Foundation Reinforcement Calcs & Connection Calcs

W01.JNB.000682 Gokwe Water Tank
1 BENDING REINFORCEMENT CALCULATION
1.1 Moment diagram giving Max Sagging Moment:
See Elastic Beam design calculations Strip A (DL + LL)
1.1.1 Required reinforcement area for Max Sagging Moment:
Mmax = 416.1 kNm
fcu = 20Mpa; fy = 450Mpa
cover = 30mm
Thickness of the beam: 500mm
Assumed diameter of reinforcement: d = 32mm
deff = 500 – 30 – 32/2 = 454mm
k = Mmax / (b x deff
2
x fcu) = 0.1  (1m strip: b=1000mm)
y = 0.5 + √0.25 − 𝑘/0.9 = 0.87
z = y x deff = 395mm
As = Mmax / (0.87 x fy x z) = 2691 mm2
/m
Adopt Y25 @175mm c/c: As = 2810 mm2
/m’
1.1.2 Required reinforcement area for Additional Sagging Moment:
Mmax = 235 kNm
cover = 30mm
deff = 500 – 30 – 32/2 = 454mm
2
x fcu) = 0.057  (1m strip: b=1000mm)
y = 0.5 + √0.25 − 𝑘/0.9 = 0.93
Max Sagging Moment
Additional Sagging
Moment

As = Mmax / (0.87 x fy x z) = 1422 mm2
/m
Adopt Y20 @200mm c/c: As = 1570 mm2
/m
1.2 Moment diagram giving Max Hogging Moment:
See Elastic Beam design calculations Strip C (DL + WL)
1.2.1 Required reinforcement area for Max Hogging Moment:
Mmax = 52.82 kNm
cover = 30mm
deff = 500 – 30 – 32/2 = 454mm
2
x fcu) = 0.013  (1m strip: b=1000mm)
y = 0.5 + √0.25 − 𝑘/0.9 = 0.985  Adopt y = 0.95
As = Mmax / (0.87 x fy x z) = 313 mm2
/m
Adopt Y12 @ 250mm c/c: As = 452 mm2
/m
Max Hogging Moment

1.3 Reinforcement sketch
1.3.1 Bottom Reinforcing – B1
1.3.2 Bottom Reinforcing – B2
Y20 @ 200 Y20 @ 200 Y20 @ 200
Y20 @ 200Y20 @ 200
Y20 @ 200 Y20 @ 200 Y20 @ 200
Y20 @ 100
Y20 @ 200 Y20 @ 200 Y20 @ 200
Y20 @ 200Y20 @ 200
Y20 @ 200 Y20 @ 200 Y20 @ 200
Y20 @ 100

1.3.3 Top Reinforcing – T1 & T2
Y12 @ 250 Y12 @ 250 Y12 @ 250
Y12 @ 250Y12 @ 250
Y12 @ 250 Y12 @ 250 Y12 @ 250
Y12 @ 250

2 UPLIFT OF FOUNDATION DUE TO COLUMN & SOIL LOADING FROM
ABOVE
2.1 Strip A (1m Strip width)
2.1.1 Uniformly Distributed Load from Column & Soil
From the reactions output (pg 1 of the foundation design): F = 361.8 kN + 489 kN + 361.8 kN = 1212.6 kN
Length of strip A: L = 10 mm
Thus the uniformly distributed load from the 3 columns located on Strip A: UDLstrip A = F/L = 121.3 kN/m
The uniformly distributed load from the 0.5m layer soil ontop of the foundation: UDLsoil = 18 x 1 x 0.5 = 9 kN/m
2.1.2 Moment Diagram giving Max Hogging Moment
Refer to the Elastic Beam Design for Strip A: Uplift due to Column & Soil Loads from the Top (no soil underneath)
for the calculation of the moments.
2.1.3 Required reinforcement area for Hogging Moment:
Mmax = 33.55 kNm
cover = 30mm
Hogging Moments
form here due to
downward load of the 3
columns and the 0.5m
layer soil on top of the
foundation
Hogging
Moments

deff = 500 – 30 – 20/2 = 460mm
2
x fcu) = 0.008  (1m strip: b=1000mm)
y = 0.5 + √0.25 − 𝑘/0.9 = 0.99  Adopt y = 0.95
As = Mmax / (0.87 x fy x z) = 196 mm2
/m
/m
2.2 Strip B (1m Strip width)
From the reactions output (pg 1 of the foundation design): F = 375.8 kN + 489 kN + 375.8 kN = 1240.6 kN
Thus the uniformly distributed load from the 3 columns located on Strip A: UDLstrip A = F/L = 103.4 kN/m
The uniformly distributed self-weight of the foundation slab = UDLself = 25 x 1 x 0.5 = 12.5 kN/m
Refer to the Elastic Beam Design for Strip B: Uplift due to Column & Soil Loads from the Top (no soil underneath)
Hogging Moments
form here due to
downward load of the 3
columns and the 0.5m
layer soil on top of the
foundation
Hogging
Moments

Mmax = 59.6 kNm
cover = 30mm
deff = 500 – 30 – 20/2 = 460mm
2
x fcu) = 0.014  (1m strip: b=1000mm)
y = 0.5 + √0.25 − 𝑘/0.9 = 0.98  Adopt y = 0.95
As = Mmax / (0.87 x fy x z) = 325 mm2
/m
/m
2.3 Strip C (1m Strip width)
From the reactions output (pg 1 of the foundation design): F = -77.3 kN +(-87.6) kN + (-77.3) kN = -242.2 kN
Thus the uniformly distributed load from the 3 columns located on Strip A: UDLstrip A = F/L = -20.2 kN/m
Refer to the Elastic Beam Design for Strip C: Uplift due to Column & Soil Loads from the Top (no soil underneath)
Hogging Moments
form here due to the
dominant upward load
of the 3 columns
(caused by dominant
wind force.

Mmax = 22.4 kNm
cover = 30mm
deff = 500 – 30 – 20/2 = 460mm
2
x fcu) = 0.005  (1m strip: b=1000mm)
y = 0.5 + √0.25 − 𝑘/0.9 = 0.99  Adopt y = 0.95
As = Mmax / (0.87 x fy x z) = 131 mm2
/m
/m
 Thus Y12 @ 250mm c/c will be sufficient
Hogging
Moments

3 CONNECTION DESIGN
3.1 Detail 1 (Fixed Connection)
Beam 1 lies on top of the column (connected to the column with a column end plate) and beam 2 (notched)
connects into beam 1. Beams 3 & 4 will then be welded to the column.
3.1.1 Column End Plate
 The axial load of the beam  shear force in the connection
 The axial load in the column  axial load in the connection
 The moment in the beam or column (the biggest one in order to be conservative)  the moment in the
connection
See Attached beam-col connection design done in Prokon.
Beam 2 (Supported Beam)
Beam 1 (Supporting Beam)
Beam 3 & 4 (Walkway Supporting Beams)
FORCES & MOMENT IN THE CONNECTION:
 V = 21.8 kN
 Axial: P = 164.7 kN (Compression)
 M = 38.5 kNm
V
M
P

3.1.2 Top Plate (to make the connection a fixed connection)
Detail 1 requires to be a fixed connection hence a top plate needs to be bolted to the top flanges of beam 1 and
beam 2 in order to fix the beam to beam connection. The concept shown below will be used for the top plate
design. A normal beam-col connection will be done in Prokon and the plate thickness and bolt sizes obtained
from that design will be used for the top plate thickness and bolt specs.
See the attached beam-col connection design for the calculation of the top plate thickness and bolt size.
3.1.3 Cleat Design
Beam 2 will notched at the top and bottom in order to fit into beam 1. Beam 2 will be bolted to an angle (both
sides) and then bolted to beam 1.
Beam 2
Beam 1
V
M
P
FORCES & MOMENT IN BEAM 2
(see beam element end forces table for connection 1)
 V = 71.23 kN
 Axial: P = 13.34 kN
 M = 39.77 kNm
Beam 2
Beam 1

The following assumptions were made:
 M16 Bolts
 3 Bolts in a row
 90 x 90 x 8 Angles
 Cleat dimensions as follows:
Shear and Bearing Resistance of Bolts in Supported Beam
 Vr = 0.6ØnmAb0.7fuvr = 170 kN > V = 71.23 kN OK
 Br = 3Øtwdboltnfubr = 299 kN > V = 71.23 kN OK
Shear and Bearing Resistance of Bolts in Supporting Beam
Shear and Bearing Resistance of Angle Cleats (2 angle cleats)
 Vr = 2(0.5ØLntfu) = 473 kN > V = 71.23 kN OK
 Br = Øtnafu = 289 kN > V = 71.23 kN OK
Tension in Bolts of Supported Beam
50
50
80
80
50 40
Øvr bolt = 0.8
Øbr bolt = 0.67
n = 3
m = 2
Ab = 201 mm2
fuvr = 420 x 10-3
tw = 6.9 mm
dbolt = 16 mm
fubr = 450 x 10-3
Øvr bolt = 0.8
Øbr bolt = 0.67
n = 6
m = 1
Ab = 201 mm2
fuvr = 420 x 10-3
tw = 6.9 mm
dbolt = 16 mm
fubr = 450 x 10-3
Øvr = 0.9
Øbr = 0.67
n = 3
a = 40
fu = 450 x 10-3
t = 8 mm
Ln = 200 – (3x18) = 146 mm
Øb = 0.8
Ab = 201
fu = 800 x 10-3
(Grade 8.8 Bolts
M = 39.77 kNm
Top bolt is in Tension
Bottom bolt is in Compression
160mm

T = C = M/distance between top bolt and bottom bolt from the centre
T = C = 39.77 / 0.08m = 497 kN
Tu = P + T = 13.34 + 497 = 510.5 kN
there are 2 cleats (on either side of beam 2’s web)
Thus: Tu = 510.5 / 2 = 255 kN
Tr = 2(0.75ØbAbfu) = 192 kN < Tu = 255 kN NOT OK
Tr = 301 kN (with M20 bolts) > Tu = 255 kN OK
Combined Shear and Tension of Bolts
Vu / Vr + Tu / Tr = (71.23 / 170) + (255 / 301) = 1.27 < 1.4 OK
Tension and Shear Block Failure of Cleat
Tr + Vr = ØAntfu + 0.6ØAnvfy = 506 kN > Tu = 255 kN OK
Use M20 Bolts
Ø = 0.9
fu = 450 x 10-3
fy = 300 x 10-3
Ant = (160 – 1x18)(8) = 1136 mm2
Agv = (40)(8) = 320 mm2
Anv = (40 – 0.25(18))(8) = 284 mm2
Thus Use M20 Bolts for Detail 1: Cleat Connection

3.2 Detail 2 (Pinned Connection)
Beam 1 lies on top of the column (connected to the column with a column end plate) and beam 2 (notched top
and bottom) connects into beam 1. Beam 3 will then be welded to the column or to beam 2.
connection
Beam 3 (Walkway Supporting Beams)
 V = 33.78 kN
 M = 76 kNm
V
M
P

3.2.2 Cleat Design
Beam 2 will notched at the top and bottom in order to fit into beam 1. Beam 2 will be bolted to an angle (both
*Note: the same bolt sizes, bolts in a row and cleat dimensions were chosen on order to keep all the cleat
connections uniform so as to simplify operations on site.
 M16 Bolts
V
M
P
 V = 50.5 kN
 Axial: P = 3.11 kN
 M = 0 kNm (beam 2 pinned to beam 1)
50
50
80
80
50 40
Øvr bolt = 0.8
Øbr bolt = 0.67
n = 3
m = 2
Ab = 201 mm2
fuvr = 420 x 10-3
tw = 6.9 mm
dbolt = 16 mm
fubr = 450 x 10-3
Øvr bolt = 0.8
Øbr bolt = 0.67
n = 6
m = 1
Ab = 201 mm2
fuvr = 420 x 10-3
tw = 8 mm
dbolt = 16 mm
fubr = 450 x 10-3

 Vr = 2(0.5ØLntfu) = 473 kN > V = 50.5 kN OK
 Br = Øtnafu = 289 kN > V = 50.5 kN OK
Tu = P = 3.11 kN
Thus: Tu = 3.11 / 2 = 1.56 kN
Tr = 2(0.75ØbAbfu) = 192 kN < Tu = 1.56 kN OK
Vu / Vr + Tu / Tr = (50.5 / 170) + (1.56 / 192) = 0.31 < 1.4 OK
Øvr = 0.9
Øbr = 0.67
n = 3
a = 40
fu = 450 x 10-3
t = 8 mm
Ln = 200 – (3x18) = 146 mm
Øb = 0.8
Ab = 201
fu = 800 x 10-3
(Grade 8.8 Bolts
P
160mm
Ø = 0.9
fu = 450 x 10-3
fy = 300 x 10-3
Ant = (160 – 1x18)(8) = 1136 mm2
Agv = (40)(8) = 320 mm2
Anv = (40 – 0.25(18))(8) = 284 mm2

3.3 Detail 3 (Fixed Connection)
connects into beam 1. Beams 3 will then be welded to the column or beam 2.
connection
Beam 3 (Walkway Supporting Beam)
 V = 12.6 kN
 Axial: P = 508 kN (Compression)
 M = 74.6 kNm
V
M
P

3.3.2 Top/Splice Plate (to make the connection a fixed connection)
Detail 3 requires to be a fixed connection hence a top plate needs to be bolted to the top flanges of beam 1 and
beam 2 in order to fix the beam to beam connection. The concept shown below will be used for the top plate
design. A normal beam-col connection will be done in Prokon and the plate thickness and bolt sizes obtained
from that design will be used for the top plate thickness and bolt specs.
See the attached beam-col connection design for the calculation of the top plate thickness and bolt size.
3.3.3 Cleat Design
Beam 2 will be notched at the top and bottom in order to fit into beam 1. Beam 2 will be bolted to an angle (both
Beam 2
Beam 1
V
M
P
 V = 260 kN
 Axial: P = 39 kN
 M = 112.73 kNm
Beam 2
Beam 1

 M20 Bolts
 Vr = 0.6ØnmAb0.7fuvr = 354.5 kN > V = 260 kN OK
 Br = 3Øtwdboltnfubr = 578 kN > V = 260 kN OK
 Vr = 0.6ØnmAb0.7fuvr = 354.5 kN > V = 260 kN OK
 Br = 3Øtwdboltnfubr = 1157 kN > V = 260 kN OK
 Vr = 2(0.5ØLntfu) = 686.9 kN > V = 260 kN OK
 Br = Øtnafu = 385.9 kN > V = 260 kN OK
45
70
70
70
50 40
Øvr bolt = 0.8
Øbr bolt = 0.67
n = 4
m = 2
Ab = 314 mm2
fuvr = 420 x 10-3
tw = 8 mm
dbolt = 20 mm
fubr = 450 x 10-3
Øvr bolt = 0.8
Øbr bolt = 0.67
n = 8
m = 1
Ab = 314 mm2
fuvr = 420 x 10-3
tw = 8 mm
dbolt = 20 mm
fubr = 450 x 10-3
Øvr = 0.9
Øbr = 0.67
n = 4
a = 40
fu = 450 x 10-3
t = 8 mm
Ln = 300 – (4x22) = 212 mm
Øb = 0.8
Ab = 314
fu = 800 x 10-3
(Grade 8.8 Bolts
M = 112.73 kNm
Top 2 bolts is in Tension
Bottom 2 bolts is in Compression
210mm
45

T = C = M/distance between top bolt and bottom bolt from the centre
T = C = 112.73 / 0.105m = 1073.6 kN per bolt and 2 bolts per cleat are in tension
T = C = 1073.6 / 2 = 536.8 kN
Tu = P + T = 39 + 536.8 = 575.8 kN
Thus: Tu = 575.8 / 2 = 288 kN
Tr = 2(0.75ØbAbfu) = kN < Tu = 301 kN OK
Vu / Vr + Tu / Tr = (260 / 345.5) + (288 / 301) = 1.7 < 1.4 NOT OK  Please advise what to do
Ø = 0.9
fu = 450 x 10-3
fy = 300 x 10-3
Ant = (210 – 1.5x22)(8) = 1416 mm2
Agv = (40)(8) = 320 mm2
Anv = (40 – 0.25(22))(8) = 276 mm2

connects into beam 1.
connection
 V 33.57 kN
 M = 151.43 kNm
V
M
P

3.4.2 End Plate Design
 M20 Bolts
 12mm End Plate
 End Plate dimensions as follows:
See attached excell sheet for end plate calculations.
V
M
P
 V = 226.42 kN
 Axial: P = 38.33 kN
 M = 0 kNm (pinned connection)
50 50
50
100
100
50
150

Beam 1 land beam 2 (horizontal members) will be welded to and end plate and bolted to the column web and
flanges respectively.
3.5.1 End Plate Design
 M16 Bolts
 10mm End Plate
 End Plate dimensions as follows:
See attached excell sheet for end plate calculations.
Beam 1 (Horizontal Member)
V M
P
 V = 0.3 kN
 Axial: P = 52 kN
 M = 0.65 kNm
50
150
50
40 4070
End Plate

3.6 Detail 5 (Weld Check)
Beam 2 (walkway supporting beam) will be fully welded to beam 1 (secondary beam).
3.6.1 Weld Check
See attached excell sheet for weld check.
Beam 1 (Secondary Beam)
Beam 2 (Walkway Supporting Beam)

3.7 Detail 6 (Corner Connection of Channels (walkway ringbeam))
PC 230 x 90 Channels
80 x 80 x 6 Angle
2 x M12 Bolts

3.8 Detail 7 (Walkway Supporting Beams)
Beam 1 (secondary beams), beam 2 (secondary 2 beams) and beam 3 (primary beam) are all flush at the top.
The walkway supporting beams are not flush with beam 1, beam 2 and beam 3. Spacers will be used in order to
obtain an equal level for the mentis grid at the top.
Walkway
Supporting Beams
Primary Beam
Secondary 2
Beams
Secondary Beams

3.9 Detail 8 (Mentis Grid Detail)
RS40 Rectagrid with 30x4.5 Nominal Bearer Bar Size

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