analysis and design for stability-slides.pdf
TRANSCRIPT
© 2015 Bentley Systems, Incorporated
Allen Adams, P.E., S.E.
Analysis and Design for Stability
2 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated2 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Analysis and Design for Stability
Allen Adams, P.E., S.E.Chief Structural Engineer, RAM Group at Bentley Systems, Inc.
Senior Product Manager, RAM Structural System
AISC Committee on Specifications
AISC 360 Task Committee 10 – Stability
AISC Committee on Manuals – Seismic Design Manual
ASCE Committee on Design of Steel Building Structures
3 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Strength
4 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stiffness
5 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability
6 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability
7 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability
8 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability
9 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability
10 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability
11 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability
12 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability
13 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
1st – Order vs 2nd – Order Analysis
14 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
1st – Order vs 2nd – Order Analysis
15 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
1st – Order vs 2nd – Order Analysis
16 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
1st – Order vs 2nd – Order Analysis
17 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
1st – Order vs 2nd – Order Analysis
1st – Order Analysis 2nd – Order Analysis
18 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability and 2nd-Order Effects
• P-D
• P-d
• Out-of-Plumbness
• Member Out-of-Straightness
• Residual Stresses
19 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability and 2nd-Order Effects
• P-D
• P-d
• Out-of-Plumbness
• Member Out-of-Straightness
• Residual Stresses
20 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
P-D
21 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability and 2nd-Order Effects
• P-D
• P-d
• Out-of-Plumbness
• Member Out-of-Straightness
• Residual Stresses
22 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability and 2nd-Order Effects
• P-D
• P-d
• Out-of-Plumbness
• Member Out-of-Straightness
• Residual Stresses
23 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
P-d
24 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability and 2nd-Order Effects
• P-D
• P-d
• Out-of-Plumbness
• Member Out-of-Straightness
• Residual Stresses
25 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Out-of-Plumbness
26 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability and 2nd-Order Effects
• P-D
• P-d
• Out-of-Plumbness
• Member Out-of-Straightness
• Residual Stresses
27 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Member Out-of-Straightness
28 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Member Out-of-Straightness
29 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability and 2nd-Order Effects
• P-D
• P-d
• Out-of-Plumbness
• Member Out-of-Straightness
• Residual Stresses
30 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability and 2nd-Order Effects
• P-D
• P-d
• Out-of-Plumbness
• Member Out-of-Straightness
• Residual Stresses
31 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
These effects can be handled by:
• Amplify the member forces obtained from a 1st-order analysis
• Reduce the available strength (the calculated allowable capacity) of the member
• Include the effects directly in the model used in the analysis
• A combination of the above
Stability and 2nd-Order Effects
32 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
P-D
• Amplified 1st-Order Elastic Analysis
– AISC B2 Factor
33 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
P-D
• Amplified 1st-Order Elastic Analysis
– AISC B2 Factor
• 2nd-Order Analysis
– Iterative
– Geometric Stiffness Method
Iterative Geometric Stiffness
34 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
P-d
• Amplified 1st-Order Elastic Analysis
– AISC B1 Factor
35 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
P-d
• Amplified 1st-Order Elastic Analysis
– AISC B1 Factor
• 2nd-Order Analysis
– Iterative
36 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
P-d
• Amplified 1st-Order Elastic Analysis
– AISC B1 Factor
• 2nd-Order Analysis
– Iterative
• Reduced Capacity
– AISC 9th ASD (1989)
37 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Out-of-Plumbness
• Direct Modeling of the displaced nodes
38 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Out-of-Plumbness
• Direct Modeling of the displaced nodes
Requires four separate
models, one for each
axis direction.
39 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Out-of-Plumbness
• Direct Modeling of the displaced nodes
• Notional Loads
40 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Notional Loads
Notional Loads are a portion of the vertical gravity load applied horizontally.
41 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
42 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
43 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
44 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Notional Loads
• Dead, Live and Roof
• Applied in each of the four directions (+/- X-axis, +/- Y-axis)
• AISC 360-10 specifies notional loads of 0.002 or 0.003 times the gravity loads
45 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Load Combinations with Notional Loads
When B2 < 1.5:
1.4 D + 1.4 ND1
1.2 D + 1.2 ND1 + 1.6 L + 1.6 NL1
1.2 D + 1.6 W1
1.2 D + 0.5 Lp + 1.6 W1
.
.
.
When B2 > 1.5:
1.4 D + 1.4 ND1
1.2 D + 1.2 ND1 + 1.6 Lp + 1.6 NL1
1.2 D + 1.2 ND1 + 1.6 W1
1.2 D + 1.2 ND1 + 0.5 Lp + 1.2 NL1 + 1.6 W1
.
.
.
In AISC 360, if B2 is greater than 1.5, the notional loads must be included with all
combinations, otherwise they need only be included with the gravity load combinations:
46 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Out-of-Plumbness
• Direct Modeling of the displaced nodes
• Notional Loads
47 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Member Out-of-Straightness
• Reduce Capacity by using the Effective Length (KL) in the strength equations
48 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Member Out-of-Straightness
• Reduce Capacity by using the Effective Length (KL) in the strength equations
• Reduced Capacity from Strength equations that are calibrated to include effects
49 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Member Out-of-Straightness
• Reduce Capacity by using the Effective Length (KL) in the strength equations
• Reduced Capacity from Strength equations that are calibrated to include effects
• Used reduced stiffnesses in the analysis
50 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Residual Stresses
• Reduce Capacity by using the Effective Length (KL) in the strength equations
51 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Residual Stresses
• Reduce Capacity by using the Effective Length (KL) in the strength equations
• Reduced Capacity from Strength equations that are calibrated to include effects
52 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Residual Stresses
• Reduce Capacity by using the Effective Length (KL) in the strength equations
• Reduced Capacity from Strength equations that are calibrated to include effects
AISC LRFD 3rd
(1999)
53 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Residual Stresses
• Reduce Capacity by using the Effective Length (KL) in the strength equations
• Reduced Capacity from Strength equations that are calibrated to include effects
• Used reduced stiffnesses in the analysis
54 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability and 2nd-Order Effects
• P-D
• P-d
• Out-of-Plumbness
• Member Out-of-Straightness
• Residual Stresses
55 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Leaning Columns
56 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Leaning Columns
57 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Leaning Columns
58 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Methods of 2nd Order Analysis
• Amplified 1st Order Elastic Analysis
– e.g., B1 and B2 Factors
• Iterative
• Geometric Stiffness Method (for P-D)
59 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Methods of 2nd Order Analysis
• Amplified 1st Order Elastic Analysis
– e.g, B1 and B2 Factors
• Iterative
• Geometric Stiffness Method (for P-D)
60 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Methods of 2nd Order Analysis
Limitations of the B2 method
• It was developed based on planar frames. It does not account for rotational effects of the 3-dimensional structure.
• May not be accurate for complex buildings.
61 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Methods of 2nd Order Analysis
Advantages of the B2 method
• Straightforward. The P-D affects are quantified (B2 is the ratio of the drift including P-D effects over the drift excluding P-D effects) so you can readily see the impact on design forces.
• Considers the effects of “Leaning Columns” if done correctly.
• Principle of Superposition applies. This allows Load Cases to be analyzed and then the results combined in combinations.
62 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Principle of Superposition
Principle of Superposition says:
(A)results + (B)results + (C)results = (A + B + C)results
For example:
(Dead)results + (Live)results + (Seismic)results = (Dead + Live + Seismic)results
However, the 2nd order effects are nonlinear, so without accounting for those:
(Dead)results + (Live)results + (Seismic)results (Dead + Live + Seismic)results
It is possible, however, to modify the analysis results such that superposition can be used:
B2(Dead)results + B2(Live)results + B2(Seismic)results (Dead + Live + Seismic)results
63 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Principle of Superposition applies when using the B2 method
The B2 method is a way of approximating a 2nd Order analysis by amplifying the results of a 1st Order analysis.
The B2 factors are calculated for each combination, based on the load case analysis results. This allows the analysis program to quickly analyze a small number of load cases (D, L, Rf, Wind, EQ, usually about 20 or so cases) and then comprehensively combine those results in the required load combinations (usually more than 160).
This is much more convenient for the user, it is quicker and it produces less analysis results to have to review.
64 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Methods of 2nd Order Analysis
• Amplified 1st Order Elastic Analysis
– e.g., B1 and B2 Factors
• Iterative
• Geometric Stiffness Method (for P-D)
65 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Methods of 2nd Order Analysis
Advantages of the Iterative P-delta method
• Theoretically most accurate of the three methods.
• Can be used for non-building structures.
66 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Methods of 2nd Order Analysis
Limitations of the Iterative P-delta method
• Live Load Reduction can not be easily applied (correctly). This can result in up to 60% error in Live Loads.
• Does not consider the effects of “Leaning Columns” unless they are included in the lateral analysis model. If not done properly the p-delta analysis could be off significantly.
• Requires that the Analysis be done on Load Combinations, not Load Cases. This can be very time-consuming and can produce an overwhelming amount of analysis data due to the large number of load combinations now required by Code.
• Impossible to do with Response Spectra?
67 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Methods of 2nd Order Analysis
• Amplified 1st Order Elastic Analysis
– e.g., B1 and B2 Factors
• Iterative
• Geometric Stiffness Method (for P-D)
68 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Methods of 2nd Order Analysis
Advantages of the Geometric Stiffness method (used by RAM Frame as an option)
• Live Load Reduction can be easily applied (correctly).
• Considers the effects of “Leaning Columns”.
• Principle of Superposition applies. This allows Load Cases to be analyzed and then the results combined in combinations.
• Valid with Response Spectra.
69 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Principle of Superposition
Principle of Superposition says:
(A)results + (B)results + (C)results = (A + B + C)results
For example:
(Dead)results + (Live)results + (Seismic)results = (Dead + Live + Seismic)results
However, the 2nd order effects are nonlinear, so without accounting for that:
(Dead)results + (Live)results + (Seismic)results (Dead + Live + Seismic)results
It is possible, however, to modify the analysis such that superposition can be used:
(Dead)results + (Live)results + (Seismic)results (Dead + Live + Seismic)results
70 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Principle of Superposition applies when using the Geometric Stiffness method
The Geometric Stiffness method is a way of modifying the analysis such that the 2nd Order analysis results can be obtained directly by performing a 1st Order analysis.
Theoretically the Geometric Stiffness method gives the same results as an iterative approach.
This allows RAM Frame to quickly analyze a small number of load cases (D, L, Rf, Wind, EQ, usually about 20 or so cases) and then comprehensively combine those results in the required load combinations (usually more than 160).
This is much more convenient for the user, it is quicker and it produces less analysis results to have to review.
71 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
• AISC 360-10 Specification for Structural Steel Buildings
• ACI 318-14 Building Code Requirements for Structural Concrete
• Eurocode 3 EN 1993-1-1:2005+A1:2014 Design of Steel Structures
• Australia AS 4100-1998 Steel Structures
Specification Requirements Related toStability and 2nd-Order Analysis
72 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
AISC 360-10
C1. GENERAL STABILITY REQUIREMENTS
Stability shall be provided for the structure as a whole and for each of its elements…
Any rational method of design for stability that considers all of the listed effects is
permitted; this includes the methods identified in Sections C1.1 and C1.2.
1. Direct Analysis Method of Design
The direct analysis method of design, which consists of the calculation of required
strengths in accordance with Section C2 and the calculation of available strengths in
accordance with Section C3, is permitted for all structures.
2. Alternative Methods of Design
The effective length method and the first-order analysis method, defined in Appendix
7, are permitted as alternatives to the direct analysis method for structures that satisfy
the constraints specified in that appendix.
73 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
• Purpose: to address the stability and 2nd-order effects
• Direct Analysis Method is not an analysis method!
– Finite Element Analysis, Response Spectra Analysis, Virtual Work, Moment Distribution, etc., are analysis methods
• It is a methodology consisting of several possible techniques for addressing the various stability effects, most notably directly modeling those effects for inclusion in the analysis
AISC 360 Direct Analysis Method
74 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
AISC 360 Direct Analysis Method
AISC 360-10 Chapter C
• P-D: Any valid method, including iterative, geometric stiffness, or B2
• P-d: Any valid method, including iterative or B1
• Out-of-Plumbness: Direct modeling of ‘leaning’ structure or Notional Loads (0.002)
• Member Out-of-Straightness: Stiffness reduction (0.8, tb)
• Residual Stresses: Stiffness reduction (0.8, tb)
75 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
AISC 360 Direct Analysis Method
RAM Frame:
76 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
AISC 360 Direct Analysis Method
RAM Frame:
77 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
AISC 360 Direct Analysis Method
RAM Frame:
78 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
AISC 360 Direct Analysis Method
RAM Frame:
79 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
AISC 360 Direct Analysis Method
RAM Frame:
80 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
AISC 360 Direct Analysis Method
RAM Frame:
81 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
AISC 360 Direct Analysis Method
RAM Frame:
82 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
AISC 360 Direct Analysis Method
K = 1.0
83 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
AISC 360-10 Stability Requirements
C1. GENERAL STABILITY REQUIREMENTS
Stability shall be provided for the structure as a whole and for each of its elements…
Any rational method of design for stability that considers all of the listed effects is
permitted; this includes the methods identified in Sections C1.1 and C1.2.
1. Direct Analysis Method of Design
The direct analysis method of design, which consists of the calculation of required
strengths in accordance with Section C2 and the calculation of available strengths in
accordance with Section C3, is permitted for all structures.
2. Alternative Methods of Design
The effective length method and the first-order analysis method, defined in Appendix
7, are permitted as alternatives to the direct analysis method for structures that satisfy
the constraints specified in that appendix.
Recommendation:
Use Direct Analysis Method for Steel Moment Frames (can use K=1)
Use Effective Length Method for Steel Braced Frames (K=1 for Braced Frames)
84 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
AISC Design Guide 28: Stability Design of Steel Buildings
Bentley Communities wiki:ASCE 7, AISC 360, and the Direct Analysis Method in the RAM Structural System
Go to: http://communities.bentley.com, and search for ASCE 7
AISC 360-10 Stability Requirements
85 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
ACI 318-14 Structural Concrete
86 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
ACI 318-14 Structural Concrete
87 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
ACI 318-14 Structural Concrete
88 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
ACI 318-14 Structural Concrete
89 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
ACI 318-14 Structural Concrete
90 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
ACI 318-14 Structural Concrete
91 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
ACI 318-14 Structural Concrete
92 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
ACI 318-14 Structural Concrete
93 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Eurocode EN 1993-1-1:2005+A1:2014 Steel
94 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Eurocode EN 1993-1-1:2005+A1:2014 Steel
95 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Eurocode EN 1993-1-1:2005+A1:2014 Steel
If acr 10, 1st-order analysis may be used.
96 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Eurocode EN 1993-1-1:2005+A1:2014 Steel
97 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
5.2.2 Structural Stability of Frames
Eurocode EN 1993-1-1:2005+A1:2014 Steel
98 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Eurocode EN 1993-1-1:2005+A1:2014 Steel
99 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Eurocode EN 1993-1-1:2005+A1:2014 Steel
100 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Eurocode EN 1993-1-1:2005+A1:2014 Steel
This is a Notional Load
101 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Eurocode EN 1993-1-1:2005+A1:2014 Steel
This is a Notional Load
102 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Eurocode EN 1993-1-1:2005+A1:2014 Steel
103 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Australia AS 4100-98 Steel Structures
104 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Australia AS 4100-98 Steel Structures
105 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Australia AS 4100-98 Steel Structures
106 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Australia AS 4100-98 Steel Structures
107 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Australia AS 4100-98 Steel Structures
108 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Australia AS 4100-98 Steel Structures
109 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Drift
• Occupant Comfort
• Protect Nonstructural Elements
• Structural Stability
Bentley Systems, Inc. On-Demand Video:
Building Drift: Understanding and Satisfying Code Requirements
Go to: http://pages.info.bentley.com/videos/
or Google the title
Purpose of Drift Limits
110 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
ASCE 7 Stability Coefficient
Section 12.8.7 P-Delta Effects:
𝜃 =𝑃𝑥𝛥𝐼𝑒𝑉𝑥ℎ𝑠𝑥𝐶𝑑
(12.8-16)
“The stability coefficient (q) shall not exceed qmax determined as follows:
𝜃𝑚𝑎𝑥 =0.5
𝛽𝐶𝑑≤ 0.25 (12.8-17)
where b is the ratio of shear demand to shear capacity…. This ratio is
permitted to be conservatively taken as 1.0.
Where q is greater than qmax, the structure is potentially unstable and shall be
redesigned.”
111 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
ASCE 7 Stability Coefficient
Section 12.8.7 P-Delta Effects:
𝜃 =𝑃𝑥𝛥𝐼𝑒𝑉𝑥ℎ𝑠𝑥𝐶𝑑
(12.8-16)
“The stability coefficient (q) shall not exceed qmax determined as follows:
𝜃𝑚𝑎𝑥 =0.5
𝛽𝐶𝑑≤ 0.25 (12.8-17)
Where the P-delta effect is included in an automated analysis, Eq. 12.8-17
shall still be satisfied, however, the value of q computed from Eq. 12.8-16
using the results of the P-delta analysis is permitted to be divided by (1+ q)
before checking 12.8-17.”
That is, compare qmax to q/(1+q).
112 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
ASCE 7 Stability Coefficient
𝜃 =𝑃𝑥𝛥𝐼𝑒𝑉𝑥ℎ𝑠𝑥𝐶𝑑
(12.8-16)
𝜃𝑚𝑎𝑥 =0.5
𝛽𝐶𝑑≤ 0.25 (12.8-17)
𝜃 1 + 𝜃 when P-delta included in analysis
113 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
ASCE 7 Stability Coefficient
𝜃 =𝑃𝑥𝛥𝐼𝑒𝑉𝑥ℎ𝑠𝑥𝐶𝑑
(12.8-16)
𝜃𝑚𝑎𝑥 =0.5
𝛽𝐶𝑑≤ 0.25 (12.8-17)
𝜃 1 + 𝜃 when P-delta included in analysis
For example, assuming b=1.0 and with Cd = 5½:
qmax = (0.5)/[(1.0)(5.5)] = 0.091.
Since P-delta included in analysis compare q/(1+q):
0.126 > 0.091 No Good
114 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability Coefficient
ASCE 7-10:
ACI 318-14:
EN 1993:
AS 4100:
AISC 360-10:
115 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Stability Coefficient
ASCE 7-10:
ACI 318-14:
EN 1994:
AS 4100:
AISC 360-10:
116 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Analysis and Design for Stability
117 | WWW.BENTLEY.COM | © 2015 Bentley Systems, Incorporated
Analysis and Design for Stability
Thanks!
Questions?