Design of Compression Members

What is the minimum total stiffness required for bracing elements to resist lateral movement of a story?

What is the acceptable percentage increase in moments due to slenderness?

How should the unsupported length of a compression member be measured when column capitals or haunches are present?

What is the maximum moment that can be used in compression members, restraining beams, or other structural members?

What is the minimum value of the modulus of elasticity for normal-weight concrete?

What is the minimum value of the moment of inertia for un-cracked walls?

What is the primary design aid used to estimate the effective length factor k?

When can slenderness effects be neglected in compression members?

What is the formula to compute the effective length factor k for a non-sway column?

What is the condition for a column to be considered braced against side-sway?

What is the formula to compute the effective length factor k for a sway column fixed at one end?

What is the condition for neglecting slenderness effects in compression members not braced against side-sway?

Slenderness Effects in Structures

Slenderness effects can be neglected in both braced and un-braced systems depending on the (klu / r) of the member.
In evaluation of un-braced systems, moments are based on first-order elastic analysis.

Effective Length Factor (k)

The primary design aid to estimate the effective length factor k is the Jackson and Moreland Alignment Charts.
k can be computed using the following formulas:
- For non-sway columns:
  - 28.1 + (64.0/ψA) + (4.1/ψB) + (3.0/ψB) + (1.0/ψA) = k
  - If the column is hinged at one end (ψA = ∞), then k = 2.3 + (4.1/ψB)
  - If the column is fixed at one end (ψA = 0), then k = 64.0 + (32.0/ψB) + (7.0/ψB)
- For sway columns:
  - 5.7 + (5.7/ψA) + (4.6/ψB) + (1.0/ψA) + (1.0/ψB) = k
  - If the column is hinged at one end (ψA = ∞), then k = 4.6 + (1.0/ψB)
  - If the column is fixed at one end (ψA = 0), then k = 5.7 + (5.7/ψB) + (4.ψB)

Slenderness Effects Neglect

Slenderness effects can be neglected in the following cases:
- For compression members not braced against side-sway, when klu/r ≤ 22
- For compression members braced against side-sway, when 12 ≤ (M1/M2) - 34/r ≤ 40

Compression Members

The unsupported length of a compression member, lu, is the clear distance between floor slabs, beams, or other members capable of providing lateral support.
Where column capitals or haunches are present, lu is measured to the lower extremity of the capital or haunch in the plane considered.
The radius of gyration, r, can be taken as:
- 0.30 times the overall dimension in the direction stability is being considered for rectangular compression members
- 0.25 times the diameter for circular compression members
- Computed for other shapes based on the gross concrete section

Second-Order Analysis

Total moment including second-order effects in compression members, restraining beams, or other structural members shall not exceed 1.4 times the moment due to first-order effects.
Nonlinear second-order analysis shall consider:
- Material nonlinearity
- Member curvature and lateral drift
- Duration of loads
- Shrinkage and creep
- Interaction with the supporting foundation

This quiz covers the design of compression members in structures, considering slenderness effects and effective length factors. It deals with the analysis of braced and un-braced systems, and the estimation of the effective length factor k.