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G. AISC 360 Direct Analysis

AISC 360-10/16 Chapter C and AISC 360-05 Appendix 7 describe a method of analysis, called "direct analysis", which accounts for the second order effects resulting from deformation in the structure due to applied loading, imperfections and reduced bending stiffness of members due to the presence of axial load.

The ANSI/AISC 360 direct analysis procedure has been adopted to incorporate the P-Delta effect into a static analysis by combining the global stiffness matrix and the global geometric stiffness matrix [K+Kg]; plus flexural stiffness reduction; plus axial stiffness reduction; plus an additional flexure reduction if member axial compression forces are above 50% of yield; plus the addition of notional loads.

This is a nonlinear, iterative analysis as the stiffness of the members is dependent upon the forces generated by the load.

  1. The primary deflections are calculated by linear static analysis based on the provided external loading for case n. The stiffness reductions and notional loads are included here. 
  2. Primary deflections are used to calculate member axial forces and plate center membrane stresses. These forces and stresses are used to calculate geometric stiffness terms. Both the large delta effects and the small delta effects are calculated. These forces and stresses are used to calculate geometric stiffness terms. These terms times the displacement results from the prior iteration create the P-Delta secondary loading. This secondary loading is then combined with the originally applied loading to create the effective load vector for the next iteration.
  3. The final triangular factorization for case n is then used to calculate displacements and member forces.

    Lateral loading must be present concurrently with the vertical loading for proper consideration of the P-Delta effect. The REPEAT LOAD facility (See TR.32.11 繰り返し荷重の設定) has been created with this requirement in mind. This facility allows you to combine previously defined primary load cases to create a new primary load case.

  4. The axial force is compared to yield force to calculate τb (see Chapter C or AISC 360-10/16 or Appendix 7 of AISC 360-05). Flexure stiffness of selected members is set to (0.80×τb · EI)
  5. Steps 2 to 4 are repeated until convergence or the iteration limit is reached.

    The analysis will iterate; in each step, changing the member characteristics until the maximum change in any τb is less than the specified τ tolerance. If the maximum change in any τb is less than 100 times the τ tolerance and the maximum change in any displacement degree of freedom is less than the specified displacement tolerance; then the solution has converged for this case.

General Procedure for Using the Direct Analysis Feature

There are three general steps required to set up a Direct Analysis:
  1. Specify the definition with the DEFINE DIRECT command.
  2. Specify the notional loads using the NOTIONAL LOAD load specification.
  3. Specify a direct analysis method with the PERFORM DIRECT ANALYSIS command. Within this command, you will specify the tolerances or iteration limits.