This document summarizes the design of a steel connection using bolts to transmit loads through a C10x30 channel to a 1-inch thick gusset plate. It determines that 12 3/4-inch A325 bolts in a bearing connection are required. It also checks that the bolts and the channel web and gusset plate meet bearing capacity requirements, with factors of safety above the 320 kip total load. Optimization of the bolt layout confirms bearing capacities of 717 kips for the channel and 533 kips for the gusset plate, sufficient for the load.

1. Steel Structure
Numerical
By
Engineer
Tayyeb Ullah Azhar

2. Design problem (ASD Method)
Determine the number of bolts required and
an appropriate layout to transmit a DL of 80
kips and a LL of 240 kips through 2c10*30
To a 1 inch gusset plate. All material is A-36
Bolts are ¾ inch A 325 bolts in a bearing
type connection with thread exclude from
the shear plans use 3 lines of bolts a cross
the Web of the channel.

3. C10x30
Ag = 8.82
Tw = 0.673 inch
gusset plate thick = 1 inch

4. Step = 01 Design Force
DL+LL
80+240=320 kips
Step = 02 Shear Design of bolts
Allowable stress= FV=30 ksi
Ab=Πd2
/4
3.14(0.75)2
/4
Ab=0.4418 In2

5. Shear Capacity of A single bolt
Fv x 2Ab =30x2x0.4418=26.50 kips shear
No of bolts=
Design Force/capacity of single bolt in
shear
320/26.50 = 12.1
Use 12 bolts
Step = 03 Bearing Design
Allowable Bearing Stress on connected
material
For A-36
Fy=36 ksi Fu=58 to 81 ksi
1.2 Fu= 1.2x58 = 69.6 ksi

6.  Le≥1.5db=1.5(3/4) =1.13in
 L>3db=3(3/4) =2.25 in
 Le min for ¾ bolt=1.25in
Governing Value
 Le=1.25 in
Bearing Area = DxT
Bearing Capacity per single bearing
surface=(1.2FU)(Dt)

7. Bearing Stress
Channel(tw=0.673)web
Bearing capacity per single bearing surface
(1.2Fu)(Dt)
1.2x58x3/4x0.673=35.13 kips
For 24 bearing surface
Total Bearing capacity
24x35.13 = 843 kips
843 > 320 kips
ok

8. Gusset plate (tg=1in)
Bearing capacity per single Bearing Surface
1.2FuDt
1.2x58x3/4x1 = 52.2 kips
For 12 Bearing Surface
Total Bearing capacity
12x52.2kips=626 kips
626kips >320 kips
ok

9. Step=04 Optimization
 Le min =1.25 inches
 L=2.0 inches
Le=2P/Fut
L=(2P/Fut)+dh/2

10.  Channel (t=0.673)
Le=2P/Fut
1.25=2P/58x0.673=24.4 kips
L=(2P/Fut)+dh/2
2.0=(2P/58x0.673)+(3/4)/2=31.37 kips
Total Bearing Capacity
2(3x24.4+31.7x9)=717 kips
717kips > 320 kips
ok

11.  Gusset Plate (t = 1in)
Le=2P/Fut
1.25=2P/58x1=36.25 kips
L=(2P/Fut)+dh/2
2.0=(2P/58x1)+(3/4)/2=47.13 kips
Total Bearing Capacity
3x36.35+9x47.13)=533 kips
533kips > 320 kips
ok