UTMOST CONSULTING Job no: 08 sheet no: 1/2 rev: 01

ENGINEERS UTM-PT 14/02/ 2021

consultation sheet RC BEAM DESIGN
JOB TITTLE: PROPOSED MIXED USE COMMERCIAL BUILDING AT Org. ref. STR/UTM-PT/14/02/2021
MUGUTHA, RUIRU KIAMBU COUNTY: PLOT 1/10246 made by MMM date: 14/11/21 chd FMG
1st, 2nd,3rdand 4th. floor typical beams Signature…………… Signature…………………….
COLUMN DESIGN
Fy 460N/mm2
Fcu 30N/mm2
Cover 25mm
H 450mm
B 200mm
References Calculations Output
DESIGN DATA
Imposed load=4 kN/m2
Finishes=0.75 kN/m2
Ceiling and services=0.8 kN/m2
Block work=2.5 kN/m2 at 2.75m height
Slab thickness=150mm
Beam size=300x600 mm
Column size=300x500 mm
Concrete grade=M30
Slab s/w=0.15x24=3.6 kN/m2
ROOF DESIGN DATA
Timber truss=1.0 kN/m2
Roof cover=0.67 kN/m2
Purlins=0.05 kN/m2
Ceiling and finishes=0.35 kN/m2
Batterns and felts=0.05 kN/m2
insulation =0.05 kN/m2

COLUMN PLAN
 COLUMN PLAN

UTMOST CONSULTING Job no: 08 sheet no: 1/2 rev: 01

ENGINEERS UTM-PT 14/02/ 2021
consultation sheet RC BEAM DESIGN
JOB TITTLE: PROPOSED MIXED USE COMMERCIAL BUILDING AT Org. ref. STR/UTM-PT/14/02/2021
MUGUTHA, RUIRU KIAMBU COUNTY: PLOT 1/10246 made by MMM date: 14/11/21 chd FMG
1st, 2nd,3rdand 4th. floor typical beams Signature…………… Signature…………………….
COLUMN DESIGN
Fy 460N/mm2
Fcu 30N/mm2
Cover 25mm
H 450mm
B 200mm
References Calculations Output
 Influence area= ( 4.352 ) x ( 2.989
2 )
=6.51m 2

AXIAL LOADING ON COLUMN C2

Roof
Roof cover, trusses, services (U.L.S) =(2.5x1.6)+(1.4x1.5)=6.1x6.51=39.72KN
Roof beam=0.3x0.45x24x3.67x1.4=16.65 KN
Floors
13.19 kN/m2x6.51x8=686.94 kN/m2
Beams
0.3x0.45x24x3.67x8x1.4=133.2kN/m2
Column(s/w)
0.3x0.5x3x24x8x1.4=120.96 kN/m2
Blockwork
0.2x2.75x20x3.67x7x1.4=395.63 kN
Total at foundation level=1393.1 kN
Factored load=947.15 kN
Unfactored load=995.1 kN
Allow for bending 30 %=1812
Column sizing
N=1812 kN
Fcu=30N/mm2
Ac=cross sectional area of column
Fy=characteristic strength of compression reinforcement
Asc=gross cross-sectional area of concrete
N=0.4Fcu +0.8 Fy. Asc
Consider, Asc=0.4% cross gross sectional area of concrete.
Ag=Asc+0.004Ag
Asc=1-0.004=0.996Ag
1812x1000=0.4x30x0.996Ag+0. 8Fy.Asc
1812 x10³=9.96Ag+14.72Ag
2812 X 100
Ag= =270.97X270.97
24.68
Minimum size of column =230x230mm allowed.
Take 300x500mm>230x230mm

Roof load on plan

UTMOST CONSULTING Job no: 08 sheet no: 1/2 rev: 01

ENGINEERS UTM-PT 14/02/ 2021
consultation sheet RC BEAM DESIGN
JOB TITTLE: PROPOSED MIXED USE COMMERCIAL BUILDING AT Org. ref. STR/UTM-PT/14/02/2021
MUGUTHA, RUIRU KIAMBU COUNTY: PLOT 1/10246 made by MMM date: 14/11/21 chd FMG
1st, 2nd,3rdand 4th. floor typical beams Signature…………… Signature…………………….
COLUMN DESIGN
Fy 460N/mm2
Fcu 30N/mm2
Cover 25mm
H 450mm
B 200mm
References Calculations Output
 Roof load on plan

Sectional view on X-X Axis

2.915 3.910
4TH FLOOR
1.0 G.K 1.4GK+1.6QK
1.4G.K+1.6QK 3RD FLOOR
1.0 g k
1.4G.K+1.6QK 1.4G.K+1.6QK 2ND FLOOR
3m 1.4G.K+1.6QK 1ST FLOOR
1.4G.K+1.6QK
3m 1.4G.K+1.6QK G FLOOR
1.4G.K+1.6QK
1.5m

FDN

UTMOST CONSULTING Job no: 08 sheet no: 1/2 rev: 01

ENGINEERS UTM-PT 14/02/ 2021
consultation sheet RC BEAM DESIGN
JOB TITTLE: PROPOSED MIXED USE COMMERCIAL BUILDING AT Org. ref. STR/UTM-PT/14/02/2021
MUGUTHA, RUIRU KIAMBU COUNTY: PLOT 1/10246 made by MMM date: 14/11/21 chd FMG
1st, 2nd,3rdand 4th. floor typical beams Signature…………… Signature…………………….
COLUMN DESIGN
Fy 460N/mm2
Fcu 30N/mm2
Cover 25mm
H 450mm
B 200mm
References Calculations Output
 Moments on column (X-X Axis) at foundation level (Beam loads )
Beam 01 and beam 02

Beam 01 length=3910mm
nlx 10.94 x 3910
P2= = =14.26kNm
3 3
2
nlx k² nlx
P4= = (1- ¿ = = [(3- ( l y ) ¿
3 3 6 lx
Unfactored
l y 3910 moment =13.22
K= = =1.252
lx 3650 kNm

10.94 x 3.65 (1.252)²

P4= ¿ 1- ¿ =9.53kNm
2 3

P2+P4=14.26+9.53=23.8 kNm

Beam 02 length =2915mm

P1 and P2
nlx 10.94 x 2.915 U.L.S =63.8
P1= = =31.9kNm
kNm
3 3
nlx 10.94 x 2.915
P3= = =31.9kNm
3 3
P1+P3=31.9+31.9=63.8 kNm
Unfactored Moments=5.93X2=11.9 kNm

UTMOST CONSULTING Job no: 08 sheet no: 1/2 rev: 01

ENGINEERS UTM-PT 14/02/ 2021
consultation sheet RC BEAM DESIGN
JOB TITTLE: PROPOSED MIXED USE COMMERCIAL BUILDING AT Org. ref. STR/UTM-PT/14/02/2021
MUGUTHA, RUIRU KIAMBU COUNTY: PLOT 1/10246 made by MMM date: 14/11/21 chd FMG
1st, 2nd,3rdand 4th. floor typical beams Signature…………… Signature…………………….
COLUMN DESIGN
Fy 460N/mm2
Fcu 30N/mm2
Cover 25mm
H 450mm
 B 200mm
References Calculations Output
LOADING COMBINATION WITH MAXIMUM MOMENT

Fixed end moments

Wl ² 11.9 x 3.9 ²
Beam: B1: = =8.43 kNm
12 12

Wl ² 63.8 x 2.915 ²
B2: = =45.18 kNm
12 12

Unbalanced moments in (X-X) Axis

∆ m=45.18-8.43=36.75 kNm

Moment of inertia of columns

0.2 x 0.35 ³
(i). Major axis: Icy= =7.15x10⁴m⁴
12
Stiffness of upper and lower column about major axis
−4
4 EICX 4 x 7.15 x 10 E
(i). Upper column: Kux=
Lupper
= =9.53X10⁻⁴E
3
4 x 7.15 x 10−4 E
(ii).Lower column Kly= =1.91X10⁻³E
1.5

MINOR AXIX-(Z-Z)

UTMOST CONSULTING Job no: 08 sheet no: 1/2 rev: 01

ENGINEERS UTM-PT 14/02/ 2021
consultation sheet RC BEAM DESIGN
JOB TITTLE: PROPOSED MIXED USE COMMERCIAL BUILDING AT Org. ref. STR/UTM-PT/14/02/2021
MUGUTHA, RUIRU KIAMBU COUNTY: PLOT 1/10246 made by MMM date: 14/11/21 chd FMG
1st, 2nd,3rdand 4th. floor typical beams Signature…………… Signature…………………….
 COLUMN DESIGN
Fy 460N/mm2
Fcu 30N/mm2
Cover 25mm
H 450mm
B 200mm
References Calculations Output
Beam loading

Beam 21-length =4900mm

l y 4900
= =1.68=k
lx 2915
nlx k² ( 2
)
P1= (1- ¿ = 10.94 x 2.915[(1− 1.68 )] =0.94kNm
3 3 2 3
l y 4900 ULS =11.13
P2= = k=1.253
kNm
lx 3910
nlx k² ( 2
) Unfactored
P= (1- ¿ = 10.94 x 3.91[(1− 1.253 )] =10.19kNm load=6.2 kNm
3 3 2 3
P1+P2=0.94+10.19=11.13 kNm

Beam 22 length =3650mm

P3 and P4
l y 3650
P3= =
lx 2915
=1.252
nlx k²
P3= (1- ¿ =7.61kNm
2 3
nlx 10.94 x 3.65
P4= = =13.31kNm
3 3
P3+P4=20.92 kNm
Factored load (U.L.S) =20.92 kNm
Unfactored load=10.25 kNm

UTMOST CONSULTING Job no: 08 sheet no: 1/2 rev: 01

ENGINEERS UTM-PT 14/02/ 2021
consultation sheet RC BEAM DESIGN
JOB TITTLE: PROPOSED MIXED USE COMMERCIAL BUILDING AT Org. ref. STR/UTM-PT/14/02/2021
MUGUTHA, RUIRU KIAMBU COUNTY: PLOT 1/10246 made by MMM date: 14/11/21 chd FMG
1st, 2nd,3rdand 4th. floor typical beams Signature…………… Signature…………………….
COLUMN DESIGN
Fy 460N/mm2
Fcu 30N/mm2
Cover 25mm
H 450mm
B 200mm
References Calculations Output
Fixed end moments
Wl ² 11.31 x 4.9 ²
Beam 21: = =22.63 kNm
12 12
Wl ² 10.25 x 3.65 ²
Beam 22: = =11.4kNm
12 12
Unbalanced moments in minor axis(Z-Z)
∆ =22.63-11.4=11.23 kNm
Moment of inertia in column
0.23 x 0.35
(i). Minor axis = =2.33x10⁻⁴
12
Icy=2.33x10⁻⁴m⁴
Stiffness of upper and lower column about major axis
4 EICy 4 x 2.33 x 10−4 E
(i). Upper column: Kuy=
3
= =3.11X10⁻⁴E
3
4 EICy 4 x 2.33 x 10−4 E
(ii).Lower column Kly=
1.5
= =6.213X10⁻⁴E
1.5

Moments of inertia of B1, B2, B21, B22

4 Ex 7.15 x 10−4 E
B1= =7.31x10⁻⁴E
3.91
4 Ex 7.15 x 10−4 E
B2= =9.81x10⁻⁴E
2.915
−4
4 Ex 7.15 x 10 E
B3= =6.08x10⁻⁴E
4.9
4 Ex 7.15 x 10−4 E
B4= =7.84x10⁻⁴E
3.65
Distributed moment on lower column about major axis
Mex Llx
Mlx=
Kux+ Klx +0.5(Kb 1+ Kb2)
36.75 x 1.91 x 10⁻ ³ E
= =18.88 kNm
1.91 x 10 E+ 9.53 x 10−4 E +0.5(7.31 x 10−4 E +9.81 x 10− 4 E)
−3

Formulae
M eKu
Mu=
K 2+ Ku+0.5 Kb
Symbols
Me=beam fixed end moment
Mes=total only balance beam fixed end moment
Mu=upper column design moment
Ml=lower column design moment
Ku=upper column stiffness
Kl=lower column stiffness

UTMOST CONSULTING Job no: 08 sheet no: 1/2 rev: 01

ENGINEERS UTM-PT 14/02/ 2021
 consultation sheet RC BEAM DESIGN

JOB TITTLE: PROPOSED MIXED USE COMMERCIAL BUILDING AT Org. ref. STR/UTM-PT/14/02/2021
MUGUTHA, RUIRU KIAMBU COUNTY: PLOT 1/10246 made by MMM date: 14/11/21 chd FMG
1st, 2nd,3rdand 4th. floor typical beams Signature…………… Signature…………………….
COLUMN DESIGN
Fy 460N/mm2
Fcu 30N/mm2
Cover 25mm
H 450mm
B 200mm
References Calculations Output
Kb1=beam stiffness Beam 1
Kb2=beam stiffness Beam 2

Distributed moment in lower column about minor axis

Mex Llx
Mlx=
Kux+ Klx +0.5(Kb 1+ Kb2)
11.23 x 6.213 x 10 ⁻ ⁴ E
= −⁴ −4 −4 −4 =4.285kNm
6.213 x 10 E+3.11 x 10 E+ 0.5(6.08 x 10 E +7.84 x 10 E)
Mx=18.88 kNm
My=4.29 kNm
N=947.15 kN
Design of column
Fcu=30N/mm2
Fy=460 N/mm2
Lo=3m
Size of column =200x350mm
Cl 3.8.4.5 Effective length=Le=0.75(3-0.35) =1990mm
1990
Slenderness= =9.95<15
200
Design as short column
Effective depth about X-X axis
H`=350-40-16-8=286mm

Effective depth (Y-Y) Axis

b` =200-40-16-8=136mm
M x 18.88 x 10⁻ ³
= =65.94
h 286

M y 4.29 x 10 ⁻³
= =31.54
b 136
 UTMOST CONSULTING Job no: 08 sheet no: 1/2 rev: 01
ENGINEERS UTM-PT 14/02/ 2021
consultation sheet RC BEAM DESIGN
JOB TITTLE: PROPOSED MIXED USE COMMERCIAL BUILDING AT Org. ref. STR/UTM-PT/14/02/2021
MUGUTHA, RUIRU KIAMBU COUNTY: PLOT 1/10246 made by MMM date: 14/11/21 chd FMG
1st, 2nd,3rdand 4th. floor typical beams Signature…………… Signature…………………….
COLUMN DESIGN
Fy 460N/mm2
Fcu 30N/mm2
Cover 25mm
H 450mm
B 200mm
References Calculations Output
M x M y
Therefore,
h
> b
: (65.94 > 31.54)
N 947.15 x 10 ³
= =0.451
bhfcu 30 x 200 x 350

β =0.4749
h
M`x =Mx+ β ( ) xMy
b
286
= 18.88+0.4749 x ( )x4.29=23.16 kNm
136
M x 23.16 x 10 ⁶
= =0.041
bh² 200 x 350 ²
Table 3.22
N 947.15 x 10 ³
= =13.53
bh 200 x 350
Eqn 40 & 41
d 286
= =0.82
h 350

Chart 27
100 As
=0.4%
bh
0.4 x 200 x 350
= =280mm2/m
Cl 3.8.4.2 100
Chart no 27 Provide 4T12 (452 mm2/m) or 4T16(804 mm2/m)
Adopt 4T16 for more rigidity at lapped areas
Links
1
x16=4mm take T8
4
Minimum spacing =12x6=192mm
B=200mm
Provide T8@200c/c links