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Brace Compression and Tension Capacity Design Charts As Per CSA S16-09 ?
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TABLE OF CONTENTS
2.1.1??
WT Brace Under Compression
2.1.1.1?? WT Brace Compression ? Non X-Brace Case
2.1.1.2?? WT Brace Compression ?X-Brace Case
2.1.2?? WT Brace
Under Tension
2.2.1??
Double Angle Brace Under Compression
2.2.1.1??
Vertical Double Angle Brace
2.2.1.1.1?? Double Angle Brace Compression ? Non X-Brace
Case
2.2.1.1.1.1?? Equal Angle Back-to-Back
2.2.1.1.1.2?? Unequal Angle Long Leg Back-to-Back
2.2.1.1.2?? Double Angle Brace Compression ?X-Brace Case
2.2.1.1.2.1?? Equal Angle Back-to-Back
2.2.1.1.2.2?? Unequal Angle Long Leg Back-to-Back
2.2.1.2??
Horizontal Double Angle Brace
2.2.1.2.1?? Double Angle Brace Compression ? Non X-Brace
Case
2.2.1.2.1.1???
Equal Angle Back-to-Back
2.2.1.2.2?? Double Angle Brace Compression ? X-Brace
Case
2.2.1.2.2.1?? Equal Angle Back-to-Back
2.2.2??
Double Angle Brace Under Tension
2.2.2.1??
Vertical Double Angle Brace
2.2.2.1.1?? Equal Angle Back-to-Back
2.2.2.1.2?? Unequal Angle Long Leg Back-to-Back
2.2.2.2??
Horizontal Double Angle Brace
2.2.2.2.1?? Equal Angle Back-to-Back
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)
2.1?? 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
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