The center gusset plate is not critical, because its thickness (16cm) is more than the combined thickness of the two outer channel web (2x6=12cm).
(1) Solve maximum force, T
Assumed four (4) 2.5cm diameter A325-SC bolts are used
Shear Capacity
Using the AISC available shear in Table 7-3 (Group A):
ФRn = (34.6 kips/bolt)x4/2.2 = 62.91 tf 3x2.5cm
Channel C200x75 Material: ASTM A992
Double channel web thickness : 12cm total
Fu = 4.60 tf/cm^2
Fu = 4.6x2.2x2.54^2 = 65.29 ksi
Using the AISC available bearing in Table 7-4:
ФRn = (113 kips/bolt/in)x(12/25.4)x4/2.2 = 97.07 tf
(b) Based on edge distance of 5cm (2 inches approximately)
Using the AISC available bearing in Table 7-5:
ФRn = (85.9 kips/bolt/in)x(12/25.4)x4/2.2 = 73.79 tf
C200x75 Tension Capacity
Bolt hole diameter = 2.5+0.2 = 2.70 Cm
Ag = 2x[20x0.6+2x(7.5-0.6)x1.25] = 58.50 Cm^2
Ae = Anet U
The whole cross section sees tension, so the shear lag factor U = 1
Ae = [58.5-4x(0.6x2.7)]x1 = 52.02 Cm^2
Tds = ФFyAg = 0.9x3.5x58.5 = 184.28 tf
Tds = ФFuAe = 0.75x4.6x52.02 = 179.47 tf
Block Shear Rupture Capacity
Agt = 10x1.2 = 12.00
Agv = 2x(10+5)x1.2 = 36.00 Cm^2
Anv = 2x(10+5-1.5x2.7)x1.2 = 26.28 Cm^2
Ant = (10-2.7)x1.2 = 8.76 Cm^2
FuAnt = 4.6x8.76 = 40.30
0.6FuAnv = 0.6x4.6x26.28 = 72.53
Since 0.6FuAnv > FuAnt
ФRn = Ф(0.6FuAnv+UbsFuAnt)
Ubs = 1 when the tensile stress is uniform
ФRn = 0.75x(0.6x4.6x26.28+1x4.6x8.76) = 84.62 tf
ФRn = Ф(0.6FuAnv+UbsFyAgt)
ФRn = 0.75x(0.6x4.6x26.28+1x3.5x12) = 85.90 tf
The smallest ФRn from above, T = 62.91 tf
(2) Solve fillet weld size, w
Try 6mm minimum double fillet weld for 1.6cm thick gusset plate
Weld length = 35cm on each side
L/w = 350/6 = 58.33 < 100 O.K.
6mm double fillet weld capacity
ФRn = Ф(0.6xFEXX)[1+0.5x(Sinθ)^1.5](t)(L)
ФRn = 0.75x(0.6x4.9)x[1+0.5x(4/5)^1.5]x(2X0.6x0.707)x(35) = 88.90 tf > 62.91 tf O.K.