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Dongxiao Wu P. Eng. (Alberta, Canada)

 

Home  >> Tutorial >>  Brace Compression and Tension Capacity Design Charts As Per CSA S16-09    ? Download PDF        ? Buy This Document

 

TABLE OF CONTENTS

 

1.0?? INTRODUCTION.. 2

2.0?? DESIGN CHARTS.. 3

2.1?? WT BRACE. 3

2.1.1?? WT Brace Under Compression. 3

2.1.1.1?? WT Brace Compression ? Non X-Brace Case. 3

2.1.1.2?? WT Brace Compression ?X-Brace Case. 32

2.1.2?? WT Brace Under Tension. 62

2.2?? DOUBLE ANGLE BRACE. 73

2.2.1?? Double Angle Brace Under Compression. 73

2.2.1.1?? Vertical Double Angle Brace. 73

2.2.1.1.1?? Double Angle Brace Compression ? Non X-Brace Case. 75

2.2.1.1.1.1?? Equal Angle Back-to-Back. 76

2.2.1.1.1.2?? Unequal Angle Long Leg Back-to-Back. 98

2.2.1.1.2?? Double Angle Brace Compression ?X-Brace Case. 111

2.2.1.1.2.1?? Equal Angle Back-to-Back. 112

2.2.1.1.2.2?? Unequal Angle Long Leg Back-to-Back. 132

2.2.1.2?? Horizontal Double Angle Brace. 145

2.2.1.2.1?? Double Angle Brace Compression ? Non X-Brace Case. 146

2.2.1.2.1.1??? Equal Angle Back-to-Back. 147

2.2.1.2.2?? Double Angle Brace Compression ? X-Brace Case. 167

2.2.1.2.2.1?? Equal Angle Back-to-Back. 168

2.2.2?? Double Angle Brace Under Tension. 188

2.2.2.1?? Vertical Double Angle Brace. 188

2.2.2.1.1?? Equal Angle Back-to-Back. 190

2.2.2.1.2?? Unequal Angle Long Leg Back-to-Back. 198

2.2.2.2?? Horizontal Double Angle Brace. 203

2.2.2.2.1?? Equal Angle Back-to-Back. 204


 

1.0?? INTRODUCTION

 

Singly symmetric sections WT and double angle are widely used in steel structure as bracing members. STAAD Pro?s code check ratio output of these singly symmetric members are useless due to the following limitations

 

1.       Eccentric Moment Not Considered in STAAD for WT and Double Angle Code Check

STAAD output code check ratio is based on pure compression/tension case, which is not correct as there is an eccentric moment applied due to brace connection. The correct code check shall consider the combination of axial tension /compression+ flexure, which actually yields a much lower capacity. From the following design charts we can see the brace actual tension/compression? resistance under combined tension/compression + flexure can be only 35% of pure tension/compression case.

2.       Complexities on Applying Eccentric Moment to Brace Member in STAAD for Code Check

The eccentricity of brace force varies based on brace type (WT or double angle) and brace location (horizontal or vertical). The eccentric moment also varies in direction based on tension or compression force, which causes the tee stem in tension or compression and different flexural capacity. Considering the different? load combinations causing different tension/compression forces in brace, it?s impractical to apply eccentric moment manually in STAAD for code check.

3.       Complexities on Defining Correct Brace Member Local Axis, In-Plane and Out-of-Plane Unsupported Length

There are tremendous complexities to get a brace member correctly modeled/defined in STADD model for correct code checking. For example, the double angle X-bracing, engineers shall define correct in-plane and out-of- plane Ly, Lz value, check member?s local axis to make sure it?s correct in terms of ry, rz corresponding to previous defined Ly, Lz etc.

4.       Code Checking on Class 4 Member Not Available in STAAD

STAAD does not design Class 4 section. Class 4 section is valid for use in steel structure. The engineers have to work

around this by defining lower yield strength in STAAD, section by section,? to make it pass the code check. This is very

time consuming process.

 

To simplify the code checking of WT and double angle bracing member, design charts and tables are created based on CSA S16-09 for quick member capacity lookup. These design charts and tables eliminate the complexities by sorting the charts and tables in different criteria. By looking up the charts and tables in the desired category, the engineers will get the correct brace design parameters (eccentricity and moment, in-plane and out-of-plane unsupported length, eccentric moment direction) automatically and find the brace tension/compression capacity in seconds.

?          For X-bracing, correct in-plane and out-of-plane unsupported length is implemented in terms of? brace location (horizontal or vertical) and brace type (WT or double angle)

?          Correct eccentric moment is applied in terms of? brace location (horizontal or vertical) and brace type (WT or double angle)

?          The eccentric moment is applied at right direction in terms of? brace location (horizontal or vertical) and brace type (WT or double angle). This will cause the WT or double angle?s stem in the correct tension or compression case.

?          Class 4 member capacity is available. Class 4 member is designed using the effective area per CSA S16-09 clause 13.3.5 (a)

 

 

2.0?? DESIGN CHARTS

 

2.1?? WT BRACE

 

2.1.1?? WT Brace Under Compression

 

2.1.1.1?? WT Brace Compression ? Non X-Brace Case

 

Design Basis & Assumption:

1.       WT compression resistance capacity for two cases, with and without eccentric moment presence are presented.

2.       The eccentric moment is calculated using gusset plate thickness =10mm. The eccentricity value is shown in each chart.

3.       The capacity curve stops if next 0.5m increase of unsupported length causes KL/r ratio exceeding 200.

4.       Assume WT unsupported length Lx = Ly =1.0L and Kx = Ky =1.0

5.       WT brace design yield strength = 50 ksi =345 MPa

6.       Section class is shown in each chart. For class 4 member, the effective area is used for calculation as per CSA S16-09 clause 13.3.5 (a)

7.       ?WT flexural capacity is calculated based on AISC 360-05 section F9

8.       Assume P-d (small delta) is not performed in steel frame stability calculation, which shall be always the case for all CIVILBAY STAAD users using Canadian code.? The U1 factor (CSA S16-09 clause 13.8.4 ) is calculated and applied for WT strength and stability check as per CSA S16-09 clause 13.8.3

 

  

 

 

 

 

 

 

 

 

 

 

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2.1.1.2?? WT Brace Compression ?X-Brace Case

 

Design Basis & Assumption

 

1.       X-Bracing Out-of-Plane Unsupported Length

In X-bracing design where two braces are connected at midpoint, some engineers may consider the brace in tension can be counted on to laterally brace the compression strut at midpoint against out-of-plane buckling. Reference is made to AISC Engineering Journal 4th Quarter 1997 "Practical Application of Energy Methods to Structural Stability Problems" by R. Shankar Nair. The out-of-plane stiffness of the intersection point of the braces must be calculated to determine if the tension member can be taken as a brace for the compression member.

Since it is not practical to do such calculation for every X-bracing and the result may not be positive even the calculation is done, we assume in X-bracing design the out-of-plane unsupported length is full length and the in-plane unsupported length is half length.

 

 

WT Brace Intersect Point Connection

 

 

WT Vertical Brace

 

 

WT Horizontal Brace

 

 


 

 

WT and Double Angle Brace Local Axis

 

 

 

For both horizontal and vertical case, used Lx = 1.0L , Ly =0.5L for all X-bracing compression capacity

calculation.

 

2.       For all design charts in this section we assume the X-bracing member can take compression force.

For Tension Only X-bracing member design please refer to tension capacity charts.

3.       WT compression resistance capacity for two cases, with and without eccentric moment presence are presented.

4.       The eccentric moment is calculated using gusset plate thickness =10mm. The eccentricity value is shown in each chart.

5.       The capacity curve stops if next 0.5m increase of unsupported length causes KL/r ratio exceeding 200.

6.       Assume WT unsupported length Lx = 1.0L , Ly =0.5L and Kx = Ky =1.0

7.       WT brace design yield strength = 50 ksi =345 MPa

8.       Section class is shown in each chart. For class 4 member, the effective area is used for calculation as per CSA S16-09 clause 13.3.5 (a)

9.       ?WT flexural capacity is calculated based on AISC 360-05 section F9

10.    Assume P-d (small delta) is not performed in steel frame stability calculation, which shall be always the case for all CIVILBAY STAAD users using Canadian code.? The U1 factor (CSA S16-09 clause 13.8.4 ) is calculated and applied for WT strength and stability check as per CSA S16-09 clause 13.8.3

11.    For all WT sections, only sections with rx > ry get higher capacity when Lx=1.0L and Ly=0.5L

These sections are

 

WT100x11????

WT125x12.5???????????????? WT125x16.5???????? WT125x19.5???????? WT125x22.5

WT155x19.5???????????????? WT155x22.5???????? WT155x26

 

These sections are marked with ?*? in the chart

 


 

 

 

 

 

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2.1.2?? WT Brace Under Tension

 

Design Basis & Assumption:

1.       WT member capacity under tension + eccentric moment governs the design. Brace connection capacity, including the effective net area caused by shear lag (CSA S16-09 clause 12.3.3.2), does not govern the design.

2.       The eccentric moment is calculated using gusset plate thickness =10mm. The eccentricity value is shown in each chart.

3.       WT maximum unsupported length is calculated as Lmax = min( rx , ry ) x 300 as per CSA S16-09 clause 10.4.2.2

4.       WT brace design yield strength = 50 ksi =345 MPa

5.       WT flexural capacity is calculated based on AISC 360-05 section F9, tee stem in compression case.


 

Tr ???? WT factored tension resistance capacity considering eccentric moment, CSA S16-09 clause 13.9

T1.0 ? ?100% of (f Ag Fy) CSA S16-09 clause 13.2 (a) (i)

T0.5 ? ?50% of (f Ag Fy) , this is normally the value used for connection design for connections without specified design force

Lmax ? Maximum allowed brace unsupported length, CSA S16-09 clause 10.4.2.2

 

 

 

 

 

 

 

 

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Tr ???? WT factored tension resistance capacity considering eccentric moment, CSA S16-09 clause 13.9

T1.0 ?? 100% of (f Ag Fy) CSA S16-09 clause 13.2 (a) (i)

T0.5 ?? 50% of (f Ag Fy) , this is normally the value used for connection design for connections without specified design force

Lmax ? Maximum allowed brace unsupported length, CSA S16-09 clause 10.4.2.2

 

 

 

 

 


 

2.2?? DOUBLE ANGLE BRACE

 

2.2.1?? Double Angle Brace Under Compression

 

2.2.1.1?? Vertical Double Angle Brace

 

Design Basis & Assumption

 

1.       Assume gusset plate thickness = 10mm ? section radius of gyration ry is calculated based on double angle back-to-back with 10mm gap

2.       Assume the double angle brace is bolt connected and this will create eccentricity between bolt center line (force center line) and section?s X-X axis line. The eccentricity is calculated as the maximum of

?          e1 calculated assuming bolt center line is at center line of angle leg

?          e2 calculated assuming bolt center line is at AISC recommended gauge line of angle leg

 

In the following example the eccentricity is calculated as e = max(e1 , e2) = 32.4mm

 

 

 


 

3.       The bolt gauge used for double angle connection is based on AISC Manual of Steel Construction 2nd Edition Figure 9-5 on Page 9-13

 

 

4.       Double angle compression resistance capacity for two cases, with and without eccentric moment presence are presented.

5.       The capacity curve stops if next 0.5m increase of unsupported length causes KL/r ratio, including modified slenderness ratio considering interconnection bolt at spacing = 1200 mm, exceeding 200.

6.       Double angle brace design yield strength =300 MPa

7.       Section class is shown in each chart. For class 4 member, the effective area is used for calculation as per CSA S16-09 clause 13.3.5 (a)

8.       Double angle flexural capacity is calculated based on AISC 360-05 section F9, stem in compression case.

9.       Assume double angle brace has interconnecting batten plate and 3/4" dia. bolt at spacing = 1200 mm

Modified slenderness ratio is used as per AISC 360-05 E6-1 to account for interconnection bolt at spacing = 1200 mm

10.    Assume P-d (small delta) is not performed in steel frame stability calculation, which shall be always the case for all CIVILBAY STAAD users using Canadian code.? The U1 factor (CSA S16-09 clause 13.8.4 ) is calculated and applied for WT strength and stability check as per CSA S16-09 clause 13.8.3


 

2.2.1.1.1?? Double Angle Brace Compression ? Non X-Brace Case

 

Design Basis & Assumption

 

1.       All Design Basis & Assumption on Section 2.2.1.1 Vertical Double Angle Brace apply to this section

2.       Assume double angle unsupported length Lx = Ly =1.0L and Kx = Ky =1.0


 

2.2.1.1.1.1?? Equal Angle Back-to-Back

 


 


 

 

 

 

 

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2.2.1.1.1.2?? Unequal Angle Long Leg Back-to-Back

 

 

 

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2.2.1.1.2?? Double Angle Brace Compression ?X-Brace Case

 

Design Basis & Assumption

 

1.       Design charts in this section apply to vertical double angle X-bracing

2.       All Design Basis & Assumption on Section 2.2.1.1 Vertical Double Angle Brace apply to this section

3.       For vertical double angle X-bracing, use unsupported length Lx = 0.5L and Ly =1.0L , Kx = Ky =1.0

 

Double Angle Section Local Axis

 

Vertical Double Angle X-Bracing

Intersect Point Connection

 

 

 

4.       For all equal leg double angle sections, ?rx < ry, all sections get higher capacity due to X-bracing?s unsupported length Lx = 0.5L and Ly =1.0L

5.       All sections getting higher capacity due to rx < ry are marked with ?*? in the chart

 

 

 

2.2.1.1.2.1?? Equal Angle Back-to-Back

 

 

 

 

 

 

 

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2.2.1.1.2.2?? Unequal Angle Long Leg Back-to-Back

 

 

 

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2.2.1.2?? Horizontal Double Angle Brace

 

Design Basis & Assumption

 

1.       Double angle section radius of gyration ry is calculated based on double angle back-to-back with 0mm gap

2.       The eccentric moment is calculated using gusset plate thickness =10mm. The eccentricity value is shown in each chart.

3.       Double angle compression resistance capacity for two cases, with and without eccentric moment presence are presented.

4.       The capacity curve stops if next 0.5m increase of unsupported length causes KL/r ratio, including modified slenderness ratio considering interconnection bolt at spacing = 1200 mm, exceeding 200.

5.       Double angle brace design yield strength =300 MPa

6.       Section class is shown in each chart. For class 4 member, the effective area is used for calculation as per CSA S16-09 clause 13.3.5 (a)

7.       Double angle flexural capacity is calculated based on AISC 360-05 section F9, stem in tension case.

8.       Assume double angle brace has interconnecting 3/4" dia. bolt at spacing = 1200 mm . Modified slenderness ratio as per AISC 360-05 E6-1 is used to account for interconnection bolt at spacing = 1200 mm .

9.       Assume P-d (small delta) is not performed in steel frame stability calculation, which shall be always the case for all CIVILBAY STAAD users using Canadian code.? The U1 factor (CSA S16-09 clause 13.8.4 ) is calculated and applied for WT strength and stability check as per CSA S16-09 clause 13.8.3


 

2.2.1.2.1?? Double Angle Brace Compression ? Non X-Brace Case

 

Design Basis & Assumption

 

1.       All Design Basis & Assumption on Section 2.2.1.2 Horizontal Double Angle Brace apply to this section

2.       Assume double angle unsupported length Lx = Ly =1.0L and Kx = Ky =1.0

 


2.2.1.2.1.1        Equal Angle Back-to-Back

 

 

 


 

 

 

 

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2.2.1.2.2?? Double Angle Brace Compression ? X-Brace Case

 

Design Basis & Assumption

 

1.       Design charts in this section apply to horizontal double angle X-bracing

2.       All Design Basis & Assumption on Section 2.2.1.2 Horizontal Double Angle Brace apply to this section

3.       For horizontal double angle X-bracing, use unsupported length Lx = 1.0L and Ly =0.5L , Kx = Ky =1.0

 

Double Angle Section Local Axis

 

Horizontal Double Angle X-Bracing

Intersect Point Connection

 

 

 

4.       For all equal leg double angle sections,? rx < ry, none of the equal leg angle section gets higher capacity due to X-bracing?s unsupported length Lx = 1.0L and Ly =0.5L

 


 

2.2.1.2.2.1?? Equal Angle Back-to-Back

 

 

 

 

 


 

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2.2.2?? Double Angle Brace Under Tension

 

2.2.2.1?? Vertical Double Angle Brace

 

Design Basis & Assumption

 

1.       Assume gusset plate thickness = 10mm ? section radius of gyration ry is calculated based on double angle back-to-back with 10mm gap

2.       Assume the double angle brace is bolt connected and this will create eccentricity between bolt center line (force center line) and section?s X-X axis line. The eccentricity is calculated as the maximum of

?          e1 calculated assuming bolt center line is at center line of angle leg

?          e2 calculated assuming bolt center line is at AISC recommended gauge line of angle leg

 

In the following example the eccentricity is calculated as e = max(e1 , e2) = 32.4mm

 

 

 


 

3.       The bolt gauge used for double angle connection is based on AISC Manual of Steel Construction 2nd Edition Figure 9-5 on Page 9-13

 

 

4.       Double angle brace design yield strength =300 MPa

5.       Section class is shown in each chart. For class 4 member, the effective area is used for calculation as per CSA S16-09 clause 13.3.5 (a)

6.       Double angle flexural capacity is calculated based on AISC 360-05 section F9, stem in tension case.

6.       Double angle member capacity under tension + eccentric moment governs the design. Brace connection capacity, including the effective net area caused by shear lag (CSA S16-09 clause 12.3.3.2), does not govern the design.

7.       Double angle maximum unsupported length is calculated as Lmax = min( rx , ry ) x 300 as per CSA S16-09 clause 10.4.2.2


 

2.2.2.1.1?? Equal Angle Back-to-Back

 

Tr ???? Double angle factored tension resistance capacity considering eccentric moment, CSA S16-09 clause 13.9

T1.0 ?? 100% of (f Ag Fy) CSA S16-09 clause 13.2 (a) (i)

T0.5 ?? 50% of (f Ag Fy) , this is normally the value used for connection design for connections without specified design force

Lmax ? Maximum allowed brace unsupported length, CSA S16-09 clause 10.4.2.2

 

 

 

 

 

 

 


 

 

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2.2.2.1.2?? Unequal Angle Long Leg Back-to-Back

 

Tr ???? Double angle factored tension resistance capacity considering eccentric moment, CSA S16-09 clause 13.9

T1.0 ?? 100% of (f Ag Fy) CSA S16-09 clause 13.2 (a) (i)

T0.5 ?? 50% of (f Ag Fy) , this is normally the value used for connection design for connections without specified design force

Lmax ? Maximum allowed brace unsupported length, CSA S16-09 clause 10.4.2.2

 

 

 


 

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Tr ???? Double angle factored tension resistance capacity considering eccentric moment, CSA S16-09 clause 13.9

T1.0 ?? 100% of (f Ag Fy) CSA S16-09 clause 13.2 (a) (i)

T0.5 ?? 50% of (f Ag Fy) , this is normally the value used for connection design for connections without specified design force

Lmax ? Maximum allowed brace unsupported length, CSA S16-09 clause 10.4.2.2

 

 

 


 

2.2.2.2?? Horizontal Double Angle Brace

 

Design Basis & Assumption

 

1.       Double angle member capacity under tension + eccentric moment governs the design. Brace connection capacity, including the effective net area caused by shear lag (CSA S16-09 clause 12.3.3.2), does not govern the design.

2.       The eccentric moment is calculated using gusset plate thickness =10mm. The eccentricity value is shown in each chart.

3.       Double angle maximum unsupported length is calculated as Lmax = min( rx , ry ) x 300 as per CSA S16-09 clause 10.4.2.2

4.       Double angle brace design yield strength = 300 MPa

5.       Double angle flexural capacity is calculated based on AISC 360-05 section F9, tee stem in compression case.

 


 

2.2.2.2.1?? Equal Angle Back-to-Back

 

Tr ???? Double angle factored tension resistance capacity considering eccentric moment, CSA S16-09 clause 13.9

T1.0 ?? 100% of (f Ag Fy) CSA S16-09 clause 13.2 (a) (i)

T0.5 ?? 50% of (f Ag Fy) , this is normally the value used for connection design for connections without specified design force

Lmax ? Maximum allowed brace unsupported length, CSA S16-09 clause 10.4.2.2

 

 

 

 

 

 


 

 

 

 

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Tr ???? Double angle factored tension resistance capacity considering eccentric moment, CSA S16-09 clause 13.9

T1.0 ?? 100% of (f Ag Fy) CSA S16-09 clause 13.2 (a) (i)

T0.5 ?? 50% of (f Ag Fy) , this is normally the value used for connection design for connections without specified design force

Lmax ? Maximum allowed brace unsupported length, CSA S16-09 clause 10.4.2.2