Chevron Braced Frame

Figure 1C-1. Four-story steel frame office building with chevron braced frames

Overview Overview Overview Overview

This Example illustrates the additional design requirements for chevron bracing designed as either an Ordinary Concentric Braced Frame (OCBF) or a Special Concentric Braced Frame (SCBF). The typical design bay from Design Example 1A is modified for use in this example. For comparison, the member forces are assumed to be the same as for Design Examples 1A and 1B. It is recommended that the reader first review Design Examples 1A and 1B before reading this example. Refer to Design Example 1A for plans and elevations of the structure (Figures 1A-1 through 1A-4).

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Outline Outline Outline Outline

This Design Example illustrates the following parts of the design process:

1.1.1.1. Bracing configuration.

2.2.2.2. Chevron bracing design under OCBF requirements.

3.3.3.3. Chevron bracing design under SCBF requirements.

4.4.4.4. Brace to beam connection design.

Calculations and Discussion Calculations and Discussion Calculations and Discussion

Calculations and Discussion Code Code ReferenceCode ReferenceCode Reference Reference

1. 1. 1. 1.

Bracing configuration. §2213.2, 2213.8

Section 2213.2 defines chevron bracing as “…that form of bracing where a pair of braces located either above or below a beam terminates at a single point within the clear beam span.” It also defines V-bracing and inverted V-bracing as chevron bracing occurring above or below the beam (Figure 1C-2).

Chevron V-bracing Chevron inverted V-bracing

Figure 1C-2. Chevron bracing elevations

As discussed in the Blue Book Commentary §C704.9, the seismic performance of chevron braces can degrade under large cyclic displacements if the diagonals have poor post-buckling behavior. For this reason, the design force for chevron bracing in OCBF systems is increased so that the bracing members remain elastic during moderate earthquakes. Chevron bracing in SCBF systems has demonstrated enhanced post-buckling behavior, due to the additional design parameters placed

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on SCBF members and connections. Chevron braces designed to SCBF requirements are therefore not subject to the load amplification factor (§2213.8.4.1, Item 1) imposed on chevron braces in OCBF systems.

Recognizing that the buckling capacity of the compression diagonals is critical to all forms of braced frame performance, §2213.8.2.3 requires that no more than 70 percent of the diagonals act in compression along any line of bracing. By providing some balance in the distribution of tension and compression diagonals, ultimate inelastic story drifts are compatible for both directions.

The typical design bay from Design Example 1A is re-configured for chevron inverted V-bracing, as shown below in Figure 1C-3.

Figure 1C-3. Typical chevron braced bay under OCBF requirements

2. 2. 2. 2.

Chevron bracing design under OCBF requirements.

For comparison, assume the forces to the diagonal bracing members are the same as for Example 1B:

TS brace @ 3^rd story:

kipsP_DL =24 kipsP_LL =11 kipsP_E = 400

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For OCBF chevron bracing, §2213.8.4.1 requires that the seismic force be increased by a factor of 1.5:

( )

^{400 600kips}

Also note that the same section requires the beam to be continuous between columns, and that the beam be capable of supporting gravity loads without support from the diagonal braces. From Design Example 1A, the W24×68 girder satisfies these conditions.

For the diagonal brace at the third story, we have the following basic ASD load combinations with no one-third increase:

4

The compressive axial load of Equation (12-9) controls.

From Design Example 1B, the capacity of a TS 10×10×58 tube section, adjusted by the stress reduction factor

( )

B of §2213.8.2.2 is:

kipsPas =342kips<453 n.g. §2213.8.2.5

The TS 10×10×58 is the largest section that satisfies the width-thickness ratio for tubes as required by §2213.8.2.5. A wide flange section using A572 grade. 50 steel

(

^{Fy =50ksi}

)

will be required in lieu of a tube section.

Effective length @ centerline: kl =^1.0

( )

^18.5 =^18.5ft §2213.8.2.1 Maximum slenderness ratio:

Fy

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Maximum width-thickness ratio 65 9.2

2 ≤ =

b AISC-ASD, Table B5.1

Try 120W12× brace:

Stress reduction factor: §2213.8.2.2

a

For SCBF chevron bracing, §2213.9.4.1 does not require the seismic force to be increased by a factor of 1.5 as is required for OCBF chevron braces. This provision is waived for SCBF chevron bracing due to an additional requirement for beam design. As for OCBF braces, §2213.9.4.1 also requires the beam to be continuous between columns, and that the beam be capable of supporting gravity loads without support from the diagonal braces. Additionally, for special chevron bracing, the beam intersected by chevron braces is to have sufficient strength to resist gravity loads combined with unbalanced brace forces. This requirement

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provides for overall frame stability, and enhanced post-buckling behavior, with reduced contribution from the buckled compression bracing members.

For comparison, assume the member forces remain the same as for Design Example 1A.

TS brace @ 3^rd story:

kipsPDL =24 kipsPLL =11 kipsP_E =348 WF beam @ 3^rd story:

600MDL =1, kip-in.

193MLL =1, kip-in.

kipsVDL =14.1 kipsVLL =72 kipsPE =72

3a. 3a. 3a. 3a.

Diagonal brace design.

The diagonal brace design for the SCBF chevron brace remains the same as that of the two-story X-brace presented in Design Example 1A.

∴Use TS 8×8×58 brace member

3b. 3b. 3b. 3b.

Beam design at the 3^rd floor.

As demonstrated in Design Example 1A, the W24×68 beam satisfies the basic load combinations of §1612.3.1. However, the unbalanced brace force specified in

§2213.9.4.1 imposes a severe mid-span point load to the beam. Using a TS 8

5 8

8× × section, the brace forces are as follows:

( )

^=17.4

^{( )}

^{46 =800.4kips}

= _y

st AF

P

( )

^{324 551kips}

7 . 1 7

.

1 = =

= _allow

sc P

P

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The maximum unbalanced brace force P is taken as the net difference of the _b

vertical components of P and _st 0.3P_sc as show in Figure 1C-4. §2213.9.4.1

Pst 0.3Psc

Figure 1C-4. Unbalanced chevron brace forces

[

^{800.4 0.3}

( )

⁵⁵¹

]

^449kips

The beam must have the strength to resist load combinations similar to the Special Seismic Combinations of §1612.4:

Pb

Neglecting consideration of composite beam action, and using the flexural strength, the minimum required plastic modulus Z is solved below (using A572 grade 50 steel).

( )

y max

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To complete the beam design, the beam-to-column connection should be checked for the reaction from vertical load plus

(

Pb ²

)

.

Comment: From the foregoing examples in Parts 2 and 3, it is apparent that compared to X-bracing, chevron bracing will require a substantial increase in member sizes. For the OCBF chevron-braced system, the brace size will increase, possibly resulting in larger demands at the connections. For the SCBF chevron bracing, the beam size increases to provide the capacity to meet the strength demand imposed by the unbalanced, post-buckling brace forces. Given their superior cyclic performance, it is recommended that SCBF chevron bracing be used in regions of moderate to high seismicity.

4. 4. 4. 4.

Brace to beam connection design. §2213.9.3.1

The brace to beam connection is shown in Figure 1C-5 below. This Example uses the SCBF bracing and forces. The design for the OCBF connection is similar, without the 2t setback between the end of the brace and the line of restraint for the gusset plate, as required for SCBF systems.

Figure 1C-5. Chevron brace-to-beam connection

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4a. 4a. 4a. 4a.

Gusset plate design.

From Design Example 1A, the TS 8×8×58 brace strength is used for connection design. The brace-to-gusset design is as given in Part 6d of Design Example 1A:

Connection force:

( )

^=800.4kips

= _y

st AF

P

Brace weld to gusset:

"

18 of ¹₂" fillet weld each side each face Gusset plate thickness:

"

1 plate gusset minimum

The gusset plate is also checked for shear and bending at the interface with the beam. From Figure 1C-5 we determine the plate length to be 86 inches.

Check plate shear stress:

( )

_1,132kips

Check plate bending stress.

From Figure 1-4, use an assumed moment couple length as distance between intersections of brace centerlines with beam flange.

( )( )

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The allowable compressive bending stress is governed by the unsupported plate length perpendicular to the beam. From Figure 1C-5:

"

2 =10

l and assume k =1.2

( ) ( )

^{1.0 41.4}

29 . 0

10 2 .

1 =

r =

kl AISC-ASD, Table C-36

ksi∴ Fa =19.08

AllowableFsc =^1.7

( )

Fa =^1.7

(

^19.08

)

=^32.4ksi>^11.0ksi o.k.

∴Use 1-inch plate gusset

4b. 4b. 4b. 4b.

Gusset to beam design.

Length of weld to beam is lw =86inches. Minimum fillet weld for 1-inch plate is 5/16-inch. Per inch of effective throat area, weld stresses are:

( ) ( )

^{12,13286 6.58ksi}

2 = =

=

w

x l

f V (x-axis)

( )

⁸⁶

( )

^8.26ksi

2 6 375 , 20

2 =

=

=

w

y S

f M (y-axis)

( ) ( )

^{6.58 2 + 8.26 2 =10.56ksi}

r =

f (resultant)

Allow Fw =^1.7

( )

^0.370=^35.7ksi §2213.4.2

Required weld size:

( )

^{35.7 0.41in.}

707 . 0

56 .

10 =

w = t

∴ Use 1/2-inch fillet weld each side plate

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Commentary Commentary Commentary Commentary

The Blue Book Commentary warns that even with the strong-beam SCBF chevron, configurations may be susceptible to large inelastic displacements and P-delta effects. To mitigate these effects, chevron configurations that use two-story X-bracing or zipper columns are recommended. These bracing configurations are presented in the section Factors That Influence Design at the beginning of Design Example 1A.

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In document SEAOC Seismic Design Manual Examples Vol 3.pdf (Page 87-99)