Question

7 A DOUBLE CHANNEL 2 -CRXP E ) Ad A TENNIO MEMBER HOW MUCH PARA LAS CAN BE APPLIED I ts 3k Fy-50 TYPE '' (1972) F4336 Hoooo Chạy 2 = 50 tri * P GUJIET AL = 36 , +1 900 2 C8x/7 29 (136) 3 SPACES CHANNEL = Laut GusSET PL - J 36

A Double Channel 2-C8x18.75 is used as a tension member. How much factored load can be applied?

Both Part A and B need to be answered for the question. Type A, (A572) Channel = 50ksi, (A36) Gusset PL = 36ksi

Type B (A36) Channel & Gusset PL = 36ksi

Thank you!

Answer 1

Cijven chamnd member: - 2 (8 x 18.75 - Oo91 Grade :- A36 member is connected with the web a poop; Given channel section to 2" has Area Agallozin? -3 spaces Web thickness t= 0.487" Bolt dia do= 7/8" No. of shear planes m=2 bolts across a section n=2 No. of bolts in line =.4 Pitch of the bolts, s=3in [along member ank) Gage of bolts . q =4 in (along Transverse axis) End distance 15 in Distance of controid from edge, x = 0.565 in. A512 grade steel has - fy = 50 ksi ; fu = 65 ksi Dia of bolt hole = 7 7 5 + 1/4 =1" A Design Strength of channel: - i lielding in the gross section: Design strength of gross section de tn= * tu Ag = 10:9)150) (11.02) _= 495.9 Kiss

4. Fracture in the Net section in An= Agon(dent = 1102- 14) 11 (0.487) 9.072 in 2 Connection hength in Loading direction Lagu - UF E=0.9 [ for web connection] Effective Area Ae= Uan = 10:9) ( 9.072) =8165 in Design Strength of Net section - Ot Tn = ø fou te = 10:75)165)(8:165) = 398 kips siiBleck Shear:- Gross section of shear Agv = 4 [ Length (a-b)] It) = 4(11) 10.487) = 20.454 in² Nel section of shear Anu= 4 [ Length (arb) ... -[(m-1)+o-s]delit) = 4 [11-13.5)(1)(0.487) = 13.636 inz

Gross section of Tension Agt = ax l length (6-2)]xt 214)(0.487) Net = 3.896 in? section of tension Ant = 2x [length (b-c)-In-der) 32x[4-119613] (0.487) = 2.922 in² Tere, o.6 fu Anu = 0.6 165)113.636) = 531.8 kips O tu Ant = 65|2.92) = 189.93 kips t o.c fu Anu>fu Ant shear fracture - Tension yielding Constrols , Design rupture Strength & Ros = 0[obtu Anut ty Agt ] =(075) 531-8 + (50) (3.896)] = 545 kips :. Design strength of Member - Min {495.9, 398, 545} . = 398 kips 8) Design Strength of Bolto: Fub = woksi lie, Tensile Strength of both 2 = 0.6013 in 2

d Design strength of bolt in shear, Ørn's (0.175):10.5) (Fub) mA = 10:75).10.5) (120) 14) 10.6013) - 54.12 kips & Design Strength of bott in bearing ho = 1.5 in? 1.5 db ? ah b , checks SE3" > 3db 1 * Design bearing strength / bolt, I O Rom + Ø (zuitu dt] ili -10:75)(204) 165) (0.875) = 49.857 kips * Design strength of both = min $49.857,54:12} = 49.857 kips | : Total design strength of botted Connectico 110 In = 8(49.857) = 398.85 kips c) Block shear strength of Gusset plate Plate thickness t= 3 = 0.375 in of shear, . Agt = 2 [hength (a-b)] It) = 2(11) 10:375) = 8.25 in? of shena Anvar [hength (a-b) - {m-1) +0.5] dh} xt 152 [11 - 3.5.113] (0.375) Gross section Net section 5.625 in?

I Gross section .. of Tension Agt = [hength (b-1)]xt = (4)(0.375) = 1.5 in z Ant = [hength (6-1)-(n-1) doh] H) --[4-(1911]0-375) = 1:125 in? lol tu Anu= (0.6) (58) 15.625) = 195-75 kips I tu Ant = 15) (113) = 65.25kips 1.0.6 tu Any > fu Ant - :. Design Rupture strength, ORbs & 0[ortu And & ty Agt ] .. =10.75)/195.75+ (36) 19.5)3 on =187.kips .. ... Design Strength of connection .....=alin { Design Strength of channel, botts & gusset plate } = min { 398, 398.85, 187.33 .., 3187.3 kips. ". ERVEREN :. Marimim factored had applicable Pric 7-8kp!

1 fiz 58 Isi : Type 'B' ' stul groole. A 36. . For Az6 steel, - ty = 36 ksi, tu= 58 ksi, bott dia do= 2 elia of bott hole dp = + = 0.875 in. A) Design Strength of Channel i vilding in gross section Hi Tha & ty Ag 10.4)186)(11.02) = 357 Kips Fracture in Net section An-11.02- 4) 10.875) 10.487) =9.316 in? . I de = u An 10.9019.316) = 8.384 in z Design strength of Net section & ft fu de i 10.75)158) (8.389) 5364,7 kips u Block shear :- - Agr = 4 [hength (a-b)]xt = 4(11)/0,487) =20.454 in2 - daz to

Any = 4 [hength la-b) – (m-1)+0:5 )ek} lt') = 4111- 13.5) 10.87597 *0.487 - 14.488 in2 Similarly, Agr - 214010487) - 3.896 in 2 Ant = 2/4 - 0110875)] 20487). . 3 3.044 inz 06 fu Any = 10-6)(58) (14,488)= 504.18 Kips fu Ant = (58)(3:04) = 176:55 tips *0.6 fu Anu> fu ant Design Rupture strength, o Ritm = 10.75) 50418+ (367/8-892)] . = 483-3 kips ... Design strength of Member = Min (357, 364.7, 483-33 : = 357 kips B, Design Strength of bolto: Ful a 150ksi. Ab = 1 1 1 1 a ² = 0.4418102

i Design shear strength / bolt = 10.75) (015) (150) (4) (0.4498) = 49-7 kips | Design bearing strength=${24 fude] =1075) (2.4) (58)[0'75) (0.487) = 38.132 kips | Design strength of bott, ØR,= 38.132 kips a Derign strength of botted Connection 618)188132) 3) Block shear a 305.06 Kips strength of Gusset plate den = 3 + 1/2 = 0.875 in Agr = 2(11) 10-395) = 8:25 in? Any = 2111- 13.5) 10.875)] 0.375 = 5-953in Age = 4/8.375) = 1.5 inz Ant = [4 - 1910875)] (0.375) = 1.172 in- osta Anv=106) (58)/5-453) = 207 16 kips tu Ant = (58)(NY) = 67.98 kips - 70.6 tu Anu> fu ant " Design Rupture Strength =1075)/207.16 (31) (15

=195-9 kips : Design strength of Connection Min{®, ® ©} =195-9 kips ... Maximum factored hood Pu=195.9k
All 3 checks are performed.