3fccd510-5b1c-4d74-ae5f-038db084d2fc 83 3 5 false false 0 decimal

ANG CMF, Fort Smith, AR

Jason McCool, PE

C9x15 Flight Header Connection Calcs

3/13/2018

Method ASD LRFD 21 mat :

plf lbf ft / :

R 3 kip * :

Reaction

Channel C6x8.2 :

Channel Size

"ASD"
"LRFD"

Method

Design method =

BoltTable Bolt Fu Fnt Fnv A307 60 ksi * 45 ksi * 27 ksi * A325N/F1852N 120 ksi * 90 ksi * 54 ksi * A325X/F1852X 120 ksi * 90 ksi * 68 ksi * A325SC 120 ksi * 90 ksi * 1 ksi * A490N/F2280N 150 ksi * 113 ksi * 68 ksi * A490X/F2280X 150 ksi * 113 ksi * 84 ksi * A490SC 150 ksi * 113 ksi * 1 ksi * 84 mat :

CTable Csize A d bf tf tw Ix Sx Zx rx Iy Sy Zy ry C15x50 14.7 15 3.72 0.65 0.716 404 53.8 68.5 5.24 11 3.77 8.14 0.865 C15x40 11.8 15 3.52 0.65 0.52 348 46.5 57.5 5.43 9.17 3.34 6.84 0.883 C15x33.9 1015 3.4 0.65 0.4 31542 50.8 5.61 8.07 3.09 6.19 0.901 C12x30 8.81 12 3.17 0.501 0.51 16227 33.8 4.29 5.12 2.05 4.32 0.762 C12x25 7.34 12 3.05 0.501 0.387 14424 29.4 4.43 4.45 1.87 3.82 0.779 C12x20.7 6.08 12 2.94 0.501 0.282 129 21.5 25.6 4.61 3.86 1.72 3.47 0.797 C10x30 8.81 10 3.03 0.436 0.673 103 20.7 26.7 3.43 3.93 1.65 3.78 0.668 C10x25 7.35 10 2.89 0.436 0.526 91.1 18.2 23.1 3.52 3.34 1.47 3.18 0.675 C10x20 5.87 10 2.74 0.436 0.379 78.9 15.8 19.4 3.67 2.8 1.31 2.7 0.69 C10x15.3 4.48 10 2.6 0.436 0.24 67.3 13.5 15.9 3.88 2.27 1.15 2.34 0.711 C9x20 5.87 9 2.65 0.413 0.448 60.9 13.5 16.9 3.22 2.41 1.17 2.46 0.64 C9x15 4.4 9 2.49 0.413 0.285 51 11.3 13.6 3.4 1.91 1.01 2.04 0.659 C9x13.4 3.94 9 2.43 0.413 0.233 47.8 10.6 12.6 3.48 1.75 0.954 1.94 0.666 C8x18.75 5.51 8 2.53 0.39 0.487 43.9 11 13.9 2.82 1.97 1.01 2.17 0.598 C8x13.75 4.03 8 2.34 0.39 0.303 36.1 9.02 11 2.99 1.52 0.848 1.73 0.613 C8x11.5 3.37 8 2.26 0.39 0.22 32.5 8.14 9.63 3.11 1.31 0.775 1.57 0.623 C7x14.75 4.33 7 2.3 0.366 0.419 27.2 7.78 9.75 2.51 1.37 0.772 1.63 0.561 C7x12.25 3.59 7 2.19 0.366 0.314 24.2 6.92 8.46 2.59 1.16 0.696 1.42 0.568 C7x9.8 2.87 7 2.09 0.366 0.21 21.2 6.07 7.19 2.72 0.957 0.617 1.26 0.578 C6x13 3.82 6 2.16 0.343 0.437 17.3 5.78 7.29 2.13 1.05 0.638 1.35 0.524 C6x10.5 3.07 6 2.03 0.343 0.314 15.1 5.04 6.18 2.22 0.86 0.561 1.14 0.529 C6x8.2 2.39 6 1.92 0.343 0.2 13.1 4.35 5.16 2.34 0.687 0.488 0.987 0.536 C5x9 2.64 5 1.89 0.32 0.325 8.89 3.56 4.39 1.84 0.624 0.444 0.913 0.486 C5x6.7 1.97 5 1.75 0.32 0.19 7.48 2.99 3.55 1.95 0.47 0.372 0.757 0.489 C4x7.25 2.13 4 1.72 0.296 0.321 4.58 2.29 2.84 1.47 0.425 0.337 0.695 0.447 C4x6.25 1.77 4 1.65 0.272 0.247 42 2.43 1.5 0.345 0.284 0.569 0.441 C4x5.4 1.58 4 1.58 0.296 0.184 3.85 1.92 2.29 1.56 0.312 0.277 0.565 0.444 C4x4.5 1.38 4 1.58 0.296 0.125 3.65 1.83 2.12 1.63 0.289 0.265 0.531 0.457 C3x6 1.76 3 1.6 0.273 0.356 2.07 1.38 1.74 1.09 0.3 0.263 0.543 0.413 C3x5 1.47 3 1.5 0.273 0.258 1.85 1.23 1.52 1.12 0.241 0.228 0.464 0.405 C3x4.1 1.2 3 1.41 0.273 0.17 1.65 1.1 1.32 1.18 0.191 0.196 0.399 0.398 C3x3.5 1.09 3 1.37 0.273 0.132 1.57 1.04 1.24 1.2 0.169 0.182 0.364 0.394 MC18x58 17.1 18 4.2 0.625 0.7 67575 95.4 6.29 17.6 5.28 10.7 1.02 MC18x51.9 15.3 18 4.1 0.625 0.6 627 69.6 87.3 6.41 16.3 5.02 9.86 1.03 MC18x45.8 13.5 184 0.625 0.5 578 64.2 79.2 6.55 14.9 4.77 9.14 1.05 MC18x42.7 12.6 18 3.95 0.625 0.45 554 61.5 75.1 6.64 14.3 4.64 8.82 1.07 MC13x50 14.7 13 4.41 0.61 0.787 314 48.3 60.8 4.62 16.4 4.77 10.2 1.06 MC13x40 11.7 13 4.19 0.61 0.56 273 41.9 51.2 4.82 13.7 4.24 8.66 1.08 MC13x35 10.3 13 4.07 0.61 0.447 252 38.8 46.5 4.95 12.3 3.97 8.04 1.09 MC13x31.8 9.35 134 0.61 0.375 239 36.7 43.4 5.05 11.4 3.79 7.69 1.1 MC12x50 14.7 12 4.14 0.7 0.835 269 44.9 56.5 4.28 17.4 5.64 10.9 1.09 MC12x45 13.2 12 4.01 0.7 0.71 251 41.9 52 4.36 15.8 5.3 10.1 1.09 MC12x40 11.8 12 3.89 0.7 0.59 23439 47.7 4.46 14.2 4.98 9.31 1.1 MC12x35 10.3 12 3.77 0.7 0.465 21636 43.2 4.59 12.6 4.64 8.62 1.11 MC12x31 9.12 12 3.67 0.7 0.37 202 33.7 39.7 4.71 11.3 4.37 8.15 1.11 MC12x14.3 4.18 12 2.12 0.313 0.25 76.1 12.7 15.9 4.27 1 0.574 1.21 0.489 MC12x10.6 3.1 12 1.5 0.309 0.19 55.3 9.22 11.6 4.22 0.378 0.307 0.635 0.349 MC10x41.1 12.1 10 4.32 0.575 0.796 157 31.5 39.3 3.61 15.7 4.85 9.49 1.14 MC10x33.6 9.87 10 4.1 0.575 0.575 139 27.8 33.7 3.75 13.1 4.35 8.28 1.15 MC10x28.5 8.37 10 3.95 0.575 0.425 126 25.3 30 3.89 11.3 3.99 7.59 1.16 MC10x25 7.34 10 3.41 0.575 0.38 11022 26.2 3.87 7.25 2.96 5.65 0.993 MC10x22 6.45 10 3.32 0.575 0.29 102 20.5 23.9 3.99 6.4 2.75 5.29 0.997 MC10x8.4 2.46 10 1.5 0.28 0.17 31.9 6.39 7.92 3.61 0.326 0.268 0.548 0.364 MC10x6.5 1.95 10 1.17 0.202 0.152 22.9 4.59 5.9 3.43 0.133 0.137 0.284 0.262 MC9x25.4 7.47 9 3.5 0.55 0.45 87.9 19.5 23.5 3.43 7.57 2.99 5.7 1.01 MC9x23.9 7.02 9 3.45 0.55 0.4 84.9 18.9 22.5 3.48 7.14 2.89 5.51 1.01 MC8x22.8 6.7 8 3.5 0.525 0.427 63.8 15.9 19.1 3.09 7.01 2.81 5.37 1.02 MC8x21.4 6.28 8 3.45 0.525 0.375 61.5 15.4 18.2 3.13 6.58 2.71 5.18 1.02 MC8x20 5.87 8 3.03 0.5 0.4 54.4 13.6 16.4 3.04 4.42 2.02 3.86 0.867 MC8x18.7 5.5 8 2.98 0.5 0.353 52.4 13.1 15.6 3.09 4.15 1.95 3.72 0.868 MC8x8.5 2.5 8 1.87 0.311 0.179 23.3 5.82 6.95 3.05 0.624 0.431 0.875 0.5 MC7x22.7 6.67 7 3.6 0.5 0.503 47.4 13.5 16.4 2.67 7.24 2.83 5.38 1.04 MC7x19.1 5.61 7 3.45 0.5 0.352 43.1 12.3 14.5 2.77 6.06 2.55 4.85 1.04 MC6x18 5.29 6 3.5 0.475 0.379 29.7 9.89 11.7 2.37 5.88 2.47 4.68 1.05 MC6x15.3 4.49 6 3.5 0.385 0.34 25.3 8.44 9.91 2.38 4.91 2.01 3.85 1.05 MC6x16.3 4.79 63 0.475 0.375 26 8.66 10.4 2.33 3.77 1.82 3.47 0.887 MC6x15.1 4.44 6 2.94 0.475 0.316 24.9 8.3 9.83 2.37 3.46 1.73 3.3 0.883 MC6x12 3.53 6 2.5 0.375 0.31 18.7 6.24 7.47 2.3 1.85 1.03 1.97 0.724 MC6x7 2.09 6 1.88 0.291 0.179 11.4 3.81 4.5 2.34 0.603 0.439 0.865 0.537 MC6x6.5 1.95 6 1.85 0.291 0.155 11 3.66 4.28 2.38 0.565 0.422 0.836 0.539 MC4x13.8 4.03 4 2.5 0.5 0.5 8.85 4.43 5.53 1.48 2.13 1.29 2.4 0.727 MC3x7.1 2.11 3 1.94 0.351 0.312 2.72 1.81 2.24 1.14 0.666 0.518 0.998 0.562 7314 mat :

C_Data CTable Channel 1 findrows :

C_Data

tw.c C_Data 6 el in * : in 0.2

d.c C_Data 3 el in * : in 6

bf.c C_Data 4 el in * : in 1.92

tf.c C_Data 5 el in * : in 0.343

d.c in 6

tw.c in 0.2

Channel Depth & Web Thickness

bf.c in 1.92

tf.c in 0.343

Channel Flange Width & Avg Thickness

Cope.L_top 3 in * :

Cope.d_top 1 in * :

Length & Depth of Top Cope

Cope.L_bot 0 in * :

Cope.d_bot 0 in * :

Length & Depth of Bottom Cope

"Bolt"
"A307"
"A325N/F1852N"
"A325X/F1852X"
"A325SC"
"A490N/F2280N"
"A490X/F2280X"
"A490SC"

Bolt.type

Dia STD OVS SSL LSL 0.5 0.5625 0.625 0.6875 1.25 0.625 0.6875 0.8125 0.875 1.5625 0.75 0.8125 0.9375 1 1.875 0.875 0.9375 1.0625 1.125 2.1875 1 1.0625 1.25 1.3125 2.5 1.125 d.b 0.0625 + d.b 0.3125 + d.b 0.375 + 2.5 d.b * 75 mat

Bolt.diam 0.75 in * :

Bolt Diameter & Type

Bolt.rows 1 :

Bolt.cols 2 :

Number of Rows & Columns of Bolts

Hole.h_C 0.8125 in * :

Hole.w_C 0.8125 in * :

Hole Vert & Horiz Dimensions in Channel (equal if round hole)

Hole.h_PL 0.8125 in * :

Hole.w_PL 1 in * :

Hole Vert & Horiz Dimensions in Plate (equal if round hole)

s.v 3 in * :

s.h 3 in * :

Bolt Vertical & Horizontal Spacing

Loc.top_hole 3 in * :

Vertical Distance from Top of Channel to Top Hole

L.PL 4 in * :

W.PL 6.5 in * :

Shear Plate Length & Width

t.PL 0.375 in * :

Shear Plate Thickness

a 2 in * :

Setback 0.5 in * :

Distance from Bolt Centerline to Support & Channel Setback from Support

L.eh_PL W.PL a - s.h Bolt.cols 1 - (* - : in 1.5

Shear Plate Horizontal Edge Distance

L.ev_PL L.PL s.v Bolt.rows 1 - (* - (2 / : in 2

Shear Plate Vertical Edge Distance

L.eh_C a Setback - : in 1.5

Channel Horizontal Edge Distance

L.ev_Ct Loc.top_hole Cope.d_top - : in 2

Vertical Edge Distances @ Top & Bottom of Channel

L.ev_Cb d.c Loc.top_hole - s.v Bolt.rows 1 - (* - Cope.d_bot - : in 3

t.weld 0.25 in * :

Weld Size from Shear Plate to Support

F.nv Bolt.type 4 el : ksi 54

Nominal Bolt Shear Strength from AISC Table J3.2

F.y_PL 36 ksi * :

F.t_PL 58 ksi * :

Yield & Tensile Strengths of Plate

F.y_C 36 ksi * :

F.t_C 58 ksi * :

Yield & Tensile Strengths of Channel

E 29000 ksi * :

Modulus of Elasticity for Steel

ν 0.3 :

Poisson's Ratio

h.o d.c Cope.d_bot - Cope.d_top - : in 5

Coped Web Depth

Method LRFD ≡ φ.vb 0.75 : φ.vy 1.0 : φ.vr 0.75 : φ.w 0.75 : φ.bb 0.75 : φ.b 0.9 : 61 line φ.vb 21 -^: φ.vy 1.50 1 -^: φ.vr 21 -^: φ.w 21 -^: φ.bb 21 -^: φ.b 1.67 1 -^: 61 line if

Resistance Value for Bolt Shear - J3.6

Resistance Value for Shear Yielding - J4.2(a)

Resistance Value for Shear Rupture - J4.2(b)

Resistance Factor for Welds - J2.4

Resistance Factor for Bolt Bearing - J3.10

Bending Resistance Factor - F1, p.9-7

ASD Safety Factors converted to LRFD Resistance Factors for calcs

dhp.w Hole.w_PL 116 / in * + : in 1.062

dhc.w Hole.w_C 116 / in * + : in 0.875

Hole sizes for rupture limit states - AISC SCM D3, Comm. B4.3b

dhp.h Hole.h_PL 116 / in * + : in 0.875

dhc.h Hole.h_C 116 / in * + : in 0.875

Bolt Shear

Bolt eccentric capacity calculated by the Elastic Method (AISC SCM, 14th Ed, p.7-8)

A.b π Bolt.diam 2^* 4 / : in 2^0.442

Bolt Area

φR.n_bv φ.vb F.nv * A.b * : kip 17.892

Factored Bolt Shear Strength

n Bolt.cols Bolt.rows * : 2

Number of Bolts

e a Bolt.cols 1 - (s.h 2 / * + : in 3.5

Eccentricity (face of support to centroid of bolt group)

CG.group_x Bolt.cols 1 - (s.h 2 / * : in 1.5

Horizontal Distance from Lower Left Bolt to Centroid of Bolt Group

CG.group_y Bolt.rows 1 - (s.v 2 / * : in 0

Vertical Distance from Lower Left Bolt to Centroid of Bolt Group

c CG.group_x 2^CG.group_y 2^+ sqrt : in 1.5

Radial Distance to Most Remote Bolt from CG

i 1 :

j 1 :

dx Bolt.rows Bolt.cols matrix :

dy Bolt.rows Bolt.cols matrix :

j 1 Bolt.cols range i 1 Bolt.rows range dx i j el s.h j 1 - (* CG.group_x - : for 11 line for

j 1 Bolt.cols range i 1 Bolt.rows range dy i j el s.v i 1 - (* CG.group_y - : for 11 line for

dx in 1.5 - 1.5 12 mat

dy in 0012 mat

I.y 0 :

I.x 0 :

j 1 Bolt.cols range i 1 Bolt.rows range I.y I.y dx i j el (2^+ : for for 11 line

j 1 Bolt.cols range i 1 Bolt.rows range I.x I.x dy i j el (2^+ : for for 11 line

I.y in 2^4.5

I.x in 2^0

I.p I.x I.y + : in 2^4.5

r.mxu R e * CG.group_y * I.p / : kip 0

r.myu R e * CG.group_x * I.p / : kip 3.5

r.pyu R n / : kip 1.5

Concentric Reaction per Bolt

r.u r.mxu 2^r.pyu r.myu + (2^+ sqrt : kip 5

Total Bolt Shear applied @ Most Extreme Bolt from Centroid

Capacity.bv φR.n_bv e 2^CG.group_y 2^* I.p 2^/ 1 n 2^/ + 2 e * CG.group_x * n I.p * / + e 2^CG.group_x 2^* I.p 2^/ + sqrt / : kip 10.735

Util.bv r.u φR.n_bv / : % 27.94

Utilization Ratio

Shear Yielding of Plate

A.gv_PL L.PL t.PL * : in 2^1.5

Gross Shear Area of Shear Plate

φR.n_vy_PL φ.vy 0.60 * A.gv_PL * F.y_PL * : kip 32.4

Plate Shear Yielding Capacity

Util.vy_PL R φR.n_vy_PL / : % 9.26

Utilization Ratio

Shear Rupture of Plate

A.nv_PL L.PL Bolt.rows dhp.h * - (t.PL * : in 2^1.172

Net Shear Area of Shear Plate

φR.n_vr_PL φ.vr 0.60 * A.nv_PL * F.t_PL * : kip 30.586

Plate Shear Rupture Capacity

Util.vr_PL R φR.n_vr_PL / : % 9.81

Utilization Ratio

Shear Yielding of Channel

A.gv_C d.c Cope.d_top - Cope.d_bot - (tw.c * : in 2^1

Gross Shear Area of Channel

φR.n_vy_C φ.vy 0.60 * A.gv_C * F.y_C * : kip 21.6

Channel Shear Yielding Capacity

Util.vy_C R φR.n_vy_C / : % 13.89

Utilization Ratio

Shear Rupture of Channel

A.nv_C d.c Cope.d_top - Cope.d_bot - Bolt.rows dhc.h * - (tw.c * :

A.nv_C in 2^0.825

Net Shear Area of Channel

φR.n_vr_C φ.vr 0.60 * A.nv_C * F.t_C * : kip 21.532

Channel Shear Rupture Capacity (Eq J4-4)

Util.vr_C R φR.n_vr_C / : % 13.93

Utilization Ratio

Block Shear Rupture of Plate

Bolt.cols 1 ≡ U.bs 1 : U.bs 0.5 : if

U.bs 0.5

Reduction Factor for nonuniform stress in connections w/ multiple bolt columns

A.bsnt_PL L.eh_PL dhp.w 2 / - s.h dhp.w - (Bolt.cols 1 - (* + (t.PL * : in 2^1.09

A.bsgv_PL L.ev_PL Bolt.rows 1 - (s.v * + (t.PL * : in 2^0.75

A.bsnv_PL A.bsgv_PL Bolt.rows 1 - (dhp.h * dhp.h 2 / + (t.PL * - : in 2^0.586

φR.n_bs_PL φ.vr 0.6 F.t_PL * A.bsnv_PL * U.bs F.t_PL * A.bsnt_PL * + 0.6 F.y_PL * A.bsgv_PL * U.bs F.t_PL * A.bsnt_PL * + 21 mat * :

φR.n_bs_PL kip 38.997 35.854 21 mat

φR.n_bs_PL φR.n_bs_PL min : kip 35.854

Factored Block Shear Strength of Plate

Util.bs_PL R φR.n_bs_PL / : % 8.37

Utilization Ratio

Block Shear Rupture of Channel

A.bsnt_C L.eh_C dhc.w 2 / - s.h dhc.w - (Bolt.cols 1 - (* + (tw.c * : in 2^0.637

A.bsgv_C L.ev_Ct Bolt.rows 1 - (s.v * + (tw.c * : in 2^0.4

A.bsnv_C A.bsgv_C Bolt.rows 1 - (dhc.h * dhc.h 2 / + (tw.c * - : in 2^0.312

φR.n_bs_C φ.vr 0.6 F.t_C * A.bsnv_C * U.bs F.t_C * A.bsnt_C * + 0.6 F.y_C * A.bsgv_C * U.bs F.t_C * A.bsnt_C * + 21 mat * :

φR.n_bs_C kip 22.022 20.346 21 mat

Factored Block Shear Strength of Channel

φR.n_bs_C φR.n_bs_C min : kip 20.346

Util.bs_C R φR.n_bs_C / : % 14.75

Utilization Ratio

Weld Capacity to Support

L.w L.PL : in 4

S.w L.w 2^3 / : in 3^in / 5.333

Weld Section Modulus per unit length (Weld treated as a line, Blodgett)

M.w R a * : kip in * 6

F.EXX 70 ksi * :

Weld Tensile Strength

f.wv R 2 L.w * / : kip in / 0.375

f.wm M.w S.w / : kip in / 1.125

f.w f.wv 2^f.wm 2^+ sqrt : kip in / 1.186

Weld Combined Design Loading

φR.n_w φ.w 0.6 * F.EXX * 0.707 * t.weld * : kip in / 5.568

Factored Weld Capacity

Util.w f.w φR.n_w / : % 21.3

Utilization Ratio

Bolt Bearing at Plate

L.c_int_PL s.v Hole.h_PL - : in 2.187

L.c_e_PL L.ev_PL 0.5 Hole.h_PL * - : in 1.594

R.n_bb_int_PL 1.2 L.c_int_PL * t.PL * F.t_PL * 2.4 Bolt.diam * t.PL * F.t_PL * 21 mat :

R.n_bb_int_PL kip 57.094 39.15 21 mat

R.n_bb_e_PL 1.2 L.c_e_PL * t.PL * F.t_PL * 2.4 Bolt.diam * t.PL * F.t_PL * 21 mat :

R.n_bb_e_PL kip 41.597 39.15 21 mat

φR.n_bb_PL φ.bb R.n_bb_e_PL min Bolt.rows 1 - (R.n_bb_int_PL min * (+ (* :

φR.n_bb_PL kip 29.363

Util.bb_PL R φR.n_bb_PL / : % 10.22

Utilization Ratio

Bolt Bearing at Channel

L.c_int_C s.v Hole.h_C - : in 2.187

Clear Distance Between Holes in Channel Web

L.c_e_C L.ev_Ct 0.5 Hole.h_C * - : in 1.594

Clear Distance from Hole to Edge of Channel Web

R.n_bb_int_C 1.2 L.c_int_C * tw.c * F.t_C * 2.4 Bolt.diam * tw.c * F.t_C * 21 mat :

R.n_bb_int_C kip 30.45 20.88 21 mat

Nominal Bolt Bearing Capacity at Interior Holes in PChannel

R.n_bb_e_C 1.2 L.c_e_C * tw.c * F.t_C * 2.4 Bolt.diam * tw.c * F.t_C * 21 mat :

R.n_bb_e_C kip 22.185 20.88 21 mat

Nominal Bolt Bearing Capacity at Edge Hole in Channel

φR.n_bb_C φ.bb R.n_bb_e_C min Bolt.rows 1 - (R.n_bb_int_C min * (+ (* :

φR.n_bb_C kip 15.66

Factored Bolt Bearing Capacity of Channel

Util.bb_C R φR.n_bb_C / : % 19.16

Utilization Ratio

Flexural Local Buckling at Channel Web (if Coped)

Check for flexural local buckling strength of beam coped at top flange only per AISC SCM 14th Ed, p.9-7, Method 1.

Cope.L_top 0 ≠ (Cope.L_bot 0 ≡ (& Cope.d_bot 0 ≡ (& Cope.L_top d.c / 1 > f 1 Cope.L_top d.c / + : f 2 Cope.L_top d.c / * : if f 1 : if

f 1

f = plate buckling model adjustment factor

Cope.L_top 0 ≠ (Cope.L_bot 0 ≡ (& Cope.d_bot 0 ≡ (& Cope.L_top h.o / 1 > k 2.2 h.o * Cope.L_top / : k 2.2 h.o Cope.L_top / (1.65^* : if k 1 : if

k 5.111

k = plate buckling coefficient

Cope.L_top 2 d.c * ≤ (Cope.d_top 0.5 d.c * ≤ (& Cope.d_bot 0 ≡ (& Cope.L_bot 0 ≡ (& (F.cr1 π 2^E * 121 ν 2^- (* / tw.c h.o / (2^* f * k * F.y_C 21 mat : F.cr1 F.cr1 min : 21 line F.cr1 0 ksi * : if

π 2^E * 121 ν 2^- (* / tw.c h.o / (2^* f * k * ksi 214.323

F.cr1 ksi 36

Check for flexural local buckling strength of beam with equally coped top & bottom flanges per AISC SCM 14th Ed, p.9-8, Method 2.

f.d 1 :

Cope.L_bot Cope.L_top ≡ (Cope.L_bot 0 ≠ (& Cope.L_top 2 d.c * ≤ (& Cope.d_top 0.2 d.c * ≤ (& (f.d 3.5 7.5 Cope.d_top d.c / (* - : F.cr2 0.62 π * E * f.d * tw.c 2^Cope.L_top h.o * / * F.y_C 21 mat : F.cr2 F.cr2 min : 31 line F.cr2 0 : if

0.62 π * E * f.d * tw.c 2^Cope.L_top h.o * / * ksi 150.629

F.cr2 ksi 0

Check for flexural local buckling strength of beam with all other coped flange conditions per AISC SCM 14th Ed, p.9-9, Method 3.

F.cr1 0 ≡ (F.cr2 0 ≡ (& λ h.o F.y_C ksi 1 -^* sqrt * 10 tw.c * 475280 h.o Cope.L_top / (2^* + sqrt * / : λ 1 : if

Q λ 0.7 < Q 1 : λ 1.41 > Q 1.3 λ 2^/ : Q 1.34 0.486 λ * - : if if :

Q 0.854

F.cr3 Q F.y_C * : ksi 30.744

Check for flexural local yielding strength of beam with tension flange cope > top flange cope per AISC SCM 14th Ed, p.9-9, Method 4.

Cope.L_bot 0 ≡ A.bf bf.c tw.c - (tf.c * : A.bf 0 : if

Cope.L_top 0 ≡ A.tf bf.c tw.c - (tf.c * : A.tf 0 : if

A.bf in 2^0.59

A.tf in 2^0

A.w tw.c h.o (* : in 2^1

A.net A.bf A.tf + A.w + : in 2^1.59

I.x_w tw.c h.o 3^* 12 / : in 4^2.083

d.f h.o tf.c - 2 / : in 2.328

I.x_C I.x_w A.bf d.f 2^* + A.tf d.f 2^* + : in 4^5.282

Q.sum tf.c 2 / A.bf * h.o 2 / A.w * + d.c tf.c 2 / - (A.tf * + : in 3^2.601

c.net Q.sum A.net / : in 1.636

S.net_C I.x_C c.net / : in 3^3.229

Cope.L_bot Cope.L_top > M.n_cty F.y_C S.net_C * : M.n_cty 0 ksi * : if

M.n_cty 0

F.cr F.cr1 F.cr2 F.cr3 31 mat : ksi 360 30.744 31 mat

F.cr F.cr max : ksi 36

φM.n_wb φ.b F.cr * S.net_C * : kip ft * 8.717

M.u_wb R Setback Cope.L_top + (* : kip ft * 0.875

Util.wb_C M.u_wb φM.n_wb / : % 10.04

Utilization Ratio

UtilRatio Util.vy_PL Util.vr_PL Util.bs_PL Util.bb_PL Util.vy_C Util.vr_C Util.bs_C Util.bb_C Util.w Util.bv Util.wb_C 111 mat : % 9.259 9.808 8.367 10.217 13.889 13.932 14.745 19.157 21.299 27.945 10.038 111 mat

Util.max UtilRatio max : % 27.94

Governing Utilization Ratio