| Applies To | |||
| Product(s): | STAAD.Pro CONNECT Edition | ||
| Version(s): | All | ||
| Environment: | N/A | ||
| Area: | Analysis Solutions | ||
| Subarea: | Direct Analysis | ||
| Original Author: |
Biswatosh Purkayastha | ||
DIRECT ANALYSIS PER THE AISC 360 AND THE IMPLEMENTATION IN STAAD
The AISC 360-16 Specification, Chapter C, specifies that the stability shall be provided for the structure as a whole and for each of its elements. That means the stability needs to be maintained for the individual members, connections, joints and other building elements as well as the structural system as a whole.
The code recommends using any method that ensures the stability of the structure as a whole and for individual building elements and meets with all the following requirements are permitted.
- Flexural, shear and axial member deformations and all other deformations that contribute to displacements of the structure.
- Second-order effects (both P-∆ and P- Ϩ effects)
- Initial geometric imperfections
- Stiffness reduction due to inelasticity
- Uncertainty in stiffness and strength
The Direct Analysis Method (DAM), as described in the AISC 360-16 Specification, Chapter C (Design for Stability), satisfies all the aforementioned conditions.
General Analysis Requirements
According to the AISC 360-16 Specification, Chapter C2.1, the second order effects (including both P-Δ and P-δ) must be considered in the analysis.
In STAAD.Pro, the second order effects (including both P-Δ and P-δ) are automatically considered when the PERFORM DIRECT ANALYSIS command is issued.
NOTES on the Direct Analysis Implementation in STAAD.Pro:
- STAAD.Pro performs the direct analysis based on the rigorous second order analysis method. The approximate second-order analysis (B1-B2 Method) is not implemented in STAAD.
- STAAD forms the (K+Kg) matrix which accounts for the Geometric non-linearity, is the combination of the Global stiffness matrix and the Global Geometric Stiffness matrix.
Consideration of Initial System Imperfections
According to the AISC 360-16 Specification, Chapter C2.2, the initial system imperfections must be considered when calculating the required strength of the lateral steel members by either directly modeling the imperfections or by applying notional loads. Notional loads are a portion of the gravity load acting on the structure horizontally. The notional load factor shall be calculated according to the AISC 360-16 Equation C2-1.
In STAAD.Pro, notional loads (along with the appropriate notional load factors) can be generated through the Automatic Load Combination Generator.
NOTE: When specifying the notional load factor, ensure that you consider the design method (LRFD or ASD) along with the method you plan to use to calculate tau-b (iterative vs. non-iterative solution).
Adjustments to Stiffness
According to the AISC 360-16 Specification, Chapter C2.3, indicates that the flexural and axial stiffness shall be reduced for the members that contribute to the lateral stability of the structure. The stiffness reductions will consider the inelastic effects due to residual stress and the uncertainty in strength and stiffness. The reduced flexural and axial stiffnesses shall be calculated as follows:
- Reduced Axial Stiffness is EA* = 0.8 EA
- Reduced Flexural Stiffness is EI* = 0.8 EI τb
τb, which is dependent on the level of axial stress, can be calculated according to the AISC 360-16 Specification, Equations C2-2a and C2.2b):
It is also permissible to assume τb equals 1.0 if the additional notional load of 0.001 times of gravity load is applied.
In STAAD.Pro, a Direct Analysis Definition is used to instruct the program to reduce the stiffness for the steel members in accordance with the AISC 360-16 Direct Analysis Method, as follows:
- FLEX parameter: Identifies members whose flexural stiffness is considered to contribute to the lateral stability of the structure, along with the initial value of τb that should be used. These members will have their EI values factored by 0.8 times τb while performing the global solution (EI*= 0. 8x τb x EI). The code check will use 100% of the flexural stiffness for each member.
- AXIAL parameter: Identifies members whose axial stiffness is considered to contribute to the lateral stability of the structure. These members will have their EA values factored by 0.80 while performing the global solution (EA*= 0.8 x EA). The code check will use 100% of the axial stiffness for each member.
STAAD.Pro can perform an iterative solution for τb if specified in the PERFORM DIRECT ANALYSIS command. If you are performing an iterative solution for τb x EI), STAAD.Pro will use the yield strength of steel, as specified in the materail properties, to calculate τb.
Direct Analysis Method Implementation in STAAD:
To learn how to implement the direct analysis method into STAAD.Pro, please see the following video for step by step instructions:
Validation Staad DAM with Benchmark problem, Case-2 (page-16.1-435) in the AISC 360-05
Input data
B=d = 5 inch , L = 500 inch , P =4 Kips , H = 2 Kip , E = 29732 Ksi , Py = 50 ksi
STAAD.Pro result
After performing the Direct Analysis in STAAD, the maximum moment and maximum displacement reported are 1290.392 Kip-in and 72.588 inch receptively .
Hand Calculation result
REFERENCES
(1) AISC 360-15, Specification for Structural Steel Buildings
(2) AISC Stability Analysis handouts
(3) Structural Steel Design by Jack .C Mormac
(4) Steel Design by William .T. Segui
(5) Benchmark Problems