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Lesson 10: K Practice
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What is K for Column AB? P P B A
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What is K for Column AB? Translation is prevented (braced)
Rotation allowed, top and bottom So, P P B A
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What is K for Column AB? Translation is prevented (braced)
Rotation allowed, top and bottom So, K = 1 P P B A
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Rigid connections keep joint at 90 degrees
What is K Now? P P B Rigid connections keep joint at 90 degrees A
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Rigid connections keep joint at 90 degrees
What is K Now? P P Infinitely Stiff Beam B Rigid connections keep joint at 90 degrees A
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What is K Now? Translation is prevented (braced)
Rotation prevented at top but full rotation is possible at the other end. P P Infinitely Stiff Beam B A
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What is K Now? Translation is prevented (braced)
Rotation prevented at top but full rotation is possible at the other end. K=0.7 P P Infinitely Stiff Beam B A
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Rigid connections keep joint at 90 degrees
What is K Now? Translation is prevented (braced) P P Wimpy Beam B Rigid connections keep joint at 90 degrees A
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What is K Now? Translation is prevented (braced) Rotation? P P
(EI =>0) B A
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What is K Now? Translation is prevented (braced)
Rotation is allowed top and bottom K = ? P P (EI =>0) B A
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What is K Now? Translation is prevented (braced)
Rotation is allowed top and bottom K = 1 P P (EI =>0) B A
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Conclusion In Real Rigid Frames:
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Conclusion In Real Rigid Frames:
(Relatively) stiff beams make columns act shorter (reduce KL, increase strength)
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Which column AB acts Shorter (Smaller KL)?
Left or Right? I = 3000 in4 I = 300 in4 A B P 30’ 15’ I = 300 in4 I = 3000 in4 A B P 30’ Left Right
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Which column AB acts Shorter (Smaller KL)?
Left or Right? I = 3000 in4 I = 300 in4 A B P 30’ 15’ I = 300 in4 I = 3000 in4 A B P 30’ Left Right Big Beam = Shorter Column: Smaller KL
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What is the lowest that KL can be?
I = 300 in4 A B P 30’ 15’
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What is the lowest that KL can be?
I = Infinite I = 300 in4 A B P 30’ 15’
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What is the lowest that KL can be?
I = Infinite I = 300 in4 A B P 30’ 15’
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What is the lowest that KL can be?
I = Infinite I = 300 in4 A B P 30’ 15’
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What is the lowest that KL can be?
I = Infinite I = 300 in4 A B P 30’ 15’ K = 2 Free to sway (so K>1). Full rotational restraint at one end => K = 2.
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What is the lowest that KL can be?
Switch to Fixed Base I = Infinite I = 300 in4 A B P 30’ 15’
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What is the lowest that KL can be?
Switch to Fixed Base I = Infinite I = 300 in4 A B P 30’ 15’
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What is the lowest that KL can be?
Switch to Fixed Base I = Infinite I = 300 in4 A B P 30’ 15’ K = 1 Free to sway (so K>1). Full rotational restraint at both ends => K = 1.
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What is the highest that KL can be?
I ~ 0 in4 I = 3000 in4 A B P 30’ 15’
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What is the highest that KL can be?
I ~ 0 in4 I = 3000 in4 A B P 30’ 15’ Is it braced?
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What is the highest that KL can be?
I ~ 0 in4 I = 3000 in4 A B P 30’ 15’ Not braced
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What is the highest that KL can be?
I ~ 0 in4 I = 3000 in4 A B P 30’ 15’ Not braced Flexible Beam: Rotation prevented?
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What is the highest that KL can be?
I ~ 0 in4 I = 3000 in4 A B P 30’ 15’ Not braced Flexible Beam: Rotation prevented? Nope.
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What is the highest that KL can be?
I ~ 0 in4 I = 3000 in4 A B P 30’ 15’ Not braced Flexible Beam: Rotation prevented? Nope.
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What is the highest that KL can be?
I ~ 0 in4 I = 3000 in4 A B P 30’ 15’ Not braced Flexible Beam: Rotation prevented? Nope.
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What is the highest that KL can be?
I ~ 0 in4 I = 3000 in4 A B P 30’ 15’ I = 3000 in4 A B P K is Infinite Zero rotational restraint and unbraced. Unstable. K is infinite. Structure collapses. People get sued.
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What is the highest that KL can be?
I ~ 0 in4 I = 3000 in4 A B P 30’ 15’ I = 3000 in4 A B P K is Infinite Zero rotational restraint and unbraced. Unstable. K is infinite. Structure collapses. People get sued.
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Which column AB has the greater KL?
Left or Right? I = 500 in4 A B P 15’ I = 500 in4 A B P 15’ Left Right
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Which column AB has the greater KL?
Left or Right? I = 500 in4 A B P 15’ I = 500 in4 A B P 15’ Left Right Unbraced Frame: K ≥ 1 Braced Frame: K ≤ 1
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Which column AB has K = 1? Left or Right? Left Right I = 500 in4 A B P
15’ I = 500 in4 A B P 15’ Left Right
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Which column AB has K = 1? Left or Right? Left Right
I = 500 in4 A B P 15’ I = 500 in4 A B P 15’ Left Right Simple (pin-ended) Braced Frame: K = 1
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Which column AB has the greater KL?
Left or Right? I = 300 in4 A B P 30’ 15’ I = 3000 in4 I = 300 in4 A B P 30’ 15’ Left Right
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Which column AB has the greater KL?
Left or Right? I = 300 in4 A B P 30’ 15’ I = 3000 in4 I = 300 in4 A B P 30’ 15’ Left Right Simple Braced Frame: K = 1 Unbraced Frame: K > 1
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What Happens to K? Right Simple Braced Frame: P I = infinite? B
30’ 15’ Right Simple Braced Frame:
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Nothing. Beam size is only relevant if connections are rigid
What Happens to K? I = infinite? I = 300 in4 A B P 30’ 15’ Nothing. Beam size is only relevant if connections are rigid Right Simple Braced Frame: K=1
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Frame Types Braced Frame Simple Connections
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Frame Types Braced Frame Unbraced Frame Simple Connections
Rigid Connections
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Frame Types Braced Frame Unbraced Frame Simple Connections
Rigid Connections Braced Frame Rigid Connections
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Frame Types Braced Frame Unbraced Frame Simple Connections
Rigid Connections Unbraced Frame Simple Connections Braced Frame Rigid Connections
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Frame Types Braced Frame Unbraced Frame Simple Connections
Rigid Connections Unbraced Frame Simple Connections Braced Frame Rigid Connections
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Frame Types Braced Frame Unbraced Frame Simple Connections
Rigid Connections Unbraced Frame Simple Connections Braced Frame Rigid Connections
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Frame Types Braced Frame Unbraced Frame Simple Connections
Rigid Connections Unstable Mess Braced Frame Rigid Connections
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Frame Types Braced Frame Unbraced Frame Simple Connections
Rigid Connections Braced Frame Rigid Connections
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Frame Types Braced Frame Unbraced Frame Simple Connections
Rigid Connections Braced Frame Rigid Connections
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Frame Types Braced Frame Unbraced Frame Simple Connections
Rigid Connections Braced Frame Rigid Connections
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Frame Types Braced Frame Unbraced Frame Simple Connections
Rigid Connections Braced Frame Rigid Connections
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Frame Types K>1 K=1 Braced Frame Unbraced Frame Simple Connections
Rigid Connections K<1 Braced Frame Rigid Connections
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