, the program will assume T type restraints at the member ends. But if a member is cantilever, then the program will keep the free end of the member unrestrained. Any user-provided input against member end restraints will override the values assumed by program.

Any value, other than 1.0, given to KZ and KY parameter will replace the automatically calculated effective length factors for the entire PMEMBER.

Any value other than 0.0 (default), given to LZ or LY parameter will replace the automatically calculated unbraced lengths for compression buckling of the entire PMEMBER.

D11.A.5.2.4 Calculation for Flexural/Flange Buckling

For calculation of member bending capacities about the principal x-axis, the PMEMBER Design uses the concept of unbraced segments against flange buckling (UNT, UNB). The unbraced segments against flange buckling are evaluated using the user defined compression bracings (PBRACE) separately for TOP and BOTTOM flange. User-defined flange restraints assigned using the PBRACE design parameter are checked to see if they are effective (i.e., if they are placed on the critical flange as per NZS3404 5.5). Flange restraints not applied to the critical flange are ineffective and hence are completely ignored.

Segment layouts for PMEMBERs may change for different load cases considered for design. Some restraints may be effective for one particular load case as they are found to apply to the critical flange, however for another load case may be found not to act on the critical flange, and found to be ineffective. In other words, the critical flange can change for each load case considered.

Typically, the critical flange will be the compression flange, except for segments with a "U" restraint at one end, in which case it will be the tension flange (as is the case for a cantilever).

Design unbraced flange segments are evaluated by "F", "P", "L", "FR", "PR", or "U" effective section restraints. L restraints are considered only if are deemed to be "effective." L restraints are only considered to be effective when positioned on the "critical" flange between F, P, FR, or FP restraints. If an L restraint is positioned on the non-critical flange it is ignored. Further, if an L restraint is positioned between a U and an F, P, FR, or FP restraint, it is ignored (regardless of whether it is on the critical or non-critical flange).

The PMEMBER Design uses the following steps to determine effective cross-section restraints for each load case considered:

first all user-defined restraints are checked to see if they are applied to the compression flange, with those that are not ignored
next a check is made to see if a "U" type restraint is found at either end of the PMEMBER. If this is the case then any adjacent "L" restraints up to the next "F", "FR", "P" or "PR" restraint are also ignored, regardless of whether they are placed on the critical or non-critical flange. Refer NZS3404 5.4.2.3.

The compression flange in step i) of the routine above is calculated based on the bending moments at the locations of the restraints being considered.

Restraint Type	Definition	Stiffness	Description
FR	Fully and rotationally restrained	Most stiff
F	Fully restrained	↓
PR	Partially and rotationally restrained	↓
P	Partially restrained	↓
L	Laterally restrained	↓	Cannot be specified at the ends of design members.
U	Unrestrained	↓	Can only be applied at the ends of design members, and must be applied to both flanges to be effective. Both top and bottom flanges cannot be unrestrained at the same location (as this is unstable).
None		Least stiff
C	Continuous restrained up to next restraint location		The flange is assumed to be continuously supported at that flange up to next restraint location. For continuously supported flange unbraced length is assumed to be zero.

Segment lengths are not automatically checked to determine if they provide full lateral restraint as per NZS3404 5.3.2.4.

For design of cantilevers, the free tip should have user-defined "U" restraints applied to both top and bottom flanges.

If the effective flange restraints for any load case consist of "U" or "L" restraints only, an error will be reported.

Hence flange restraints automate following design calculations for each unbraced flange segment for bending about both the principle axis:

Unbraced length of top flange in bending compression – only when no value is assigned to UNT
Unbraced length of bottom flange in bending compression – only when no value is assigned to UNB
Moment modification factor, αm, per NZS3404 5.6.1.1 – only when no value is assigned to ALM
Load height factor, kl, given in Table 5.6.3(2) - only when no value is assigned to SKL
Lateral rotation restraint factor, kr, given in Table 5.6.3(3) - only when no value is assigned to SKR
Twist restraint factor, kt, given in Table 5.6.3(1) - only when no value is assigned to SKT

Notes:

If PMEMBER list is not provided, all the PMEMBERS are restrained by same configuration
It is not necessary to provide the restraint locations in sequence as the program sorts them automatically
Unless specified, PMEMBER ends are assumed to be Fully Restrained (F)
While designing any section of the member, effective restraints are searched on each side of the section along the critical flange

The types of restraints applied to the top and bottom flanges at each location determines the effective section restraints. These are outlined in the table below:

Case	Flange	Restraint on a Critical Flange	Restraint on a Non-Critical Flange	Effective Section Restraint
I		U	U	U
II	1	L	Nothing	L
II	2	Nothing	L	None
III	1	P or F	Nothing or U	F
III	2	Nothing or U	P or F	P
IV	1	PR or FR	Nothing or U	FR
IV	2	Nothing or U	PR or FR	PR
V	1	L, P or F	L, P, F, FR or PR	F
V	2	FR or PR	L, P, F, FR or PR	FR

D11.A.5.2.5 Automated PMEMBER Design Calculations

The NZS3404 PMEMBER Design automates many design calculations, including those required for segment / sub-segment design.

Automated Design Calculations	PMEMBER Design Parameter	Comments
αb compression member section constant per NZS3404 6.3.3.	Not applicable	Calculated from table 6.3.3.
αm moment modification factor per NZS3404 5.6.1.1 or Table 5.6.2 depending on if the segment is restrained at on/both ends.	ALM	Calculated based on moments distribution for individual segments and sub-segments.
f_u tensile strength per NZS3404 2.1.2 and AS4100 table 2.1.	FU	Based on nominal steel grade specified using SGR design parameter and element thickness.
fy yield stress per NZS3404 2.1.1 and AS4100 table 2.1.	FYLD	Based on nominal steel grade specified using SGR design parameter and element thickness.
Residual stress category for NZS3404 Table 5.2 and 6.2.4.	IST	Based on section type.
Segment and sub-segment layout for flange unbraced length.	PBRACE	Refer to the Segment or Sub-Segment for Flexural/Flange Buckling for details.
Unbraced length of top and bottom flange for flange buckling.	UNT, UNB
Segment layout for compression buckling unbraced length.	PBCRES	Refer to the Segment for Compression Buckling for details.
Effective length factor ( ke ) for compression buckling	KZ, KY
Unbrace length for compression buckling	LZ, LY
k_t twist restraint factor as per NZS3404 Table 5.6.3(1).	SKT	Based on effective end restraints for each segment / sub-segment.
k_l load height factor as per NZS3404 Table 5.6.3(2).	SKL, LHT	Based on effective end restraints for each segment / sub-segment, and LHT design parameter.
k_r lateral rotation restraint factor as per NZS3404 Table 5.6.3(3).	SKR	Based on effective end restraints for each segment / sub-segment. This is where the distinction between "F" and "FR", as well as "P" and "PR" is used.

D11.A.5.2.6 Load Height Position

When LHT is set to 1.0 to specify a top flange load height position, STAAD.Pro takes the top to be the positive local y-axis of the member.

Tip: This may not literally be the top flange for say a column or beam with a beta angle. The local member axes can be viewed in the user interface by selecting Beam Orientation in the Diagrams Labels dialog (or press <Ctrl+O>).

To automate kl using NZS3404 Table 5.6.3(2), the longitudinal position of the load also needs to be considered, i.e., as either "within segment" or "at segment end."

To determine which of these applies, the shear forces at the ends of each design segment / sub-segment is considered. If the shear force is found to have the same direction and magnitude at both ends, it is assumed that loads act at the segment end.

If on the other hand, the shear force at each end is found to have different directions or magnitudes, loads are assumed to act within the segment.

Tip: The above method includes an allowance for the self-weight of the member to be considered, as the self-weight always acts through the shear center.

The net sum of the end shears is also used to determine if the load is acting in the positive or negative local member y-axis direction. If LHT is set to 1.0 for top flange loading, the net sum is used to determine whether the top flange loading is acting to stabilize or destabilize the member for lateral torsional buckling. Negative local y-axis net loads act to destabilize the segments / sub-segments, whereas positive local y-axis net loads act to stabilize segments / sub-segments.