Rafter to column top connection design
Given data:
Pu = 10Kips
=0.315in
Throut = W(0.707)
Tube 6x3x0.315
A = 5.6in2
Analysis data:
Rn = 0.75 x 0.707 x W x 0.6Fexx (1.066)
Rn = 0.75 x 0.707 x 10/25 x 0.6 x 60 x 1.066 = 8.1 Kips/in
Shear yield strength of rafter boxes.
Rn = x (0.6Fy) x t
>>> Rn = 1 x 0.6 x 36 x 0.315 = 6.8Kips/in.control.
Shear rupture strength of rafter boxes
Rn = x (0.6Fu) x t
>>> Rn = 0.75 x 0.6 x 58 x 0.315 = 8.22Kips/in
Weld length
Lw = 10/6.8 = 1.5in or 0.75in in each side of tube connection ( rafter) with top plate .but provided weld
sizes in drawing fillet 10mm with total length = 6.8cm
Design of bolts for top plate and column connection:
Combined shear and tension
1- selected bolt type bolt A325-N diameter in ~ 20mm
2- Taken the moment force ,shear force and axial force from ETABS program .
Tu = 10 Sin17 = 3kips
Vu =10 Cos 17 = 9.6kips
The tension force one bolt Tu = 3/4 = 0.75kips/bolt
there are 4 bolt in connection which:
and
the shear force
Vu = 9.6/4 = 2.4 kips/bolt
Using table (J3.5 LRFD) and table 4.14.1 steel structure design behavior computing the tensile capacity of
bolts for bearing type connections.
[
[
[
Therefore the 4 bolts with dia(20mm) are conservatively ok for bearing type connection.
Check top plates connection for applied load:
Finally the selected bolt and plate are more conservative for structure
ROOF FASTENERS CALCUALTION:
Calculation for attachment of GI sheet to purlin
Rn = nominal resistance (strength) of one screw
= resistance factor, 0.75 for fracture in tension, shear on high-strength screw,
and bearing of screw against side of hole.
m = the number of shear planes participating (double shear = 2).
Ab = gross cross sectional area across the unthreaded shank of the screw.
Fu = tensile strength of the screw material (827.37 MPa for screw).
The fasteners spacing is 570mm in longitudinal direction and 300mm in transvers direction.
Assume wind pressure Conservatively 100kg/m2
and
effective area for each screw is
(0.57*0.3)=0.171m2
since the wind force for each screw =100*0.171=17.1 kg
Which uplift force = 0.1KN/screw and shear force = 0.16 KN/screw
Assumed screw diameter = 12mm Ab=113mm2 Fu =827.37 MPa
Design Tension Strength:
Rn = 0.75(0.75 Fu)Ab
Rn = 0.75 (0.75*827.37)*113/1000 =52.58
Rn = 52.58KN/Screw
>
0.1KN/screw ok against uplifting force
Design shear strength-No threads in shear planes:
Rn = 0.75(0.5 Fu)mAb
Rn = 0.75(0.5*827.37)*2*113/1000 =70
Rn = 70 KN/Screw > 0.16KN/screw ok against shear force
Design shear strength- Threads in shear planes:
Rn = 0.75(0.40 Fu)mAb
Rn = 0.75 (0.4*827.37)*2*113/1000 = 56.1KN/Screw
Rn = 56.1 KN/Screw > 0.16KN/screw ok against shear force
Base plate design:
Tube Base Plate Design Based on AISC Manual 13th Edition (AISC 360-05)
INPUT DATA & DESIGN SUMMARY
AXIAL LOAD OF COMPRESSION
Pa =
12.13
STEEL PLATE YIELD STRESS
Fy =
36
kips, ASD
ksi
CONCRETE STRENGTH
COLUMN SIZE
BASE PLATE SIZE
fc' =
4
ksi
HSS6X6X5/16
=>
HSS6X6X5/16
N =
13.4
in
B =
13.4
in
2
AREA OF CONCRETE SUPPORT
A2 =
1156 in
(geometrically similar to and concentric with the loaded area.)
USE
13.4
x
13.4
3/8 in thick plate
ANALYSIS
CHECK BEARING PRESSURE (AISC 360-05 J8)
P p / Wc
Where
MIN 0.85MAX A2 , 1 , 1.7
Wc
A1
f 'c A1
A1
180
Wc
2.50
488.40 kips
in2, actual area of base plate.
DETERMINE VALUES OF m, n, n', X , and l (AISC 13th Page 14-5)
m = 0.5 (N - 0.95 d) =
3.85
in
n = 0.5 (B - 0.95 b ) =
3.85
in
n' = 0.25 (d b ) 0.5 =
1.50
in
4db
W c P a , 1
0.02
X MIN
d b 2 P p
2 X
l MIN
, 1
1 1 X
Where
d
b
0.16
=
=
6.00
6.00
in, depth of column section.
in, width of column section.
DETERMINE REQUIRED THICKNESS OF BASE PLATE (AISC 13th Page 14-6)
t min l
Where
3.33P a
F yBN
0.30
in
l = MAX ( m, n, l n' ) =
3.85
in
>
Pa
[Satisfactory]
Design of Anchor rods:
Data INPUT:
Maximum Total Factored Loads:
Tension ( Nua_total ) =
Maximum Shear in X-Direction ( Vx ) =
12 kip
2.66 kip
Assupmtions:
1- Tension Force is distributed equally on all anchors
2- No sleeve is used for anchors
3- Shear force is assumed to be carried by 4 anchor rods
Note: All formulas used in this calculation referred to ACI318-08
Pier / Concrete Data:
Compresive Strength of Concrete (fc ) =
Concrete Height ( H ) =
Concrete Cover (C) =
Side Cover (SC) =
Width of pier (b1) =
Length of pier (b2) =
Anchor Dist. From edge of pier(Wid) C1 =
Anchor Dist. From edge of pier(Len) C2 =
No. of Anchors Used =
Threads per in. =
Anchor Data:
Fy =
Fu =
Table2.1, ASTM A36, T for ductile steel=
Table2.1, ASTM A36, V for ductile steel=
Anchor Diameter (d0) =
Reinforcing Bars:
Fy =
Vertical (Reinforcing Bars) diameter db=
Shear Reinfrocing Bars diameter d(tie) =
Center-to-Center distance between anchors =
Determining the Size of Anchors:
Tension is Devided by No. of Anchors (Nua) =
Max. Shear Force Carried by 1 Anchor (X) (Vua)=
Max. Shear Force Carried by 1 Anchor (Y) =
Effe. Cross Section Area (Ase)= (pi/4)(d0 - (0.9743/nt))2=
Steel Strength of 1 Anchor in tension(Nsa) = Ase* Fu
Steel Strength of 1 Anchor in Shear(Vsa)=0.8*0.6*Ase*Fu
Note: Shear Strength of Anchors with grout pad must be
multiplied by 0.8
4000
38
3
3
18
18
10.24
10.24
4
12
psi
in
in
in
in
in
in
in
36
58
0.75
0.65
ksi
ksi
0.98
in
60
0.55118
0.3937
9
ksi
in
in
in =
=
=
5405 kg
1198 kg
kgf / cm2
mm
mm
mm
mm
mm
mm
mm
280
950
75
75
440
440
260
260
25 mm
4200
As(b) =
As(tie) =
220
kgf / cm
0.23848 in2
0.12167 in2
mm
4.8 kips
0.665 kips
0 kips
0.63417 in2
36.7817 kips
17.6552 kips
.According ACI-318R-08, Section RD.5.1.2
T * Nsa= 27.5863 kips > Nua Then OK
V * Vsa= 11.4759 kips > Vua Then OK
T * Nsa > Nua & V * Vsa > Vua.
According ACI-318R-08 App.D, Sec. D.4.1.1
Checking Interaction Equation: According to ACI318R-08,
Sec. D.7.3. (Nua / T * Nsa) + (Vua / V * Vsa) < 1.2
Minimum Effective Height of Anchor (Hef.) = 12 * d0
Flat to Flat Distance of Nuts =
Abrg = 0.855 * (flat to flat dist. of nuts) 2- (5/4) * (d0)2 =
0-p = 1 Assume the concrete cracks!
= 0.70 According Sec.D.4.4C
Pull Out Resistance of Anchor in Tension
(ACI318R-08, Sec. D.5.3.1) Npn = 0-p * 8 * Abrg * fc =
0.23195
< 1.2
Then OK Vua > 0.2 v * Vsa & Nua > 0.2 T * Nsa
Then Sec. D.7.3 Corresponds this Interaction Equation!
11.76 in
6.7 in
170 mm
37.0993 in2
According to ACI318R-08, Sec. D.5.3.6
1187.18 kips
*N pn = 831.024 kips >Nua.Then OK
Checking the Side - Face Blowout Resistance of Anchor in Tension:
According to Sec. D.5.4.1. & D.5.4.2.:
Following Figure illustrated for Defining the Notations & Abbreviations:
For One Single headed anchor with deep embedment to an edge (hef > 2.5 Ca1), the Nominal side-face blowout resistance is:
D.5.4.1.
hef =
Ca1 = C1=
2.5 Ca1 =
hef < 2.5 Ca1
20 in
10 in
25
.. Then no need to calculate the blowout resistance Nsb,
For Multiple headed anchor with deep embedment to an edge (hef > 2.5 Ca1), the Nominal side-face blowout resistance is:
.D.5.4.2
hef < 2.5 Ca1
.. Then no need to calculate the blowout resistance Nsbg,
Checking the minimum thickness requiremetns to preclude splitting failure:
According to ACI318R-08, Sec. D.8.1, D.8.2 & D.8.4:
3.92 in
Center-to-Center spacing between anchors is = 3.543307 in 90
mm
Thus: Anchor Spacing is OK
Minimun edge distance of anchors shall be based on minimun cover requirements for untourqued cast in anchors & 6d 0 for tourqued:
Edge Distance in DWGs =
10.24 in
=
135 mm
Min. Edge Distance (6 d0) =
5.88 in
= 149.352 mm
According Sec. D.8.2 ACI318R -08
Thus:
The Min. Edge Distance is OK
Minimun center -to- center spacing between anchors shall be 4d 0 for untourqued cast in anchors:
Checking concrete breakout strength of anchors in tension:
Nominal concrete breakout strenght for group of anchors in tension shall not exceed the following:
According to ACI-318-R-08, Section D.5.2.1., Equation D-5
In above formula the (e'N) is eccentricity, since we do not have eccentrical tensile loading, the tension load acted directly in center (e' N) =0
ec,N = 1
..According Section D.5.2.4
If Ca,min 1.5 hef then ed,N=1.0
Ca,min = C1 = C2 =
..According Section D.5.2.5
10 in
1.5 hef =
17.64 in
Ca,min > 1.5 hef
c,N = 1.25
..According Section D.5.2.6
If Ca,min Cac then cp,N=1.0
..According Section D.5.2.7, Equation D-12
Cac =4 hef=
..According Section D.8.6
47.04
Ca,min < Cac then cp,N= Ca,min / Cac
cp,N = Ca,min / Cac =
0.212585
Nb= Kc (f' c)0.5 (hef )1.5= 61214.206
Kc = 24
= 1.0
ANC =
..According Section D.5.2.7, Equation D-13
44.305 kips
..According Section D.5.2.2, Equation D-7
..According Section D.5.2.2
..According Section 8.6.1 of ACI-318R-08
..According Figure RD.5.2.1 of ACI-318R-08
987.424228 in
..According Figure RD.5.2.1 of ACI-318R-08
ANCO =
Ncb =
1244.6784 in
12.9045108 kips
Total Tension Must Not Exceed the (Ncb), Thus:
Concrete Breakout Strength is OK
Checking concrete breakout strength of anchors in Shear:
Nominal concrete breakout strenght for group of anchors in shear shall not exceed the following:
..According Section D.6.2.1 of ACI-318R-08
AVC =
393.216 in
AVCO =
471.8592 in
ec,V =
..According Figure RD.6.2.1 of ACI-318R-08
..According Section D.6.2.5 of ACI-318R-08
In above formula the (e'V) is eccentricity, since we do not have eccentrical tensile loading, the tension load acted directly in center (e' V) =0
..According Section D.6.2.6 of ACI-318R-08
ed,V =
c,v =
0.9
..According Section D.6.2.6 of ACI-318R-08
..According Section D.6.2.7 of ACI-318R-08
..According Section D.6.2.8 of ACI-318R-08
h,v =
0.63577553
..According Section D.6.2.8 of ACI-318R-08
..According Section D.6.2.2 of ACI-318R-08
le = hef
Vb =
23606.2639 lb
Vcbg =
11.2562137 kips
= 23.60626389
kips
Total Shear Must Not Exceed the (Vcbg), Thus:
Concrete Breakout Strength is OK
Checking concrete pryout strength of anchors in Shear:
For group of anchors the following corresponds:
..According Section D.6.3.1 of ACI-318R-08
Vcpg =
25.8090216 kips
..According Section D.6.3.1 of ACI-318R-08
Thus:
The shear force that we have is very lower than the pryout strength and we are in safe stage
