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 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) = 0.057 (1m strip: b=1000mm)

y = 0.5 + √0.25 − 𝑘/0.9 = 0.93

Max Sagging Moment

Additional Sagging Moment


z = y x deff = 422mm 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:


2 x fcu) = 0.013 (1m strip: b=1000mm)

y = 0.5 + √0.25 − 𝑘/0.9 = 0.985 Adopt y = 0.95

z = y x deff = 431mm 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 @ 200 Y20 @ 200

Y20 @ 200 Y20 @ 200 Y20 @ 200

Y20 @ 100

Y20 @ 200 Y20 @ 200 Y20 @ 200

Y20 @ 200 Y20 @ 200

Y20 @ 200 Y20 @ 200 Y20 @ 200

Y20 @ 100


1.3.3 Top Reinforcing – T1 & T2

Y12 @ 250 Y12 @ 250 Y12 @ 250

Y12 @ 250 Y12 @ 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 fcu = 20Mpa; fy = 450Mpa cover = 30mm Thickness of the beam: 500mm Assumed diameter of reinforcement: d = 20mm

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 k = Mmax / (b x deff

2 x fcu) = 0.008 (1m strip: b=1000mm)

y = 0.5 + √0.25 − 𝑘/0.9 = 0.99 Adopt y = 0.95


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) for the calculation of the moments.

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




2 x fcu) = 0.014 (1m strip: b=1000mm)

y = 0.5 + √0.25 − 𝑘/0.9 = 0.98 Adopt y = 0.95


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) for the calculation of the moments.

Hogging Moments form here due to the dominant upward load of the 3 columns (caused by dominant

wind force.




2 x fcu) = 0.005 (1m strip: b=1000mm)

y = 0.5 + √0.25 − 𝑘/0.9 = 0.99 Adopt y = 0.95


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 = 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

16

0m

m


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 sides) and then bolted to beam 1.


*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

3 Bolts in a row

90 x 90 x 8 Angles





V M



V = 50.5 kN

Axial: P = 3.11 kN

M = 0 kNm (beam 2 pinned to beam 1)



50

50

80

80

50 40




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 there are 2 cleats (on either side of beam 2’s web) 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


P

16

0m

m

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) 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 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 sides) and then bolted to beam 1.

Beam 2

Beam 1

V M



V = 260 kN

Axial: P = 39 kN

M = 112.73 kNm

Beam 2

Beam 1



M20 Bolts

4 Bolts in a row

90 x 90 x 8 Angles


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 = 0.9 Øbr = 0.67 n = 4 a = 40

fu = 450 x 10-3 t = 8 mm Ln = 300 – (4x22) = 212 mm


M = 112.73 kNm

Top 2 bolts is in Tension

Bottom 2 bolts is in Compression

21

0m

m

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 there are 2 cleats (on either side of beam 2’s web) 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


3.4 Detail 4 (Pinned 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.





connection






V 33.57 kN


M = 151.43 kNm

V M

P


3.4.2 End Plate Design



M20 Bolts

3 Bolts in a row

12mm End Plate

End Plate dimensions as follows:

See attached excell sheet for end plate calculations.

V M



V = 226.42 kN

Axial: P = 38.33 kN

M = 0 kNm (pinned connection)



50 50

50

100

100

50

150


3.5 Detail 5 (Pinned Connection) 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

2 Bolts in a row

10mm End Plate

End Plate dimensions as follows:

See attached excell sheet for end plate calculations.

Beam 1 (Horizontal Member)


V M

P

FORCES & MOMENT IN BEAM 2


V = 0.3 kN

Axial: P = 52 kN

M = 0.65 kNm



50

150

50

40 40 70

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

foundation reinforcement calcs & connection calcs

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