AISC Effective Length KL Method for Buckling and
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects Braced Frame Pure Axial
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects K=? Braced Frame Pure Axial
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects K=1 Braced Frame Pure Axial
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects KL= ½-Sine Length K=1 Braced Frame Pure Axial
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects KL= ½-Sine Length K=1 K=? Braced Frame Pure Axial Unbraced Frame
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects KL= ½-Sine Length K=1 K>1 Braced Frame Pure Axial Unbraced Frame (“Sway Frame”)
AISC “Effective Length (KL) Method” for Buckling K depends on relative and 2 nd Order Effects Beam Stiffness KL= ½-Sine Length K=1 K>1 Braced Frame Pure Axial Unbraced Frame (“Sway Frame”)
AISC “Effective Length (KL) Method” for Buckling K depends on relative and 2 nd Order Effects Beam Stiffness GA, GB KL= ½-Sine Length K=1 K>1 Braced Frame Pure Axial Unbraced Frame (“Sway Frame”)
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects K=1 Braced Frame Axial & Bending Mnt – 1 st Order “no translation” Moment
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects d K=1 Braced Frame Axial & Bending Mnt – 1 st Order “no translation” Moment
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects d KL= ½-Sine Length K=1 Braced Frame Axial & Bending Mnt – 1 st Order “no translation” Moment P – Axial Force
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects KL= ½-Sine Length K=1 Braced Frame Axial & Bending Mnt – 1 st Order “no translation” Moment P – Axial Force 2 nd Order Effect. Amplified Moment
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects KL= ½-Sine Length K=1 Braced Frame Axial & Bending Mnt – 1 st Order “no translation” Moment P – Axial Force M = B 1 Mnt 2 nd Order Effect. Amplified Moment
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects KL= ½-Sine Length K=1 Braced Frame Axial & Bending Mnt – 1 st Order “no translation” Moment P – Axial Force M = B 1 Mnt 2 nd Order Effect. Amplified Moment
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects KL= ½-Sine Length K=1 Braced Frame Axial & Bending Mnt – 1 st Order “no translation” Moment P – Axial Force 2 nd Order Effect. Amplified Moment Where: Cm = 0. 6 -0. 4(M 1/M 2) Pe = Euler Load P = Applied Load M = B 1 Mnt M 1, M 2 = End-Moments
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects K>1 Unbraced Frame (“Sway Frame”) M = B 1 Mnt
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects K>1 Unbraced Frame (“Sway Frame”) Mlt – 1 st Order “lateral translation” Moment P – Axial Force M = B 1 Mnt
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects D K>1 Unbraced Frame (“Sway Frame”) Mlt – 1 st Order “lateral translation” Moment P – Axial Force M = B 1 Mnt
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects K>1 Unbraced Frame (“Sway Frame”) 2 nd Order Effect. Amplified Moment M = B 1 Mnt Mlt – 1 st Order “lateral translation” Moment P – Axial Force M = B 2 Mlt
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects: IN GENERAL M = B 1 Mnt +B 2 Mlt
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects: IN GENERAL d K=1 Braced Frame M = B 1 Mnt +B 2 Mlt Amplifies due to d
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects: IN GENERAL D d K=1 K>1 Braced Frame Unbraced Frame M = B 1 Mnt +B 2 Mlt Amplifies due to d Amplifies due to D
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects: IN GENERAL D d d K=1 K>1 Braced Frame Unbraced Frame M = B 1 Mnt +B 2 Mlt Amplifies due to d Amplifies due to D
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects: IN GENERAL D d d K=1 K>1 Braced Frame Unbraced Frame M = B 1 Mnt +B 2 Mlt Amplifies due to d Amplifies due to D d = deflection along length of member (“braced deflection”) D = deflection of member end (“unbraced deflection”)
AISC “Effective Length (KL) Method” for Buckling and 2 nd Order Effects: IN GENERAL D d d K=1 K>1 Braced Frame Unbraced Frame M = B 1 Mnt +B 2 Mlt Amplifies due to d Amplifies due to D d = deflection along length of member (“braced deflection”) D = deflection of member end (“unbraced deflection”)
HOWEVER, the “Effective Length (KL) Method” is considered archaic • Old • Only found in Appendix 8
AISC Preferred Method for 2 nd Order Effects: DIRECT ANALYSIS METHOD (DAM) • Found in Chapter C (the main specifications)
Principles of the DIRECT ANALYSIS METHOD (DAM)
Principles of the DIRECT ANALYSIS METHOD (DAM) 1. Buckling does not cause failure.
Principles of the DIRECT ANALYSIS METHOD (DAM) 1. Buckling does not cause failure. Buckling predicts failure
Principles of the DIRECT ANALYSIS METHOD (DAM) 1. Buckling does not cause failure. Buckling predicts failure Euler – Either the column is: Straight
Principles of the DIRECT ANALYSIS METHOD (DAM) 1. Buckling does not cause failure. Buckling predicts failure Euler – Either the column is: Straight, or Buckled
Principles of the DIRECT ANALYSIS METHOD (DAM) 1. Buckling does not cause failure. Buckling predicts failure
Principles of the DIRECT ANALYSIS METHOD (DAM) 1. Buckling does not cause failure. Buckling predicts failure Math does not make the column fail. Stresses do.
Principles of the DIRECT ANALYSIS METHOD (DAM) 1. Buckling does not cause failure. Buckling predicts failure Math does not make the column fail. Stresses do.
Principles of the DIRECT ANALYSIS METHOD (DAM) 1. Buckling predicts failure Stress and deformations Are real and measureable. Buckling is mathematical Abstraction.
Principles of the DIRECT ANALYSIS METHOD (DAM) 1. Buckling predicts failure 2. Failure is caused by Stress. – Stress is caused by Axial and Bending – Bending is caused by 1 st Order Effects & 2 nd Order Effects Stress and deformations Are real and measureable. Buckling is mathematical Abstraction.
Principles of the DIRECT ANALYSIS METHOD (DAM) 1. Buckling predicts failure 2. Failure is caused by Stress. – Stress is caused by Axial and Bending – Bending is caused by 1 st Order Effects & 2 nd Order Effects Stress and deformations Are real and measureable. Buckling is mathematical Abstraction.
DIRECT ANALYSIS METHOD (DAM) Therefore: • Computer model all deformations and material inelasticity – Includes out-of-straightness and other fabrication/construction tolerances.
DIRECT ANALYSIS METHOD (DAM) Therefore: • Computer model all deformations and material inelasticity – Includes out-of-straightness and other fabrication/construction tolerances. Frame out-of-straightness accounted for in computer model
DIRECT ANALYSIS METHOD (DAM) Therefore: • Computer model all deformations and material inelasticity – Includes out-of-straightness and other fabrication/construction tolerances. • Run the model with a true non-linear P-delta analysis to capture 2 nd Order Effects.
DIRECT ANALYSIS METHOD (DAM) Therefore: • Computer model all deformations and material inelasticity – Includes out-of-straightness and other fabrication/construction tolerances. • Run the model with a true non-linear P-delta analysis to capture 2 nd Order Effects.
DIRECT ANALYSIS METHOD (DAM) Therefore: • Computer model all deformations and material inelasticity – Includes out-of-straightness and other fabrication/construction tolerances. • Run the model with a true non-linear P-delta analysis to capture 2 nd Order Effects (the moments WILL INCREASE).
DIRECT ANALYSIS METHOD (DAM) Therefore: • Computer model all deformations and material inelasticity – Includes out-of-straightness and other fabrication/construction tolerances. • Run the model with a true non-linear P-delta analysis to capture 2 nd Order Effects. • Use AISC column equations as usual, but K is always 1.
DIRECT ANALYSIS METHOD (DAM) Therefore: • Computer model all deformations and material inelasticity – Includes out-of-straightness and other fabrication/construction tolerances. • Run the model with a true non-linear P-delta analysis to capture 2 nd Order Effects. • Use AISC column equations as usual, but K is always 1.
DIRECT ANALYSIS METHOD (DAM) Therefore: • Computer model all deformations and material inelasticity – Includes out-of-straightness and other fabrication/construction tolerances. • Run the model with a true non-linear P-delta analysis to capture 2 nd Order Effects. • Use AISC column equations as usual, but K is always 1. – WTF? Whimpy frame: Big D
DIRECT ANALYSIS METHOD (DAM) Therefore: • Computer model all deformations and material inelasticity – Includes out-of-straightness and other fabrication/construction tolerances. • Run the model with a true non-linear P-delta analysis to capture 2 nd Order Effects. • Use AISC column equations as usual, but K is always 1. – WTF? The idea is that all of the actual causes of failure already included. Whimpy frame: Big D
DIRECT ANALYSIS METHOD (DAM) Therefore: • Computer model all deformations and material inelasticity – Includes out-of-straightness and other fabrication/construction tolerances. • Run the model with a true non-linear P-delta analysis to capture 2 nd Order Effects. • Use AISC column equations as usual, but K is always 1. – WTF? The idea is that all of the actual causes of failure already included. Whimpy frame: Big D Stiffer frame: Smaller D
DIRECT ANALYSIS METHOD (DAM) Please Note: • For BRACED FRAMES (the focus of this course), there is no meaningful difference between DIRECT ANALYSIS METHOD (DAM) and the familiar EFFECTIVE LENGTH METHOD (ELM). Braced Frame
DIRECT ANALYSIS METHOD (DAM) Specifics: AISC Chapter C 2 The Analysis Must: 1. 2. 3. Be 2 nd Order and consider P-D and P-d. (SAP!) Consider initial imperfections (crookedness, etc. ) Consider reduction in stiffness due to partial inelasticity. i. e. , as the applied stresses approach yielding (due to residual stresses), the EI and EA of the members must be reduced.
EXAMPLE
EXAMPLE Frame: All sections W 10 x 33. Wind: 10 kips. Live: 1 kip/ft 1 st Order Analysis: D = 2. 06” M = 96. 9 kip-ft
EXAMPLE Frame: All sections W 10 x 33. Wind: 10 kips. Live: 1 kip/ft 1 st Order Analysis: D = 2. 06” M = 96. 9 kip-ft
EXAMPLE Frame: All sections W 10 x 33. Wind: 10 kips. Live: 1 kip/ft 1 st Order Analysis: D = 2. 06” M = 96. 9 kip-ft 2 nd Order Analysis: D = 2. 18” M = 100. 1 kip-ft
EXAMPLE Frame: All sections W 10 x 33. Wind: 10 kips. Live: 1 kip/ft 1 st Order Analysis: D = 2. 06” M = 96. 9 kip-ft 2 nd Order Analysis: D = 2. 18” M = 100. 1 kip-ft Now, add: 2. initial imperfections (crookedness: make the frame out of plumb) 3. Inelastic stiffness reduction
EXAMPLE Frame: All sections W 10 x 33. Wind: 10 kips. Live: 1 kip/ft 1 st Order Analysis: D = 2. 06” M = 96. 9 kip-ft 2 nd Order Analysis: D = 2. 18” M = 100. 1 kip-ft Now, add: 2. initial imperfections (crookedness: make the frame out of plumb) 3. Inelastic stiffness reduction.
EXAMPLE Frame: All sections W 10 x 33. Wind: 10 kips. Live: 1 kip/ft 1 st Order Analysis: D = 2. 06” M = 96. 9 kip-ft 2 nd Order Analysis: D = 2. 18” M = 100. 1 kip-ft Now, add: 2. initial imperfections (crookedness: make the frame out of plumb) 3. Inelastic stiffness reduction. Final Result: D = 2. 74” M = 101. 3 kip-ft
EXAMPLE 2 Repeat, but make the beam very wimpy.
- Slides: 59