Design of Portal Frames: by Dr. G.S.Suresh, Professor, Civil Engineering Department, NIE, Mysore
Design of Portal Frames: by Dr. G.S.Suresh, Professor, Civil Engineering Department, NIE, Mysore
Design of Portal Frames: by Dr. G.S.Suresh, Professor, Civil Engineering Department, NIE, Mysore
45 . 0
10 3 . 14 10 18
10 3 . 14
K
K
D
5 5
5
BC
BC
BC
=
+
= =
= = t
p
t
=100x 942/(400x600)=0.39~0.4
Permissible stress for p
t
=0.4 from table 19 t
c
=0.432 < t
v
Hence shear reinforcement
is required to be designed
Strength of concrete V
uc
=0.432 x 400 x 600/1000 = 103 kN
Shear to be carried by steel V
us
=162-103 = 59 kN
Spacing 2 legged 8 mm dia stirrup s
v
= 367
10 59
600 50 2 415 87 . 0
V
d A f 87 . 0
3
us
sv y
=
=
Two legged #8 stirrups are provided at 300 mm c/c (equal to maximum spacing)
8
Step5:Design of columns:
Cross-section of column = 400 mm x 600 mm
Ultimate axial load P
u
=1.5 x 108 = 162 kN (Axial load = shear force in beam)
Ultimate moment M
u
= 1.5 x 102 = 153 kN-m ( Maximum)
Assuming effective cover d = 50 mm; d/D ~0.1
053 . 0
600 400 20
10 153
bD f
M
2
6
2
ck
u
=
=
9
033 . 0
600 400 20
10 162
bD f
P
3
ck
u
=
=
Referring to chart 32 of SP16, p/f
ck
=0.03; p=20 x 0.03 = 0.6
Minimum steel in column should be 0.8 %, Hence min steel percentage shall be adopted
A
st
=0.8x400x600/100 = 1920 mm
2
No. of bars required = 1920/314 = 6.1
Provide 8 bars of #20
8mm diameter tie shall have pitch least of the following
i) Least lateral dimension = 400 mm
ii) 16 times diameter of main bar = 320 mm
iii) 48 times diameter of tie bar = 384
iv) 300mm
Provide 8 mm tie @ 300 mm c/c
Step6:Design of Footing:
Load:
Axial Working load on column = 108 kN
Self weight of footing @10% = 11 kN
Total load= 119~120 kN
Working load moment at base = 51 kN-m
Approximate area footing required = Load on column/SBC
= 108/150 =0.72 m
2
However the area provided shall be more than required to take care of effect of
moment. The footing size shall be assumed to be 2mx3m (Area=6 m
2
)
2m
1.2m
3m
0.6m
0.4m
X
X
600
Tie #8 @300 c/c
8-#20
400
10
Maximum pressure q
max
=P/A+M/Z = 108/6+6x51/2x3
2
= 35 kN/m
2
Minimum pressure q
min
=P/A-M/Z = 108/6-6x51/2x3
2
= 1 kN/m
2
Average pressure q = (35+1) = 18 kN/m
2
Bending moment at X-X = 18 x 2 x 1.2
2
/2 = 25.92 kN-m
Factored moment M
u
~39 kN-m
Over all depth shall be assumed as 300 mm and effective depth as 250 mm,
312 . 0
250 2000
10 39
bd
M
2
6
2
u
=
=
Corresponding percentage of steel from Table 2 of
SP16 is p
t
= 0.1%, Minimum p
t
=0.12%
Area of steel per meter width of footing is A
st
=0.12x1000x250/100=300 mm
2
Spacing of 12 mm diameter bar = 113x1000/300 = 376 mm c/c
Provide #12 @ 300 c/c both ways
Check for Punching Shear
Length of punching influence plane = a
o
= 600+250 = 850 mm
Width of punching influence plane = b
o
= 400+250 = 650 mm
Punching shear Force = V
punch
=108-18x(0.85x0.65)=98 kN
Punching shear stress t
punch
= V
punch
/ (2x(a
o
+b
o
)d =98x10
3
/(2x(850+650)250)
= 0.13 MPa
Permissible shear stress = 0.25\f
ck
=1.18 MPa > t
punch
Safe
Check for One Way Shear
Shear force at a distance d from face of column
V= 18x2x0.95 = 34.2 kN
Shear stress t
v
=34.2x10
3
/(2000x250)=0.064 MPa
Referring to table 19 of IS456 this stress is very small and hence safe
Details of reinforcement provided in footing is shown in Fig.6.7
Fig.6.7
11
LONGITUDINAL ELEVATION
Cross-Sections of Beam
Cross-Section of Column
12
2. A portal frame hinged at base has following data:
Spacing of portal frames = 4m
Height of columns = 4m
Distance between column centers = 10m
Live load on roof = 1.5 kN/m
2
RCC slab continuous over portal frames. Safe bearing capacity of soil=200 kN/m
2
Adopt M-20 grade concrete and Fe-415 steel. Design the slab, portal frame and
foundations and sketch the details of reinforcements.
Solution:
Data given:
Spacing of frames = 4m
Span of portal frame = 10m
Height of columns = 4m
Live load on roof = 1.5 kN/m
2
Concrete: M20 grade
Steel: Fe 415
Three dimensional view of the frame with and without the slab is shown in Fig 6.8
Fig. 6.8
13
Step1:Design of slab
Assume over all depth of slab as 120mm and effective depth as 100mm
Self weight of slab = 0.12 x 24 = 2.88 kN/m
2
Weight of roof finish = 0.50 kN/m
2
(assumed)
Ceiling finish = 0.25 kN/m
2
(assumed)
Total dead load w
d
= 3.63 kN/m
2
Live load w
L
= 1.50 kN/m
2
(Given in the data)
Maximum service load moment at interior support =
9
L w
10
L w
2
L
2
d
+ = 8.5 kN-m
M
u
=1.5 x 8.5 = 12.75 kN-m/m
M
ulim
=Q
lim
bd
2
= 2.76 x 1000 x 100
2
/ 1 x 10
6
= 27.6 kN-m > 12.75 kN-m (Q
lim
=2.76)
275 . 1
100 x 1000
10 x 75 . 12
bd
M
2
6
2
u
= =
From table 2 of SP16 p
t
=0.384; A
st
=(0.384 x 1000 x 100)/100= 384 mm
2
Spacing of 10 mm dia bars = (78.54 x 1000)/384= 204.5 mm c/c
Provide #10 @ 200 c/c
Area of distribution steel A
dist
=0.12 x 1000 x 120 / 100 = 144 mm
2
Spacing of 8 mm dia bars = (50.26 x 1000)/144= 349 mm c/c
Provide #8 @ 340 c/c. Main and dist. reinforcement in the slab is shown in Fig.6.9
Step2: Preliminary design of beams and columns
Beam:
Effective span = 10m
Effective depth based on deflection criteria = 10000/13 = 769.23mm
Assume over all depth as 750 mm with effective depth = 700mm, breadth b = 450mm
and column section equal to 450 mm x 600 mm.
Step3: Analysis
Load on frame
i) Load from slab = (3.63+1.5) x 4 =20.52 kN/m
ii) Self weight of rib of beam = 0.45x0.63x24 = 6.80 kN/m
Total ~ 28.00 kN/m
Height of beam above hinge = 4+0.1-075/2 =3.72 m
14
The portal frame subjected to the udl considered for analysis is shown in Fig. 6.10
Fig. 6.10
The moments in the portal frame hinged at the base and loaded as shown in Fig. 6.10
are analysed by moment distribution
I
AB
= 450 x 600
3
/12 = 81 x 10
8
mm
4
, I
BC
= 450 x 750
3
/12 = 158.2 x 10
8
mm
4
Stiffness Factor:
K
BA
= I
AB
/ L
AB
= 21.77 x 10
5
K
BC
= I
BC
/ L
BC
= 15.8 x 10
5
Distribution Factor:
5 . 0
10 8 . 15 10 77 . 21
10 77 . 21
K
K
D D
5 5
5
BA
BA
BC BA
=
+
= =
= = t
p
t
=100x 1256/(450x700)=0.39~0.4
Permissible stress for p
t
=0.4 from table 19 t
c
=0.432 < t
v
Hence shear reinforcement
is required to be designed
Strength of concrete V
uc
=0.432 x 450 x 700/1000 = 136 kN
Shear to be carried by steel V
us
=210-136 = 74 kN
Spacing 2 legged 8 mm dia stirrup
s
v
= 53 . 341
10 74
700 50 2 415 87 . 0
V
d A f 87 . 0
3
us
sv y
=
=
Two legged #8 stirrups are provided at 300 mm c/c (equal to maximum spacing)
17
18
Step5:Design of columns:
Cross-section of column = 450 mm x 600 mm
Ultimate axial load P
u
=1.5 x 140 = 210 kN (Axial load = shear force in beam)
Ultimate moment M
u
= 1.5 x 156 = 234 kN-m ( Maximum)
Assuming effective cover d = 50 mm; d/D ~0.1
07 . 0
600 450 20
10 234
bD f
M
2
6
2
ck
u
=
=
04 . 0
600 450 20
10 210
bD f
P
3
ck
u
=
=
Referring to chart 32 of SP16, p/f
ck
=0.04; p=20 x 0.04 = 0.8 %
Equal to Minimum percentage stipulated by IS456-2000 (0.8 % )
A
st
=0.8x450x600/100 = 2160 mm
2
No. of bars required = 2160/314 = 6.8
Provide 8 bars of #20
8mm diameter tie shall have pitch least of the following
v) Least lateral dimension = 450 mm
vi) 16 times diameter of main bar = 320 mm
vii) 48 times diameter of tie bar = 384
viii) 300mm
Provide 8 mm tie @ 300 mm c/c
Step6:Design of Hinge:
At the hinge portion, concrete is under triaxial stress and can withstand higher
permissible stress.
Permissible compressive stress in concrete at hinge= 2x0.4f
ck
=16 MPa
Factored thrust =P
u
=210kN
Cross sectional area of hinge required = 210x10
3
/16=13125 mm
2
Provide concrete area of 200 x100 (Area =20000mm
2
) for the hinge
Shear force at hinge = Total moment in column/height = 156/3.72=42
Ultimate shear force = 1.5x42=63 kN
Inclination of bar with vertical = u= tan
-1
(30/50) =31
o
Ultimate shear force = 0.87 f
y
A
st
sinu
2
o
3
st
mm 339
31 sin 415 87 . 0
10 63
A =
=
Provide 4-#16 (Area=804 mm
2
)
600
Tie #8 @300 c/c
8-#20
450
19
Step7:Design of Foundations:
Load:
Axial Working load on column = 140 kN
Self weight of column=0.45 x 0.6 x3.72x 24 = 24
Self weight of footing @10% = 16 kN
Total load= 180 kN
Working moment at base = 42 x 1 =42 kN-m
Approximate area footing required = Load on column/SBC
= 180/200 =0.9 m
2
However the area provided shall be more than required to take care of effect of
moment. The footing size shall be assumed to be 1mx2m (Area=2 m
2
)
Maximum pressure q
max
=P/A+M/Z = 180/2+6x42/1x2
2
= 153 kN/m
2
Minimum pressure q
min
=P/A-M/Z = 180/2-6x42/1x2
2
= 27 kN/m
2
Average pressure q = (153+27)/2 = 90 kN/m
2
Bending moment at X-X = 90 x 1 x 0.7
2
/2 = 22 kN-m
Factored moment M
u
~33 kN-m
Over all depth shall be assumed as 300 mm and effective depth as 250 mm,
528 . 0
250 1000
10 33
bd
M
2
6
2
u
=
=
Corresponding percentage of steel from Table 2 of
SP16 is p
t
= 0.15% > Minimum p
t
=0.12%
Area of steel per meter width of footing is A
st
=0.15x1000x250/100=301 mm
2
Spacing of 12 mm diameter bar = 113x1000/375 = 376 mm c/c
Provide #12 @ 300 c/c both ways
Check for Punching Shear
Length of punching influence plane = a
o
= 600+250 = 850 mm
Width of punching influence plane = b
o
= 450+250 = 700 mm
Punching shear Force = V
punch
=180-90x(0.85x0.7)=126.5 kN
Punching shear stress t
punch
= V
punch
/ (2x(a
o
+b
o
)d =126.5x10
3
/(2x(850+700)250)
= 0.16 MPa
Permissible shear stress = 0.25\f
ck
=1.18 MPa > t
punch
Safe
Check for One Way Shear
Shear force at a distance d from face of column
V= 90x1x0.45 = 40.5 kN
Shear stress t
v
=40.5x10
3
/(1000x250)=0.162 MPa
For p
t
=0.15 , the permissible stress t
c
= 0.28 (From table 19 of IS456-2000)
2m X
1m
0.7m
0.6m
X
0.45m
20
Details of reinforcement provided in footing is shown in Fig.6.13
Fig.6.13
21
Cross-Sections of Beam
Cross-Section of Column
LONGITUDINAL ELEVATION
22
Reference Books
N.Krishna Raju Advanced Reinforced concrete Design
Jaikrishna and O.P.Jain Plain and reinforced concrete Vol2
B.C.Punmia Reinforced Concrete Structures Vol2
Problems for Practice
1. A portal frame ABCD has fixed supports at A and D. The columns AB and
CD are 5m in height while the beam BC is 10 m in length. The frames are
spaced at 3.5m intervals. The live load on the roof slab which is 100 mm thick
may be taken as 1.5 kN/m
2
. Design the beam, column and footing and sketch
the details of reinforcements. Adopt M-20 concrete, Fe-415 steel and
SBC=200 kN/m
2
2. The roof of an assembly hall 30m long and 12 m wide between centres of
columns, consists of a continuous reinforced concrete slab over rectangular
portal frames spaced 3m apart. The columns are provided with independent
footings and hinged at the bottom. The ceiling height is 3.5m above the hinge
level. Adopting M-20 concrete and Fe-415 for steel, design the continuous
roof slab and the portal frame and foundation footing for the columns assume
safe bearing capacity of the soil as 150 kN/m
2
. Sketch the details of
reinforcements in the portal frame.
**************