Att 13-Dental Final Support Doc 5 of 8.pdf

BUEHLER & BUEHLER

STRUCTURAL ENGINEERS, INC.

JOB

JOB NO. DATE 7/12/2019

CLIENT BY KRH PAGE NO. 5

A

B

C

D

E f t

4 ft f t

.5 f t

.5 f t

142.5 ft f t

W in d o

Plan view - Gable roof

C

84 ft f t

Side face

A

A

142.5 ft f t

Windward face

B

142.5 ft f t

Leeward face

05.3.5

BUEHLER & BUEHLER

STRUCTURAL ENGINEERS, INC.

JOB

JOB NO. DATE 7/12/2019

CLIENT BY KRH PAGE NO. 6

A B C D

9.5 ft 9.5 ft 19 ft 104.5 ft

142.5 ft f tWind - 90o

Plan view - Gable roof

C

142.5 ft f t

Side face

A

A

A

84 ft f t

Windward face

B

84 ft f t

Leeward face

05.3.6

BF1

SPECIAL CONCENTRIC BRACED FRAME DESIGN (SCBF) - AISC 341-16

Brace Geometry

H = 14.0 ft W = 23.3 ft

LWP-WP = 18.22 ft LUNBRACED = 18.22 ft

LOFFSET = 2.0 ft

K = 1.00 KLBRACE = 14.22 ft

Q = 39.80 deg (For Connection Design) γ = 50.20 deg

Brace Properties

1. Choose Type of Member: HSS

2. Specify Brace Member: HSS4X4X5/16 Fy = 50 ksi A = 4.1 in2

3. Brace Configuration: E = 29000 ksi rx = 1.49 in

Material: Ry = 1.3 ry = 1.49 in

(KLUNBRACED)/r = 114.5 < 200 OK (AISC 341 F2.5b) h/t = 10.7 < 0.65√(E/RyFy) = 13.7 OK (AISC 341 F2.5a and Section D1.1) b/t = 10.7 < 0.65√(E/RyFy) = 13.7 OK (AISC 341 F2.5a and Section D1.1)

Brace Demands Brace Capacities & Design

VEQ = 18.4 k (@ 1.0E) ρ = 1 φC = 0.90

SDS = 1.22 φT = 0.90

Β2 = 1.00

Brace D1a D1b Brace D1a D1b

PDL 4.7 k 4.7 k Fcr 19.13 ksi 19.13 ksi α = 1.0

PLL 3.9 k 3.9 k φPn 70.6 k 70.6 k Pstory = 150.0 k f1 0.5 0.5 DCR 0.33 0.33 RM = 1.0

PEQ 14.4 k 14.4 k H = 400.0 k

Pu 23.1 k 23.1 k φTn 184.5 k 184.5 k ΔH = 3.36 in.

Tu 11.3 k 11.3 k DCR 0.06 0.06 Pe story = 20000.0 k

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+f1PLL+Β2(ρQE)] Tu = [-(0.9-0.2SDS)PDL + Β2(ρQE)]

Chevron BraceX-Brace or Single Diagonal

Chevron

ASTM A500 Grade C

Second Order Effects Considered in Analysis?

Yes

'H' and 'W' are dimensioned between work points.

VEQ

W

H

VEQ

W

H γ θ γ θ

C

C

C

C

05.4.1

V V

Column Demands and Design

Material: ASTM A992 Grade 50 FY-COL = 50 ksi RY-COL = 1.1

PDL 6.9 k Column Size W10X45 PDL 6.9 k Column Size W10X45

PLL 4.4 k b/2tf 6.5 Highly Ductile PLL 4.4 k b/2tf 6.5 Highly Ductile f1 0.5 h/tw 22.5 Highly Ductile f1 0.5 h/tw 22.5 Highly Ductile

PEQ 0.0 k KL/r 83.6 PEQ 0.0 k KL/r 83.6

PEmh 92.1 k Ca 0.158 PEmh 92.1 k Ca 0.158

Pu 104.2 k φPn 359.1 k Pu 104.2 k φPn 359.1 k

TEQ 0.0 k DCR 0.29 TEQ 0.0 k DCR 0.29

TEmh 68.0 k φTn -598.5 k TEmh 68.0 k φTn -598.5 k

Tu 0.0 k DCR 0.00 Tu 0.0 k DCR 0.00

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+f1PLL+PEmh] Tu = [(0.9-0.2SDS)PDL - TEmh]

Expected Strength of Brace in Compression (F2.3): Expected Strength of Brace in Tension (F2.3):

Pcompression = min(Ry-BRACE*Fy*A, 1.14*Fcre*A) Ptension = RY-BRACE*Fy*Ag

Fcre = 19.1 ksi

Pcomp= 89.4 k Pten = 266.5 k

Unbalanced Veritcal Force at Midspan of Beam (Chevron Only) F2.3(a) F2.3(b) R1 = (Pcomp*sin(ɣ) - Pten*sin(ɣ)) = -136.0 k -184.1 k

RCOL = R1 / 2 = -68.0 k -92.1 k Per Column

Foundation Reactions: Capacity Limited per AISC 341-16 for Base Connection Design

Ru = Pu + Pcomp1*sin(ɣ1) Ru = Tu - Pten1*sin(ɣ1)

C1 C2 C1 C2

Ru = 148.9 k 148.9 k Tu = -132.2 k -132.2 k

Foundation Reactions: Including Overstrength per ASCE 7-16 for Concrete Design Ωo = 2.0

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+ f1PLL+ ΩoPE] Tu = [(0.9-0.2SDS)PDL - ΩoTE]

PE = 11.0 k TE = -11.0 k

C1 C2 C1 C2

Ru = 34.2 k 34.2 k Ru = -17.6 k -17.6 k

Foundation Reactions: Alternative Basic Load Combinations for Soil Bearing and Uplift Design

Pu = PDL+ PLL+ ρPE/1.4 Tu = 0.9PDL - ρTE/1.4

PE/1.4 = 7.9 k TE/1.4 = -7.9 k

C1 C2 C1 C2

Ru = 19.2 k 19.2 k Ru = -1.7 k -1.7 k

Column C1 Column C2

Columns are designed using the load combinations noted below. The seismic demands considereding the load combinations from AISC 341-16 Section F2.3 are used to determine the Emh seismic demands. Depending on the orientation of the braces, the demands may be due to a brace connection at the top of the column or a reaction due to unbalanced loads at the midspan of the beam. For single diagonal configurations, columns without a brace attached to the top have no seismic demands. For Chevron configuartions, columns have no seismic demands for the ASCE 7-16 load combinations as the loads in the braces are assumed to be balanced so there is no seismic shear reaction at the ends of the beam.

Because the seismic component of the column required strenth comes from the mechanism analysis of AISC Seismic Provisions Section F2.3 and is based on expected strengths of the braces, P-Δ effects need not be considered and Β2 from AISC Specification Appendix 8 need not be applied. See additional discussion in AISC Seismic Manual Page 5-140.

Reaction are calculated using the same load combinations and loading considerations as the columns. In addition to the column loads, loading from braces at the base of the columns is combined with the column loading to determine the design reactions for base plate and anchor rod design.

05.4.2

V V

Beam Design @ Chevron Frame

Beam Properties

1. Choose Type of Member: WF L = 23.3 ft rx = 10.20 in. bf/2tf = 6.70

2. Specify Beam Member: W24X131 Ry(Beam) = 1.1 ry = 2.97 in. h/tw = 35.60

Fy = 50 ksi A = 38.50 in2 Ix = 4020 in4

E = 29000 ksi d = 24.50 in. tw = 0.61 in.

Ca = 0.120 bf = 12.90 in. ho = 23.54 in.

3. Check Element Ductility Per AISC 341 Table D1.1:

Flange Ductility: bf/2tf = 6.70 λhd = 7.35 Highly Ductile

Web Ductility: h/tw = 35.60 λhd = 51.74 Highly Ductile

Axial and Flexural Demands at Midspan

Expected Post-Buckling Brace Strength Beam End Restraints: Pinned-Pinned PPB = 0.3*min(RyBRACE*Fy*A, 1.14*Fcre*A) MDL = 65.0 k-in

MLL = 54.2 k-in

Qb = 136.0 k F2.3(a) - Vert

Qb = 184.1 k F2.3(b) - Vert

Qh = 227.8 k F2.3(a) - Axial

Qh = 187.8 k F2.3(b) - Axial

F2.3(a) F2.3(b) MEg = 9522 k-in 12888 k-in

MEL = 349 k-in 288 k-in eb = 12.25 in.

Mu = 9994 k-in 13298 k-in [Β1(1.2+0.2SDS)MDL+Β1f1MLL+MEg+MEL]

[Β1(1.2+0.2SDS)MDL+Β1f1MLL+MEg]

Axial and Flexural Capacity φ = 0.90 K = 1.0

Beam Axial Capacity (X-Axis) Beam Axial Capacity (Y-Axis)

Lbx = 11.70 Lby = 5.80 Pe1 = 14680.2 k

KLx/rx = 13.8 KLy/ry = 23.4 α = 1.0

Fe = 1510.7 ksi Fe = 521.2 ksi Cm = 1.0

Fcr = 49.31 ksi Fcr = 48.03 ksi αPr = 227.8 k 187.8 k φPn = 1708.7 k φPn = 1664.3 k --> Controls B1 = 1.02 1.01

Strong Axis Flexural Capacity Lb = 5.8 ft

Zx = 370 in.3

Mr = 20350 k-in

Lb,max = 24.8 ft F2.4b(b), Section D1.2a for Moderately Ductile Members Lp = 10.5 ft Lr = 31.8 ft

Pbr = 17.3 k AISC 360 Eq A-6-7

Βbr = 165.6 k/in. AISC 360 Eq A-6-8 Interaction

Mn = 18500 k-in Bending Axis: X-Axis φ = 0.90 Axial Load Ratio to Beam: 100% φMn = 16650 k-in F2.3(a) F2.3(b) φPu/Pn = 0.14 0.11 < 0.2, Use Interaction Equation H1-1b

Beam Shear Demand (at Midspan) D/C = 0.67 0.86 < 1.0 OK

VDL = 9.4 k

VLL = 7.8 k Beam Shear Capacity

Lg = 46.7 in. h/tw < 2.24(E/Fy)

0.5 53.95 > 35.6 OK

F2.3(a) F2.3(b) Cv = 1.0

VEg = 68.0 k 92.1 k Vn = 444.7 k

D/C = 0.25 < 1.0 OK

VEmh = 68.0 k 92.1 k

Vu = 85.5 k 109.5 k [(1.2+0.2SDS)VDL+f1VLL+1.0(VEmh)]

Preliminary Design Considering Gusset Local Effects (Final Design Verified During Gusset Design)

VEL = 119.6 k 98.6 k

VEmh = 119.6 k 98.6 k D/C = 0.31

Vu = 137.1 k 116.1 k [(1.2+0.2SDS)VDL+f1VLL+1.0(VEmh)]

Beams are designed based on the global loading on the beam, as well the unbalanced forces from the braces per AISC 341. In addition, chevron effects at the gussets are considered based on the recommendations in 'The Chevron Effect and Analysis of Chevron Beams - A Paradigm Shift' by Fortney and Thornton (2017).

Qb = (-Pten1 + Pcomp1)sin γ1

Note: Lb is the length between points that are either braced against lateral displacement of both flanges or braced with point torsional bracing. At a minimum, the point of intersection of the braces is required to be braced.

< 1.0 OK

Qh = (Pten1 + PPB1)cos γ1

Qh = (Pten1 + Pcomp1)cos γ1

Qb = (-Pten1 + PPB1)sin γ1

Second-Order Effects

05.4.3

BF2

Brace Geometry

H = 14.0 ft W = 33.2 ft

LWP-WP = 21.72 ft LUNBRACED = 21.72 ft

LOFFSET = 2.0 ft

K = 1.00 KLBRACE = 17.72 ft

Q = 49.86 deg (For Connection Design) γ = 40.14 deg

Brace Properties

1. Choose Type of Member: HSS

2. Specify Brace Member: HSS4X4X5/16 Fy = 50 ksi A = 4.1 in2

3. Brace Configuration: E = 29000 ksi rx = 1.49 in

Material: Ry = 1.3 ry = 1.49 in

(KLUNBRACED)/r = 142.7 < 200 OK (AISC 341 F2.5b) h/t = 10.7 < 0.65√(E/RyFy) = 13.7 OK (AISC 341 F2.5a and Section D1.1) b/t = 10.7 < 0.65√(E/RyFy) = 13.7 OK (AISC 341 F2.5a and Section D1.1)

Brace Demands Brace Capacities & Design

VEQ = 26.1 k (@ 1.0E) ρ = 1 φC = 0.90

SDS = 1.22 φT = 0.90

Β2 = 1.00

Brace D1a D1b Brace D1a D1b

PDL 3.7 k 3.7 k Fcr 12.33 ksi 12.33 ksi α = 1.0

PLL 3.1 k 3.1 k φPn 45.5 k 45.5 k Pstory = 150.0 k f1 0.5 0.5 DCR 0.53 0.53 RM = 1.0

PEQ 17.1 k 17.1 k H = 400.0 k

Pu 24.0 k 24.0 k φTn 184.5 k 184.5 k ΔH = 3.36 in.

Tu 14.6 k 14.6 k DCR 0.08 0.08 Pe story = 20000.0 k

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+f1PLL+Β2(ρQE)] Tu = [-(0.9-0.2SDS)PDL + Β2(ρQE)]

Second Order Effects Considered in Analysis?

Yes

X-Brace or Single Diagonal Chevron Brace

Chevron

ASTM A500 Grade C

'H' and 'W' are dimensioned between work points.

VEQ

W

H

VEQ

W

H γ θ γ θ

C

C

C

C

05.4.4

V V

Column Demands and Design

Material: ASTM A992 Grade 50 FY-COL = 50 ksi RY-COL = 1.1

PDL 13.4 k Column Size W10X45 PDL 13.4 k Column Size W10X45

PLL 6.8 k b/2tf 6.5 Highly Ductile PLL 6.8 k b/2tf 6.5 Highly Ductile f1 0.5 h/tw 22.5 Highly Ductile f1 0.5 h/tw 22.5 Highly Ductile

PEQ 0.0 k KL/r 83.6 PEQ 0.0 k KL/r 83.6

PEmh 80.3 k Ca 0.157 PEmh 80.3 k Ca 0.157

Pu 103.1 k φPn 359.1 k Pu 103.1 k φPn 359.1 k

TEQ 0.0 k DCR 0.29 TEQ 0.0 k DCR 0.29

TEmh 67.3 k φTn -598.5 k TEmh 67.3 k φTn -598.5 k

Tu 0.0 k DCR 0.00 Tu 0.0 k DCR 0.00

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+f1PLL+PEmh] Tu = [(0.9-0.2SDS)PDL - TEmh]

Expected Strength of Brace in Compression (F2.3): Expected Strength of Brace in Tension (F2.3):

Pcompression = min(Ry-BRACE*Fy*A, 1.14*Fcre*A) Ptension = RY-BRACE*Fy*Ag

Fcre = 12.3 ksi

Pcomp= 57.6 k Pten = 266.5 k

Unbalanced Veritcal Force at Midspan of Beam (Chevron Only) F2.3(a) F2.3(b) R1 = (Pcomp*sin(ɣ) - Pten*sin(ɣ)) = -134.7 k -160.7 k

RCOL = R1 / 2 = -67.3 k -80.3 k Per Column

Foundation Reactions: Capacity Limited per AISC 341-16 for Base Connection Design

Ru = Pu + Pcomp1*sin(ɣ1) Ru = Tu - Pten1*sin(ɣ1)

C1 C2 C1 C2

Ru = 127.2 k 127.2 k Tu = -95.7 k -95.7 k

Foundation Reactions: Including Overstrength per ASCE 7-16 for Concrete Design Ωo = 2.0

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+ f1PLL+ ΩoPE] Tu = [(0.9-0.2SDS)PDL - ΩoTE]

PE = 11.0 k TE = -11.0 k

C1 C2 C1 C2

Ru = 44.8 k 44.8 k Ru = -13.2 k -13.2 k

Foundation Reactions: Alternative Basic Load Combinations for Soil Bearing and Uplift Design

Pu = PDL+ PLL+ ρPE/1.4 Tu = 0.9PDL - ρTE/1.4

PE/1.4 = 7.9 k TE/1.4 = -7.9 k

C1 C2 C1 C2

Ru = 28.1 k 28.1 k Ru = 0.0 k 0.0 k

Columns are designed using the load combinations noted below. The seismic demands considereding the load combinations from AISC 341-16 Section F2.3 are used to determine the Emh seismic demands. Depending on the orientation of the braces, the demands may be due to a brace connection at the top of the column or a reaction due to unbalanced loads at the midspan of the beam. For single diagonal configurations, columns without a brace attached to the top have no seismic demands. For Chevron configuartions, columns have no seismic demands for the ASCE 7-16 load combinations as the loads in the braces are assumed to be balanced so there is no seismic shear reaction at the ends of the beam.

Because the seismic component of the column required strenth comes from the mechanism analysis of AISC Seismic Provisions Section F2.3 and is based on expected strengths of the braces, P-Δ effects need not be considered and Β2 from AISC Specification Appendix 8 need not be applied. See additional discussion in AISC Seismic Manual Page 5-140.

Column C1 Column C2

Reaction are calculated using the same load combinations and loading considerations as the columns. In addition to the column loads, loading from braces at the base of the columns is combined with the column loading to determine the design reactions for base plate and anchor rod design.

05.4.5

V V

Beam Design @ Chevron Frame

Beam Properties

1. Choose Type of Member: WF L = 33.2 ft rx = 9.36 in. bf/2tf = 4.57

2. Specify Beam Member: W21X166 Ry(Beam) = 1.1 ry = 2.99 in. h/tw = 25.00

Fy = 50 ksi A = 48.80 in2 Ix = 4280 in4

E = 29000 ksi d = 22.50 in. tw = 0.75 in.

Ca = 0.103 bf = 12.40 in. ho = 21.14 in.

3. Check Element Ductility Per AISC 341 Table D1.1:

Flange Ductility: bf/2tf = 4.57 λhd = 7.35 Highly Ductile

Web Ductility: h/tw = 25.00 λhd = 52.72 Highly Ductile

Axial and Flexural Demands at Midspan

Expected Post-Buckling Brace Strength Beam End Restraints: Pinned-Pinned PPB = 0.3*min(RyBRACE*Fy*A, 1.14*Fcre*A) MDL = 133.0 k-in

MLL = 111.0 k-in

Qb = 134.7 k F2.3(a) - Vert

Qb = 160.7 k F2.3(b) - Vert

Qh = 247.8 k F2.3(a) - Axial

Qh = 216.9 k F2.3(b) - Axial

F2.3(a) F2.3(b) MEg = 13412 k-in 16002 k-in

MEL = 348 k-in 305 k-in eb = 11.25 in.

Mu = 14016 k-in 16562 k-in [Β1(1.2+0.2SDS)MDL+Β1f1MLL+MEg+MEL]

[Β1(1.2+0.2SDS)MDL+Β1f1MLL+MEg]

Axial and Flexural Capacity φ = 0.90 K = 1.0

Beam Axial Capacity (X-Axis) Beam Axial Capacity (Y-Axis)

Lbx = 16.60 Lby = 8.30 Pe1 = 7718.0 k

KLx/rx = 21.3 KLy/ry = 33.3 α = 1.0

Fe = 631.9 ksi Fe = 257.9 ksi Cm = 1.0

Fcr = 48.37 ksi Fcr = 46.10 ksi αPr = 247.8 k 216.9 k φPn = 2124.5 k φPn = 2024.9 k --> Controls B1 = 1.03 1.03

Strong Axis Flexural Capacity Lb = 8.3 ft

Zx = 432 in.3

Mr = 23760 k-in

Lb,max = 25.0 ft F2.4b(b), Section D1.2a for Moderately Ductile Members Lp = 10.6 ft Lr = 39.8 ft

Pbr = 22.5 k AISC 360 Eq A-6-7

Βbr = 150.5 k/in. AISC 360 Eq A-6-8 Interaction

Mn = 21600 k-in Bending Axis: X-Axis φ = 0.90 Axial Load Ratio to Beam: 100% φMn = 19440 k-in F2.3(a) F2.3(b) φPu/Pn = 0.12 0.11 < 0.2, Use Interaction Equation H1-1b

Beam Shear Demand (at Midspan) D/C = 0.78 0.91 < 1.0 OK

VDL = 13.4 k

VLL = 11.2 k Beam Shear Capacity

Lg = 66.4 in. h/tw < 2.24(E/Fy)

0.5 53.95 > 25 OK

F2.3(a) F2.3(b) Cv = 1.0

VEg = 67.3 k 80.3 k Vn = 506.3 k

D/C = 0.21 < 1.0 OK

VEmh = 67.3 k 80.3 k

Vu = 92.3 k 105.3 k [(1.2+0.2SDS)VDL+f1VLL+1.0(VEmh)]

Preliminary Design Considering Gusset Local Effects (Final Design Verified During Gusset Design)

VEL = 84.0 k 73.5 k

VEmh = 84.0 k 80.3 k D/C = 0.22

Vu = 108.9 k 105.3 k [(1.2+0.2SDS)VDL+f1VLL+1.0(VEmh)]

< 1.0 OK

Beams are designed based on the global loading on the beam, as well the unbalanced forces from the braces per AISC 341. In addition, chevron effects at the gussets are considered based on the recommendations in 'The Chevron Effect and Analysis of Chevron Beams - A Paradigm Shift' by Fortney and Thornton (2017).

Qb = (-Pten1 + Pcomp1)sin γ1

Qb = (-Pten1 + PPB1)sin γ1

Qh = (Pten1 + Pcomp1)cos γ1

Qh = (Pten1 + PPB1)cos γ1

Second-Order Effects

Note: Lb is the length between points that are either braced against lateral displacement of both flanges or braced with point torsional bracing. At a minimum, the point of intersection of the braces is required to be braced.

05.4.6

BF3

Brace Geometry

H = 15.0 ft W = 20.3 ft

LWP-WP = 18.12 ft LUNBRACED = 18.12 ft

LOFFSET = 2.0 ft

K = 1.00 KLBRACE = 14.12 ft

Q = 34.12 deg (For Connection Design) γ = 55.88 deg

Brace Properties

1. Choose Type of Member: HSS

2. Specify Brace Member: HSS4X4X5/16 Fy = 50 ksi A = 4.1 in2

3. Brace Configuration: E = 29000 ksi rx = 1.49 in

Material: Ry = 1.3 ry = 1.49 in

(KLUNBRACED)/r = 113.7 < 200 OK (AISC 341 F2.5b) h/t = 10.7 < 0.65√(E/RyFy) = 13.7 OK (AISC 341 F2.5a and Section D1.1) b/t = 10.7 < 0.65√(E/RyFy) = 13.7 OK (AISC 341 F2.5a and Section D1.1)

Brace Demands Brace Capacities & Design

VEQ = 35.8 k (@ 1.0E) ρ = 1 φC = 0.90

SDS = 1.22 φT = 0.90

Β2 = 1.00

Brace D1a D1b Brace D1a D1b

PDL 0.0 k 0.0 k Fcr 19.41 ksi 19.41 ksi α = 1.0

PLL 0.0 k 0.0 k φPn 71.6 k 71.6 k Pstory = 150.0 k f1 0.5 0.5 DCR 0.45 0.45 RM = 1.0

PEQ 31.9 k 31.9 k H = 400.0 k

Pu 31.9 k 31.9 k φTn 184.5 k 184.5 k ΔH = 3.60 in.

Tu 31.9 k 31.9 k DCR 0.17 0.17 Pe story = 20000.0 k

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+f1PLL+Β2(ρQE)] Tu = [-(0.9-0.2SDS)PDL + Β2(ρQE)]

Second Order Effects Considered in Analysis?

Yes

X-Brace or Single Diagonal Chevron Brace

Chevron

ASTM A500 Grade C

'H' and 'W' are dimensioned between work points.

VEQ

W

H

VEQ

W

H γ θ γ θ

C

C

C

C

05.4.7

V V

Column Demands and Design

Material: ASTM A992 Grade 50 FY-COL = 50 ksi RY-COL = 1.1

PDL 13.4 k Column Size W10X45 PDL 13.4 k Column Size W10X45

PLL 6.8 k b/2tf 6.5 Highly Ductile PLL 6.8 k b/2tf 6.5 Highly Ductile f1 0.5 h/tw 22.5 Highly Ductile f1 0.5 h/tw 22.5 Highly Ductile

PEQ 0.0 k KL/r 89.6 PEQ 0.0 k KL/r 89.6

PEmh 99.0 k Ca 0.185 PEmh 99.0 k Ca 0.185

Pu 121.8 k φPn 333.0 k Pu 121.8 k φPn 333.0 k

TEQ 0.0 k DCR 0.37 TEQ 0.0 k DCR 0.37

TEmh 72.8 k φTn -598.5 k TEmh 72.8 k φTn -598.5 k

Tu 0.0 k DCR 0.00 Tu 0.0 k DCR 0.00

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+f1PLL+PEmh] Tu = [(0.9-0.2SDS)PDL - TEmh]

Expected Strength of Brace in Compression (F2.3): Expected Strength of Brace in Tension (F2.3):

Pcompression = min(Ry-BRACE*Fy*A, 1.14*Fcre*A) Ptension = RY-BRACE*Fy*Ag

Fcre = 19.4 ksi

Pcomp= 90.7 k Pten = 266.5 k

Unbalanced Veritcal Force at Midspan of Beam (Chevron Only) F2.3(a) F2.3(b) R1 = (Pcomp*sin(ɣ) - Pten*sin(ɣ)) = -145.5 k -198.1 k

RCOL = R1 / 2 = -72.8 k -99.0 k Per Column

Foundation Reactions: Capacity Limited per AISC 341-16 for Base Connection Design

Ru = Pu + Pcomp1*sin(ɣ1) Ru = Tu - Pten1*sin(ɣ1)

C1 C2 C1 C2

Ru = 170.6 k 170.6 k Tu = -139.1 k -139.1 k

Foundation Reactions: Including Overstrength per ASCE 7-16 for Concrete Design Ωo = 2.0

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+ f1PLL+ ΩoPE] Tu = [(0.9-0.2SDS)PDL - ΩoTE]

PE = 26.4 k TE = -26.4 k

C1 C2 C1 C2

Ru = 75.6 k 75.6 k Ru = -44.0 k -44.0 k

Foundation Reactions: Alternative Basic Load Combinations for Soil Bearing and Uplift Design

Pu = PDL+ PLL+ ρPE/1.4 Tu = 0.9PDL - ρTE/1.4

PE/1.4 = 18.9 k TE/1.4 = -18.9 k

C1 C2 C1 C2

Ru = 39.1 k 39.1 k Ru = -6.8 k -6.8 k

Columns are designed using the load combinations noted below. The seismic demands considereding the load combinations from AISC 341-16 Section F2.3 are used to determine the Emh seismic demands. Depending on the orientation of the braces, the demands may be due to a brace connection at the top of the column or a reaction due to unbalanced loads at the midspan of the beam. For single diagonal configurations, columns without a brace attached to the top have no seismic demands. For Chevron configuartions, columns have no seismic demands for the ASCE 7-16 load combinations as the loads in the braces are assumed to be balanced so there is no seismic shear reaction at the ends of the beam.

Because the seismic component of the column required strenth comes from the mechanism analysis of AISC Seismic Provisions Section F2.3 and is based on expected strengths of the braces, P-Δ effects need not be considered and Β2 from AISC Specification Appendix 8 need not be applied. See additional discussion in AISC Seismic Manual Page 5-140.

Column C1 Column C2

Reaction are calculated using the same load combinations and loading considerations as the columns. In addition to the column loads, loading from braces at the base of the columns is combined with the column loading to determine the design reactions for base plate and anchor rod design.

05.4.8

V V

Beam Design @ Chevron Frame

Beam Properties

1. Choose Type of Member: WF L = 20.3 ft rx = 8.09 in. bf/2tf = 4.25

2. Specify Beam Member: W18X143 Ry(Beam) = 1.1 ry = 2.72 in. h/tw = 22.00

Fy = 50 ksi A = 42.10 in2 Ix = 2750 in4

E = 29000 ksi d = 19.50 in. tw = 0.73 in.

Ca = 0.096 bf = 11.20 in. ho = 18.18 in.

3. Check Element Ductility Per AISC 341 Table D1.1:

Flange Ductility: bf/2tf = 4.25 λhd = 7.35 Highly Ductile

Web Ductility: h/tw = 22.00 λhd = 53.11 Highly Ductile

Axial and Flexural Demands at Midspan

Expected Post-Buckling Brace Strength Beam End Restraints: Pinned-Pinned PPB = 0.3*min(RyBRACE*Fy*A, 1.14*Fcre*A) MDL = 464.0 k-in

MLL = 387.0 k-in

Qb = 145.5 k F2.3(a) - Vert

Qb = 198.1 k F2.3(b) - Vert

Qh = 200.4 k F2.3(a) - Axial

Qh = 164.8 k F2.3(b) - Axial

F2.3(a) F2.3(b) MEg = 8875 k-in 12081 k-in

MEL = 244 k-in 201 k-in eb = 9.75 in.

Mu = 9996 k-in 13156 k-in [Β1(1.2+0.2SDS)MDL+Β1f1MLL+MEg+MEL]

[Β1(1.2+0.2SDS)MDL+Β1f1MLL+MEg]

Axial and Flexural Capacity φ = 0.90 K = 1.0

Beam Axial Capacity (X-Axis) Beam Axial Capacity (Y-Axis)

Lbx = 10.15 Lby = 5.00 Pe1 = 13224.9 k

KLx/rx = 15.1 KLy/ry = 22.1 α = 1.0

Fe = 1262.7 ksi Fe = 588.2 ksi Cm = 1.0

Fcr = 49.18 ksi Fcr = 48.25 ksi αPr = 200.4 k 164.8 k φPn = 1863.4 k φPn = 1828.3 k --> Controls B1 = 1.02 1.01

Strong Axis Flexural Capacity Lb = 5.0 ft

Zx = 322 in.3

Mr = 17710 k-in

Lb,max = 22.7 ft F2.4b(b), Section D1.2a for Moderately Ductile Members Lp = 9.6 ft Lr = 39.6 ft

Pbr = 19.5 k AISC 360 Eq A-6-7

Βbr = 216.5 k/in. AISC 360 Eq A-6-8 Interaction

Mn = 16100 k-in Bending Axis: X-Axis φ = 0.90 Axial Load Ratio to Beam: 75% φMn = 14490 k-in F2.3(a) F2.3(b) φPu/Pn = 0.08 0.07 < 0.2, Use Interaction Equation H1-1b

Beam Shear Demand (at Midspan) D/C = 0.74 0.95 < 1.0 OK

VDL = 7.4 k

VLL = 6.2 k Beam Shear Capacity

Lg = 40.7 in. h/tw < 2.24(E/Fy)

0.5 53.95 > 22 OK

F2.3(a) F2.3(b) Cv = 1.0

VEg = 72.8 k 99.0 k Vn = 427.1 k

D/C = 0.26 < 1.0 OK

VEmh = 72.8 k 99.0 k

Vu = 86.5 k 112.8 k [(1.2+0.2SDS)VDL+f1VLL+1.0(VEmh)]

Preliminary Design Considering Gusset Local Effects (Final Design Verified During Gusset Design)

VEL = 96.1 k 79.0 k

VEmh = 96.1 k 99.0 k D/C = 0.26

Vu = 109.9 k 112.8 k [(1.2+0.2SDS)VDL+f1VLL+1.0(VEmh)]

< 1.0 OK

Beams are designed based on the global loading on the beam, as well the unbalanced forces from the braces per AISC 341. In addition, chevron effects at the gussets are considered based on the recommendations in 'The Chevron Effect and Analysis of Chevron Beams - A Paradigm Shift' by Fortney and Thornton (2017).

Qb = (-Pten1 + Pcomp1)sin γ1

Qb = (-Pten1 + PPB1)sin γ1

Qh = (Pten1 + Pcomp1)cos γ1

Qh = (Pten1 + PPB1)cos γ1

Second-Order Effects

Note: Lb is the length between points that are either braced against lateral displacement of both flanges or braced with point

05.4.9

BF4

Brace Geometry

H = 15.0 ft W = 22.0 ft

LWP-WP = 18.60 ft LUNBRACED = 18.60 ft

LOFFSET = 2.0 ft

K = 1.00 KLBRACE = 14.60 ft

Q = 36.25 deg (For Connection Design) γ = 53.75 deg

Brace Properties

1. Choose Type of Member: HSS

2. Specify Brace Member: HSS4X4X5/16 Fy = 50 ksi A = 4.1 in2

3. Brace Configuration: E = 29000 ksi rx = 1.49 in

Material: Ry = 1.3 ry = 1.49 in

(KLUNBRACED)/r = 117.6 < 200 OK (AISC 341 F2.5b) h/t = 10.7 < 0.65√(E/RyFy) = 13.7 OK (AISC 341 F2.5a and Section D1.1) b/t = 10.7 < 0.65√(E/RyFy) = 13.7 OK (AISC 341 F2.5a and Section D1.1)

Brace Demands Brace Capacities & Design

VEQ = 57.6 k (@ 1.0E) ρ = 1 φC = 0.90

SDS = 1.22 φT = 0.90

Β2 = 1.00

Brace D1a D1b Brace D1a D1b

PDL 0.0 k 0.0 k Fcr 18.15 ksi 18.15 ksi α = 1.0

PLL 0.0 k 0.0 k φPn 67.0 k 67.0 k Pstory = 150.0 k f1 0.5 0.5 DCR 0.73 0.73 RM = 1.0

PEQ 48.7 k 48.7 k H = 400.0 k

Pu 48.7 k 48.7 k φTn 184.5 k 184.5 k ΔH = 3.60 in.

Tu 48.7 k 48.7 k DCR 0.26 0.26 Pe story = 20000.0 k

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+f1PLL+Β2(ρQE)] Tu = [-(0.9-0.2SDS)PDL + Β2(ρQE)]

Second Order Effects Considered in Analysis?

Yes

X-Brace or Single Diagonal Chevron Brace

Chevron

ASTM A500 Grade C

'H' and 'W' are dimensioned between work points.

VEQ

W

H

VEQ

W

H γ θ γ θ

C

C

C

C

05.4.10

V V

Column Demands and Design

Material: ASTM A992 Grade 50 FY-COL = 50 ksi RY-COL = 1.1

PDL 14.6 k Column Size W10X45 PDL 14.6 k Column Size W10X45

PLL 7.3 k b/2tf 6.5 Highly Ductile PLL 7.3 k b/2tf 6.5 Highly Ductile f1 0.5 h/tw 22.5 Highly Ductile f1 0.5 h/tw 22.5 Highly Ductile

PEQ 0.0 k KL/r 89.6 PEQ 0.0 k KL/r 89.6

PEmh 97.2 k Ca 0.185 PEmh 97.2 k Ca 0.185

Pu 121.9 k φPn 333.0 k Pu 121.9 k φPn 333.0 k

TEQ 0.0 k DCR 0.37 TEQ 0.0 k DCR 0.37

TEmh 73.2 k φTn -598.5 k TEmh 73.2 k φTn -598.5 k

Tu 0.0 k DCR 0.00 Tu 0.0 k DCR 0.00

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+f1PLL+PEmh] Tu = [(0.9-0.2SDS)PDL - TEmh]

Expected Strength of Brace in Compression (F2.3): Expected Strength of Brace in Tension (F2.3):

Pcompression = min(Ry-BRACE*Fy*A, 1.14*Fcre*A) Ptension = RY-BRACE*Fy*Ag

Fcre = 18.2 ksi

Pcomp= 84.8 k Pten = 266.5 k

Unbalanced Veritcal Force at Midspan of Beam (Chevron Only) F2.3(a) F2.3(b) R1 = (Pcomp*sin(ɣ) - Pten*sin(ɣ)) = -146.5 k -194.4 k

RCOL = R1 / 2 = -73.2 k -97.2 k Per Column

Foundation Reactions: Capacity Limited per AISC 341-16 for Base Connection Design

Ru = Pu + Pcomp1*sin(ɣ1) Ru = Tu - Pten1*sin(ɣ1)

C1 C2 C1 C2

Ru = 166.4 k 166.4 k Tu = -132.1 k -132.1 k

Foundation Reactions: Including Overstrength per ASCE 7-16 for Concrete Design Ωo = 2.0

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+ f1PLL+ ΩoPE] Tu = [(0.9-0.2SDS)PDL - ΩoTE]

PE = 39.3 k TE = -39.3 k

C1 C2 C1 C2

Ru = 103.3 k 103.3 k Ru = -69.0 k -69.0 k

Foundation Reactions: Alternative Basic Load Combinations for Soil Bearing and Uplift Design

Pu = PDL+ PLL+ ρPE/1.4 Tu = 0.9PDL - ρTE/1.4

PE/1.4 = 28.1 k TE/1.4 = -28.1 k

C1 C2 C1 C2

Ru = 50.0 k 50.0 k Ru = -14.9 k -14.9 k

Columns are designed using the load combinations noted below. The seismic demands considereding the load combinations from AISC 341-16 Section F2.3 are used to determine the Emh seismic demands. Depending on the orientation of the braces, the demands may be due to a brace connection at the top of the column or a reaction due to unbalanced loads at the midspan of the beam. For single diagonal configurations, columns without a brace attached to the top have no seismic demands. For Chevron configuartions, columns have no seismic demands for the ASCE 7-16 load combinations as the loads in the braces are assumed to be balanced so there is no seismic shear reaction at the ends of the beam.

Because the seismic component of the column required strenth comes from the mechanism analysis of AISC Seismic Provisions Section F2.3 and is based on expected strengths of the braces, P-Δ effects need not be considered and Β2 from AISC Specification Appendix 8 need not be applied. See additional discussion in AISC Seismic Manual Page 5-140.

Column C1 Column C2

Reaction are calculated using the same load combinations and loading considerations as the columns. In addition to the column loads, loading from braces at the base of the columns is combined with the column loading to determine the design reactions for base plate and anchor rod design.

05.4.11

V V

Beam Design @ Chevron Frame

Beam Properties

1. Choose Type of Member: WF L = 22.0 ft rx = 10.20 in. bf/2tf = 6.70

2. Specify Beam Member: W24X131 Ry(Beam) = 1.1 ry = 2.97 in. h/tw = 35.60

Fy = 50 ksi A = 38.50 in2 Ix = 4020 in4

E = 29000 ksi d = 24.50 in. tw = 0.61 in.

Ca = 0.109 bf = 12.90 in. ho = 23.54 in.

3. Check Element Ductility Per AISC 341 Table D1.1:

Flange Ductility: bf/2tf = 6.70 λhd = 7.35 Highly Ductile

Web Ductility: h/tw = 35.60 λhd = 52.32 Highly Ductile

Axial and Flexural Demands at Midspan

Expected Post-Buckling Brace Strength Beam End Restraints: Pinned-Pinned PPB = 0.3*min(RyBRACE*Fy*A, 1.14*Fcre*A) MDL = 540.0 k-in

MLL = 450.0 k-in

Qb = 146.5 k F2.3(a) - Vert

Qb = 194.4 k F2.3(b) - Vert

Qh = 207.8 k F2.3(a) - Axial

Qh = 172.7 k F2.3(b) - Axial

F2.3(a) F2.3(b) MEg = 9668 k-in 12829 k-in

MEL = 318 k-in 264 k-in eb = 12.25 in.

Mu = 11004 k-in 14109 k-in [Β1(1.2+0.2SDS)MDL+Β1f1MLL+MEg+MEL]

[Β1(1.2+0.2SDS)MDL+Β1f1MLL+MEg]

Axial and Flexural Capacity φ = 0.90 K = 1.0

Beam Axial Capacity (X-Axis) Beam Axial Capacity (Y-Axis)

Lbx = 11.00 Lby = 5.50 Pe1 = 16508.8 k

KLx/rx = 12.9 KLy/ry = 22.2 α = 1.0

Fe = 1709.0 ksi Fe = 579.6 ksi Cm = 1.0

Fcr = 49.39 ksi Fcr = 48.23 ksi αPr = 207.8 k 172.7 k φPn = 1711.4 k φPn = 1671.1 k --> Controls B1 = 1.01 1.01

Strong Axis Flexural Capacity Lb = 5.5 ft

Zx = 370 in.3

Mr = 20350 k-in

Lb,max = 24.8 ft F2.4b(b), Section D1.2a for Moderately Ductile Members Lp = 10.5 ft Lr = 31.8 ft

Pbr = 17.3 k AISC 360 Eq A-6-7

Βbr = 174.6 k/in. AISC 360 Eq A-6-8 Interaction

Mn = 18500 k-in Bending Axis: X-Axis φ = 0.90 Axial Load Ratio to Beam: 75% φMn = 16650 k-in F2.3(a) F2.3(b) φPu/Pn = 0.09 0.08 < 0.2, Use Interaction Equation H1-1b

Beam Shear Demand (at Midspan) D/C = 0.72 0.90 < 1.0 OK

VDL = 8.4 k

VLL = 7.0 k Beam Shear Capacity

Lg = 44.0 in. h/tw < 2.24(E/Fy)

0.5 53.95 > 35.6 OK

F2.3(a) F2.3(b) Cv = 1.0

VEg = 73.2 k 97.2 k Vn = 444.7 k

D/C = 0.25 < 1.0 OK

VEmh = 73.2 k 97.2 k

Vu = 88.9 k 112.8 k [(1.2+0.2SDS)VDL+f1VLL+1.0(VEmh)]

Preliminary Design Considering Gusset Local Effects (Final Design Verified During Gusset Design)

VEL = 115.7 k 96.1 k

VEmh = 115.7 k 97.2 k D/C = 0.30

Vu = 131.3 k 112.8 k [(1.2+0.2SDS)VDL+f1VLL+1.0(VEmh)]

< 1.0 OK

Beams are designed based on the global loading on the beam, as well the unbalanced forces from the braces per AISC 341. In addition, chevron effects at the gussets are considered based on the recommendations in 'The Chevron Effect and Analysis of Chevron Beams - A Paradigm Shift' by Fortney and Thornton (2017).

Qb = (-Pten1 + Pcomp1)sin γ1

Qb = (-Pten1 + PPB1)sin γ1

Qh = (Pten1 + Pcomp1)cos γ1

Qh = (Pten1 + PPB1)cos γ1

Second-Order Effects

Note: Lb is the length between points that are either braced against lateral displacement of both flanges or braced with point

05.4.12

BF5

Brace Geometry

H = 15.0 ft W = 20.1 ft

LWP-WP = 18.06 ft LUNBRACED = 18.06 ft

LOFFSET = 2.0 ft

K = 1.00 KLBRACE = 14.06 ft

Q = 33.82 deg (For Connection Design) γ = 56.18 deg

Brace Properties

1. Choose Type of Member: HSS

2. Specify Brace Member: HSS4X4X5/16 Fy = 50 ksi A = 4.1 in2

3. Brace Configuration: E = 29000 ksi rx = 1.49 in

Material: Ry = 1.3 ry = 1.49 in

(KLUNBRACED)/r = 113.2 < 200 OK (AISC 341 F2.5b) h/t = 10.7 < 0.65√(E/RyFy) = 13.7 OK (AISC 341 F2.5a and Section D1.1) b/t = 10.7 < 0.65√(E/RyFy) = 13.7 OK (AISC 341 F2.5a and Section D1.1)

Brace Demands Brace Capacities & Design

VEQ = 42.6 k (@ 1.0E) ρ = 1 φC = 0.90

SDS = 1.22 φT = 0.90

Β2 = 1.00

Brace D1a D1b Brace D1a D1b

PDL 1.3 k 1.3 k Fcr 19.59 ksi 19.59 ksi α = 1.0

PLL 1.1 k 1.1 k φPn 72.3 k 72.3 k Pstory = 150.0 k f1 0.5 0.5 DCR 0.56 0.56 RM = 1.0

PEQ 38.3 k 38.3 k H = 400.0 k

Pu 40.7 k 40.7 k φTn 184.5 k 184.5 k ΔH = 3.60 in.

Tu 37.4 k 37.4 k DCR 0.20 0.20 Pe story = 20000.0 k

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+f1PLL+Β2(ρQE)] Tu = [-(0.9-0.2SDS)PDL + Β2(ρQE)]

Second Order Effects Considered in Analysis?

Yes

X-Brace or Single Diagonal Chevron Brace

Chevron

ASTM A500 Grade C

'H' and 'W' are dimensioned between work points.

VEQ

W

H

VEQ

W

H γ θ γ θ

C

C

C

C

05.4.13

V V

Column Demands and Design

Material: ASTM A992 Grade 50 FY-COL = 50 ksi RY-COL = 1.1

PDL 4.4 k Column Size W10X45 PDL 4.4 k Column Size W10X45

PLL 3.2 k b/2tf 6.5 Highly Ductile PLL 3.2 k b/2tf 6.5 Highly Ductile f1 0.5 h/tw 22.5 Highly Ductile f1 0.5 h/tw 22.5 Highly Ductile

PEQ 0.0 k KL/r 89.6 PEQ 0.0 k KL/r 89.6

PEmh 99.3 k Ca 0.163 PEmh 99.3 k Ca 0.163

Pu 107.2 k φPn 333.0 k Pu 107.2 k φPn 333.0 k

TEQ 0.0 k DCR 0.32 TEQ 0.0 k DCR 0.32

TEmh 72.7 k φTn -598.5 k TEmh 72.7 k φTn -598.5 k

Tu 0.0 k DCR 0.00 Tu 0.0 k DCR 0.00

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+f1PLL+PEmh] Tu = [(0.9-0.2SDS)PDL - TEmh]

Expected Strength of Brace in Compression (F2.3): Expected Strength of Brace in Tension (F2.3):

Pcompression = min(Ry-BRACE*Fy*A, 1.14*Fcre*A) Ptension = RY-BRACE*Fy*Ag

Fcre = 19.6 ksi

Pcomp= 91.6 k Pten = 266.5 k

Unbalanced Veritcal Force at Midspan of Beam (Chevron Only) F2.3(a) F2.3(b) R1 = (Pcomp*sin(ɣ) - Pten*sin(ɣ)) = -145.3 k -198.6 k

RCOL = R1 / 2 = -72.7 k -99.3 k Per Column

Foundation Reactions: Capacity Limited per AISC 341-16 for Base Connection Design

Ru = Pu + Pcomp1*sin(ɣ1) Ru = Tu - Pten1*sin(ɣ1)

C1 C2 C1 C2

Ru = 156.7 k 156.7 k Tu = -145.8 k -145.8 k

Foundation Reactions: Including Overstrength per ASCE 7-16 for Concrete Design Ωo = 2.0

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+ f1PLL+ ΩoPE] Tu = [(0.9-0.2SDS)PDL - ΩoTE]

PE = 31.8 k TE = -31.8 k

C1 C2 C1 C2

Ru = 71.5 k 71.5 k Ru = -60.7 k -60.7 k

Foundation Reactions: Alternative Basic Load Combinations for Soil Bearing and Uplift Design

Pu = PDL+ PLL+ ρPE/1.4 Tu = 0.9PDL - ρTE/1.4

PE/1.4 = 22.7 k TE/1.4 = -22.7 k

C1 C2 C1 C2

Ru = 30.3 k 30.3 k Ru = -18.7 k -18.7 k

Columns are designed using the load combinations noted below. The seismic demands considereding the load combinations from AISC 341-16 Section F2.3 are used to determine the Emh seismic demands. Depending on the orientation of the braces, the demands may be due to a brace connection at the top of the column or a reaction due to unbalanced loads at the midspan of the beam. For single diagonal configurations, columns without a brace attached to the top have no seismic demands. For Chevron configuartions, columns have no seismic demands for the ASCE 7-16 load combinations as the loads in the braces are assumed to be balanced so there is no seismic shear reaction at the ends of the beam.

Because the seismic component of the column required strenth comes from the mechanism analysis of AISC Seismic Provisions Section F2.3 and is based on expected strengths of the braces, P-Δ effects need not be considered and Β2 from AISC Specification Appendix 8 need not be applied. See additional discussion in AISC Seismic Manual Page 5-140.

Column C1 Column C2

Reaction are calculated using the same load combinations and loading considerations as the columns. In addition to the column loads, loading from braces at the base of the columns is combined with the column loading to determine the design reactions for base plate and anchor rod design.

05.4.14

V V

Beam Design @ Chevron Frame

Beam Properties

1. Choose Type of Member: WF L = 20.1 ft rx = 10.20 in. bf/2tf = 6.70

2. Specify Beam Member: W24X131 Ry(Beam) = 1.1 ry = 2.97 in. h/tw = 35.60

Fy = 50 ksi A = 38.50 in2 Ix = 4020 in4

E = 29000 ksi d = 24.50 in. tw = 0.61 in.

Ca = 0.105 bf = 12.90 in. ho = 23.54 in.

3. Check Element Ductility Per AISC 341 Table D1.1:

Flange Ductility: bf/2tf = 6.70 λhd = 7.35 Highly Ductile

Web Ductility: h/tw = 35.60 λhd = 52.59 Highly Ductile

Axial and Flexural Demands at Midspan

Expected Post-Buckling Brace Strength Beam End Restraints: Pinned-Pinned PPB = 0.3*min(RyBRACE*Fy*A, 1.14*Fcre*A) MDL = 144.0 k-in

MLL = 120.0 k-in

Qb = 145.3 k F2.3(a) - Vert

Qb = 198.6 k F2.3(b) - Vert

Qh = 199.3 k F2.3(a) - Axial

Qh = 163.6 k F2.3(b) - Axial

F2.3(a) F2.3(b) MEg = 8764 k-in 11974 k-in

MEL = 305 k-in 251 k-in eb = 12.25 in.

Mu = 9340 k-in 12495 k-in [Β1(1.2+0.2SDS)MDL+Β1f1MLL+MEg+MEL]

[Β1(1.2+0.2SDS)MDL+Β1f1MLL+MEg]

Axial and Flexural Capacity φ = 0.90 K = 1.0

Beam Axial Capacity (X-Axis) Beam Axial Capacity (Y-Axis)

Lbx = 10.00 Lby = 5.00 Pe1 = 19777.4 k

KLx/rx = 11.8 KLy/ry = 20.2 α = 1.0

Fe = 2067.9 ksi Fe = 701.3 ksi Cm = 1.0

Fcr = 49.50 ksi Fcr = 48.53 ksi αPr = 199.3 k 163.6 k φPn = 1715.1 k φPn = 1681.6 k --> Controls B1 = 1.01 1.01

Strong Axis Flexural Capacity Lb = 5.0 ft

Zx = 370 in.3

Mr = 20350 k-in

Lb,max = 24.8 ft F2.4b(b), Section D1.2a for Moderately Ductile Members Lp = 10.5 ft Lr = 31.8 ft

Pbr = 17.3 k AISC 360 Eq A-6-7

Βbr = 192.1 k/in. AISC 360 Eq A-6-8 Interaction

Mn = 18500 k-in Bending Axis: X-Axis φ = 0.90 Axial Load Ratio to Beam: 100% φMn = 16650 k-in F2.3(a) F2.3(b) φPu/Pn = 0.12 0.10 < 0.2, Use Interaction Equation H1-1b

Beam Shear Demand (at Midspan) D/C = 0.62 0.80 < 1.0 OK

VDL = 2.6 k

VLL = 2.2 k Beam Shear Capacity

Lg = 40.2 in. h/tw < 2.24(E/Fy)

0.5 53.95 > 35.6 OK

F2.3(a) F2.3(b) Cv = 1.0

VEg = 72.7 k 99.3 k Vn = 444.7 k

D/C = 0.23 < 1.0 OK

VEmh = 72.7 k 99.3 k

Vu = 77.5 k 104.1 k [(1.2+0.2SDS)VDL+f1VLL+1.0(VEmh)]

Preliminary Design Considering Gusset Local Effects (Final Design Verified During Gusset Design)

VEL = 121.5 k 99.7 k

VEmh = 121.5 k 99.7 k D/C = 0.28

Vu = 126.3 k 104.6 k [(1.2+0.2SDS)VDL+f1VLL+1.0(VEmh)]

< 1.0 OK

Beams are designed based on the global loading on the beam, as well the unbalanced forces from the braces per AISC 341. In addition, chevron effects at the gussets are considered based on the recommendations in 'The Chevron Effect and Analysis of Chevron Beams - A Paradigm Shift' by Fortney and Thornton (2017).

Qb = (-Pten1 + Pcomp1)sin γ1

Qb = (-Pten1 + PPB1)sin γ1

Qh = (Pten1 + Pcomp1)cos γ1

Qh = (Pten1 + PPB1)cos γ1

Second-Order Effects

Note: Lb is the length between points that are either braced against lateral displacement of both flanges or braced with point

05.4.15

BF6

Brace Geometry

H = 14.5 ft W = 26.5 ft

LWP-WP = 19.64 ft LUNBRACED = 19.64 ft

LOFFSET = 2.0 ft

K = 1.00 KLBRACE = 15.64 ft

Q = 42.42 deg (For Connection Design) γ = 47.58 deg

Brace Properties

1. Choose Type of Member: HSS

2. Specify Brace Member: HSS4X4X5/16 Fy = 50 ksi A = 4.1 in2

3. Brace Configuration: E = 29000 ksi rx = 1.49 in

Material: Ry = 1.3 ry = 1.49 in

(KLUNBRACED)/r = 126.0 < 200 OK (AISC 341 F2.5b) h/t = 10.7 < 0.65√(E/RyFy) = 13.7 OK (AISC 341 F2.5a and Section D1.1) b/t = 10.7 < 0.65√(E/RyFy) = 13.7 OK (AISC 341 F2.5a and Section D1.1)

Brace Demands Brace Capacities & Design

VEQ = 61.7 k (@ 1.0E) ρ = 1 φC = 0.90

SDS = 1.22 φT = 0.90

Β2 = 1.00

Brace D1a D1b Brace D1a D1b

PDL 0.9 k 0.9 k Fcr 15.82 ksi 15.82 ksi α = 1.0

PLL 0.7 k 0.7 k φPn 58.4 k 58.4 k Pstory = 150.0 k f1 0.5 0.5 DCR 0.81 0.81 RM = 1.0

PEQ 45.7 k 45.7 k H = 400.0 k

Pu 47.3 k 47.3 k φTn 184.5 k 184.5 k ΔH = 3.48 in.

Tu 45.2 k 45.2 k DCR 0.24 0.24 Pe story = 20000.0 k

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+f1PLL+Β2(ρQE)] Tu = [-(0.9-0.2SDS)PDL + Β2(ρQE)]

Second Order Effects Considered in Analysis?

Yes

X-Brace or Single Diagonal Chevron Brace

Chevron

ASTM A500 Grade C

'H' and 'W' are dimensioned between work points.

VEQ

W

H

VEQ

W

H γ θ γ θ

C

C

C

C

05.4.16

V V

Column Demands and Design

Material: ASTM A992 Grade 50 FY-COL = 50 ksi RY-COL = 1.1

PDL 7.2 k Column Size W10X45 PDL 7.2 k Column Size W10X45

PLL 4.3 k b/2tf 6.5 Highly Ductile PLL 4.3 k b/2tf 6.5 Highly Ductile f1 0.5 h/tw 22.5 Highly Ductile f1 0.5 h/tw 22.5 Highly Ductile

PEQ 0.0 k KL/r 86.6 PEQ 0.0 k KL/r 86.6

PEmh 90.2 k Ca 0.156 PEmh 90.2 k Ca 0.156

Pu 102.7 k φPn 346.0 k Pu 102.7 k φPn 346.0 k

TEQ 0.0 k DCR 0.30 TEQ 0.0 k DCR 0.30

TEmh 71.1 k φTn -598.5 k TEmh 71.1 k φTn -598.5 k

Tu 0.0 k DCR 0.00 Tu 0.0 k DCR 0.00

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+f1PLL+PEmh] Tu = [(0.9-0.2SDS)PDL - TEmh]

Expected Strength of Brace in Compression (F2.3): Expected Strength of Brace in Tension (F2.3):

Pcompression = min(Ry-BRACE*Fy*A, 1.14*Fcre*A) Ptension = RY-BRACE*Fy*Ag

Fcre = 15.8 ksi

Pcomp= 73.9 k Pten = 266.5 k

Unbalanced Veritcal Force at Midspan of Beam (Chevron Only) F2.3(a) F2.3(b) R1 = (Pcomp*sin(ɣ) - Pten*sin(ɣ)) = -142.2 k -180.4 k

RCOL = R1 / 2 = -71.1 k -90.2 k Per Column

Foundation Reactions: Capacity Limited per AISC 341-16 for Base Connection Design

Ru = Pu + Pcomp1*sin(ɣ1) Ru = Tu - Pten1*sin(ɣ1)

C1 C2 C1 C2

Ru = 138.2 k 138.2 k Tu = -120.9 k -120.9 k

Foundation Reactions: Including Overstrength per ASCE 7-16 for Concrete Design Ωo = 2.0

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+ f1PLL+ ΩoPE] Tu = [(0.9-0.2SDS)PDL - ΩoTE]

PE = 33.8 k TE = -33.8 k

C1 C2 C1 C2

Ru = 80.1 k 80.1 k Ru = -62.8 k -62.8 k

Foundation Reactions: Alternative Basic Load Combinations for Soil Bearing and Uplift Design

Pu = PDL+ PLL+ ρPE/1.4 Tu = 0.9PDL - ρTE/1.4

PE/1.4 = 24.1 k TE/1.4 = -24.1 k

C1 C2 C1 C2

Ru = 35.6 k 35.6 k Ru = -17.6 k -17.6 k

Columns are designed using the load combinations noted below. The seismic demands considereding the load combinations from AISC 341-16 Section F2.3 are used to determine the Emh seismic demands. Depending on the orientation of the braces, the demands may be due to a brace connection at the top of the column or a reaction due to unbalanced loads at the midspan of the beam. For single diagonal configurations, columns without a brace attached to the top have no seismic demands. For Chevron configuartions, columns have no seismic demands for the ASCE 7-16 load combinations as the loads in the braces are assumed to be balanced so there is no seismic shear reaction at the ends of the beam.

Because the seismic component of the column required strenth comes from the mechanism analysis of AISC Seismic Provisions Section F2.3 and is based on expected strengths of the braces, P-Δ effects need not be considered and Β2 from AISC Specification Appendix 8 need not be applied. See additional discussion in AISC Seismic Manual Page 5-140.

Column C1 Column C2

Reaction are calculated using the same load combinations and loading considerations as the columns. In addition to the column loads, loading from braces at the base of the columns is combined with the column loading to determine the design reactions for base plate and anchor rod design.

05.4.17

V V

Beam Design @ Chevron Frame

Beam Properties

1. Choose Type of Member: WF L = 26.5 ft rx = 10.20 in. bf/2tf = 6.70

2. Specify Beam Member: W24X131 Ry(Beam) = 1.1 ry = 2.97 in. h/tw = 35.60

Fy = 50 ksi A = 38.50 in2 Ix = 4020 in4

E = 29000 ksi d = 24.50 in. tw = 0.61 in.

Ca = 0.120 bf = 12.90 in. ho = 23.54 in.

3. Check Element Ductility Per AISC 341 Table D1.1:

Flange Ductility: bf/2tf = 6.70 λhd = 7.35 Highly Ductile

Web Ductility: h/tw = 35.60 λhd = 51.72 Highly Ductile

Axial and Flexural Demands at Midspan

Expected Post-Buckling Brace Strength Beam End Restraints: Pinned-Pinned PPB = 0.3*min(RyBRACE*Fy*A, 1.14*Fcre*A) MDL = 134.0 k-in

MLL = 112.0 k-in

Qb = 142.2 k F2.3(a) - Vert

Qb = 180.4 k F2.3(b) - Vert

Qh = 229.6 k F2.3(a) - Axial

Qh = 194.7 k F2.3(b) - Axial

F2.3(a) F2.3(b) MEg = 11302 k-in 14339 k-in

MEL = 352 k-in 298 k-in eb = 12.25 in.

Mu = 11908 k-in 14891 k-in [Β1(1.2+0.2SDS)MDL+Β1f1MLL+MEg+MEL]

[Β1(1.2+0.2SDS)MDL+Β1f1MLL+MEg]

Axial and Flexural Capacity φ = 0.90 K = 1.0

Beam Axial Capacity (X-Axis) Beam Axial Capacity (Y-Axis)

Lbx = 13.30 Lby = 6.70 Pe1 = 11378.1 k

KLx/rx = 15.6 KLy/ry = 27.1 α = 1.0

Fe = 1169.0 ksi Fe = 390.6 ksi Cm = 1.0

Fcr = 49.11 ksi Fcr = 47.39 ksi αPr = 229.6 k 194.7 k φPn = 1701.8 k φPn = 1642.1 k --> Controls B1 = 1.02 1.02

Strong Axis Flexural Capacity Lb = 6.7 ft

Zx = 370 in.3

Mr = 20350 k-in

Lb,max = 24.8 ft F2.4b(b), Section D1.2a for Moderately Ductile Members Lp = 10.5 ft Lr = 31.8 ft

Pbr = 17.3 k AISC 360 Eq A-6-7

Βbr = 143.4 k/in. AISC 360 Eq A-6-8 Interaction

Mn = 18500 k-in Bending Axis: X-Axis φ = 0.90 Axial Load Ratio to Beam: 100% φMn = 16650 k-in F2.3(a) F2.3(b) φPu/Pn = 0.14 0.12 < 0.2, Use Interaction Equation H1-1b

Beam Shear Demand (at Midspan) D/C = 0.79 0.95 < 1.0 OK

VDL = 1.7 k

VLL = 1.4 k Beam Shear Capacity

Lg = 53.0 in. h/tw < 2.24(E/Fy)

0.5 53.95 > 35.6 OK

F2.3(a) F2.3(b) Cv = 1.0

VEg = 71.1 k 90.2 k Vn = 444.7 k

D/C = 0.21 < 1.0 OK

VEmh = 71.1 k 90.2 k

Vu = 74.2 k 93.3 k [(1.2+0.2SDS)VDL+f1VLL+1.0(VEmh)]

Preliminary Design Considering Gusset Local Effects (Final Design Verified During Gusset Design)

VEL = 106.2 k 90.0 k

VEmh = 106.2 k 90.2 k D/C = 0.25

Vu = 109.3 k 93.3 k [(1.2+0.2SDS)VDL+f1VLL+1.0(VEmh)]

< 1.0 OK

Beams are designed based on the global loading on the beam, as well the unbalanced forces from the braces per AISC 341. In addition, chevron effects at the gussets are considered based on the recommendations in 'The Chevron Effect and Analysis of Chevron Beams - A Paradigm Shift' by Fortney and Thornton (2017).

Qb = (-Pten1 + Pcomp1)sin γ1

Qb = (-Pten1 + PPB1)sin γ1

Qh = (Pten1 + Pcomp1)cos γ1

Qh = (Pten1 + PPB1)cos γ1

Second-Order Effects

Note: Lb is the length between points that are either braced against lateral displacement of both flanges or braced with point

05.4.18

BF7

Brace Geometry

H = 14.0 ft W = 17.4 ft

LWP-WP = 16.48 ft LUNBRACED = 16.48 ft

LOFFSET = 2.0 ft

K = 1.00 KLBRACE = 12.48 ft

Q = 31.86 deg (For Connection Design) γ = 58.14 deg

Brace Properties

1. Choose Type of Member: HSS

2. Specify Brace Member: HSS4X4X5/16 Fy = 50 ksi A = 4.1 in2

3. Brace Configuration: E = 29000 ksi rx = 1.49 in

Material: Ry = 1.3 ry = 1.49 in

(KLUNBRACED)/r = 100.5 < 200 OK (AISC 341 F2.5b) h/t = 10.7 < 0.65√(E/RyFy) = 13.7 OK (AISC 341 F2.5a and Section D1.1) b/t = 10.7 < 0.65√(E/RyFy) = 13.7 OK (AISC 341 F2.5a and Section D1.1)

Brace Demands Brace Capacities & Design

VEQ = 16.5 k (@ 1.0E) ρ = 1 φC = 0.90

SDS = 1.22 φT = 0.90

Β2 = 1.00

Brace D1a D1b Brace D1a D1b

PDL 1.9 k 1.9 k Fcr 23.88 ksi 23.88 ksi α = 1.0

PLL 1.6 k 1.6 k φPn 88.1 k 88.1 k Pstory = 150.0 k f1 0.5 0.5 DCR 0.22 0.22 RM = 1.0

PEQ 15.6 k 15.6 k H = 400.0 k

Pu 19.2 k 19.2 k φTn 184.5 k 184.5 k ΔH = 3.36 in.

Tu 14.4 k 14.4 k DCR 0.08 0.08 Pe story = 20000.0 k

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+f1PLL+Β2(ρQE)] Tu = [-(0.9-0.2SDS)PDL + Β2(ρQE)]

Second Order Effects Considered in Analysis?

Yes

X-Brace or Single Diagonal Chevron Brace

Chevron

ASTM A500 Grade C

'H' and 'W' are dimensioned between work points.

VEQ

W

H

VEQ

W

H γ θ γ θ

C

C

C

C

05.4.19

V V

Column Demands and Design

Material: ASTM A992 Grade 50 FY-COL = 50 ksi RY-COL = 1.1

PDL 5.6 k Column Size W10X45 PDL 5.6 k Column Size W10X45

PLL 3.7 k b/2tf 6.5 Highly Ductile PLL 3.7 k b/2tf 6.5 Highly Ductile f1 0.5 h/tw 22.5 Highly Ductile f1 0.5 h/tw 22.5 Highly Ductile

PEQ 0.0 k KL/r 83.6 PEQ 0.0 k KL/r 83.6

PEmh 98.4 k Ca 0.165 PEmh 98.4 k Ca 0.165

Pu 108.3 k φPn 359.1 k Pu 108.3 k φPn 359.1 k

TEQ 0.0 k DCR 0.30 TEQ 0.0 k DCR 0.30

TEmh 63.9 k φTn -598.5 k TEmh 63.9 k φTn -598.5 k

Tu 0.0 k DCR 0.00 Tu 0.0 k DCR 0.00

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+f1PLL+PEmh] Tu = [(0.9-0.2SDS)PDL - TEmh]

Expected Strength of Brace in Compression (F2.3): Expected Strength of Brace in Tension (F2.3):

Pcompression = min(Ry-BRACE*Fy*A, 1.14*Fcre*A) Ptension = RY-BRACE*Fy*Ag

Fcre = 24.8 ksi

Pcomp= 116.1 k Pten = 266.5 k

Unbalanced Veritcal Force at Midspan of Beam (Chevron Only) F2.3(a) F2.3(b) R1 = (Pcomp*sin(ɣ) - Pten*sin(ɣ)) = -127.8 k -196.8 k

RCOL = R1 / 2 = -63.9 k -98.4 k Per Column

Foundation Reactions: Capacity Limited per AISC 341-16 for Base Connection Design

Ru = Pu + Pcomp1*sin(ɣ1) Ru = Tu - Pten1*sin(ɣ1)

C1 C2 C1 C2

Ru = 172.4 k 172.4 k Tu = -158.8 k -158.8 k

Foundation Reactions: Including Overstrength per ASCE 7-16 for Concrete Design Ωo = 2.0

Compression: Tension:

Pu = [(1.2+0.2SDS)PDL+ f1PLL+ ΩoPE] Tu = [(0.9-0.2SDS)PDL - ΩoTE]

PE = 13.3 k TE = -13.3 k

C1 C2 C1 C2

Ru = 36.5 k 36.5 k Ru = -22.9 k -22.9 k

Foundation Reactions: Alternative Basic Load Combinations for Soil Bearing and Uplift Design

Pu = PDL+ PLL+ ρPE/1.4 Tu = 0.9PDL - ρTE/1.4

PE/1.4 = 9.5 k TE/1.4 = -9.5 k

C1 C2 C1 C2

Ru = 18.8 k 18.8 k Ru = -4.4 k -4.4 k

Columns are designed using the load combinations noted below. The seismic demands considereding the load combinations from AISC 341-16 Section F2.3 are used to determine the Emh seismic demands. Depending on the orientation of the braces, the demands may be due to a brace connection at the top of the column or a reaction due to unbalanced loads at the midspan of the beam. For single diagonal configurations, columns without a brace attached to the top have no seismic demands. For Chevron configuartions, columns have no seismic demands for the ASCE 7-16 load combinations as the loads in the braces are assumed to be balanced so there is no seismic shear reaction at the ends of the beam.

Because the seismic component of the column required strenth comes from the mechanism analysis of AISC Seismic Provisions Section F2.3 and is based on expected strengths of the braces, P-Δ effects need not be considered and Β2 from AISC Specification Appendix 8 need not be applied. See additional discussion in AISC Seismic Manual Page 5-140.

Column C1 Column C2

Reaction are calculated using the same load combinations and loading considerations as the columns. In addition to the column loads, loading from braces at the base of the columns is combined with the column loading to determine the design reactions for base plate and anchor rod design.

05.4.20

V V

Beam Design @ Chevron Frame

Beam Properties

1. Choose Type of Member: WF L = 17.4 ft rx = 10.00 in. bf/2tf = 4.59

2. Specify Beam Member: W24X103 Ry(Beam) = 1.1 ry = 1.99 in. h/tw = 39.20

Fy = 50 ksi A = 30.30 in2 Ix = 3000 in4

E = 29000 ksi d = 24.50 in. tw = 0.55 in.

Ca = 0.135 bf = 9.00 in. ho = 23.52 in.

3. Check Element Ductility Per AISC 341 Table D1.1:

Flange Ductility: bf/2tf = 4.59 λhd = 7.35 Highly Ductile

Web Ductility: h/tw = 39.20 λhd = 51.43 Highly Ductile

Axial and Flexural Demands at Midspan

Expected Post-Buckling Brace Strength Beam End Restraints: Pinned-Pinned PPB = 0.3*min(RyBRACE*Fy*A, 1.14*Fcre*A) MDL = 195.0 k-in

MLL = 163.0 k-in

Qb = 127.8 k F2.3(a) - Vert

Qb = 196.8 k F2.3(b) - Vert

Qh = 201.9 k F2.3(a) - Axial

Qh = 159.0 k F2.3(b) - Axial

F2.3(a) F2.3(b) MEg = 6669 k-in 10272 k-in

MEL = 309 k-in 244 k-in eb = 12.25 in.

Mu = 7345 k-in 10881 k-in [Β1(1.2+0.2SDS)MDL+Β1f1MLL+MEg+MEL]

[Β1(1.2+0.2SDS)MDL+Β1f1MLL+MEg]

Axial and Flexural Capacity φ = 0.90 K = 1.0

Beam Axial Capacity (X-Axis) Beam Axial Capacity (Y-Axis)

Lbx = 8.70 Lby = 8.70 Pe1 = 19695.1 k

KLx/rx = 10.4 KLy/ry = 52.5 α = 1.0

Fe = 2626.0 ksi Fe = 104.0 ksi Cm = 1.0

Fcr = 49.60 ksi Fcr = 40.89 ksi αPr = 201.9 k 159.0 k φPn = 1352.7 k φPn = 1115.0 k --> Controls B1 = 1.01 1.01

Strong Axis Flexural Capacity Lb = 8.7 ft

Zx = 280 in.3

Mr = 15400 k-in

Lb,max = 16.6 ft F2.4b(b), Section D1.2a for Moderately Ductile Members Lp = 7.0 ft Lr = 21.9 ft

Pbr = 13.1 k AISC 360 Eq A-6-7

Βbr = 83.6 k/in. AISC 360 Eq A-6-8 Interaction

Mn = 13389 k-in Bending Axis: X-Axis φ = 0.90 Axial Load Ratio to Beam: 100% φMn = 12050 k-in F2.3(a) F2.3(b) φPu/Pn = 0.18 0.14 < 0.2, Use Interaction Equation H1-1b

Beam Shear Demand (at Midspan) D/C = 0.70 0.97 < 1.0 OK

VDL = 3.8 k

VLL = 3.2 k Beam Shear Capacity

Lg = 34.8 in. h/tw < 2.24(E/Fy)

0.5 53.95 > 39.2 OK

F2.3(a) F2.3(b) Cv = 1.0

VEg = 63.9 k 98.4 k Vn = 404.3 k

D/C = 0.26 < 1.0 OK

VEmh = 63.9 k 98.4 k

Vu = 71.0 k 105.5 k [(1.2+0.2SDS)VDL+f1VLL+1.0(VEmh)]

Preliminary Design Considering Gusset Local Effects (Final Design Verified During Gusset Design)

VEL = 142.2 k 112.0 k

VEmh = 142.2 k 112.0 k D/C = 0.37

Vu = 149.3 k 119.1 k [(1.2+0.2SDS)VDL+f1VLL+1.0(VEmh)]

< 1.0 OK

Beams are designed based on the global loading on the beam, as well the unbalanced forces from the braces per AISC 341. In addition, chevron effects at the gussets are considered based on the recommendations in 'The Chevron Effect and Analysis of Chevron Beams - A Paradigm Shift' by Fortney and Thornton (2017).

Qb = (-Pten1 + Pcomp1)sin γ1

Qb = (-Pten1 + PPB1)sin γ1

Qh = (Pten1 + Pcomp1)cos γ1

Qh = (Pten1 + PPB1)cos γ1

Second-Order Effects

Note: Lb is the length between points that are either braced against lateral displacement of both flanges or braced with point

05.4.21

BF8

Brace Geometry

H = 14.0 ft W = 12.3 ft

LWP-WP = 18.66 ft LUNBRACED = 18.66 ft

LOFFSET = 2.0 ft

K = 1.00 KLBRACE = 14.66 ft

Q = 41.37 deg (For Connection Design) γ = 48.63 deg

Brace Properties

1. Choose Type of Member: HSS

2. Specify Brace Member: HSS4X4X5/16 Fy = 50 ksi A = 4.1 in2

3. Brace Configuration: E = 29000 ksi rx = 1.49 in

Material: Ry = 1.3 ry = 1.49 in

(KLUNBRACED)/r = 118.0 < 200 OK (AISC 341 F2.5b) h/t = 10.7 < 0.65√(E/RyFy) = 13.7 OK (AISC 341 F2.5a and Section D1.1) b/t = 10.7 < 0.65√(E/RyFy) = 13.7 OK (AISC 341 F2.5a and Section D1.1)

Brace Demands Brace Capacities & Design

VEQ = 6.5 k (@ 1.0E) ρ = 1 φC = 0.90

SDS = 1.22 φT = 0.90

Β2 = 1.00

Brace D1a D1b Brace…