RAFT FOUNDATION DESIGN (BS8110 : Part 1 : 1997) - AESL ...

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Section

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rev.



1



Calc. by

Kevin Miller

Date

16/05/2008

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RAFT FOUNDATION DESIGN (BS8110 : Part 1 : 1997)

TEDDS calculation versio
n 1.0.02
;

Library item
-

Raft title


h
edge
b
edge
a
edge
h
slab
h
hcoreslab
h
hcorethick
A
sslabtop
A
sedgetop
A
sslabbtm
A
sedgebtm
A
sedgelink


Soil and raft definition

Soil definition

Allowable bearing pressure;

q
allow

=
50.0

kN/m
2

Number of types of soil forming sub
-
soil;

Two or more types

Soil density;

Firm

Depth of hardcore beneath slab;

h
hcoreslab

=
150

mm;
(Dispersal allowed for bearing pressure check)

Depth of hardcore beneath thickenings;

h
hcorethick

=
250

mm;
(Dispersal allowed for bearing pressure check)

Density of hardcore;


hcore

=
19.0

kN/m
3

Basic assumed diameter of local depression;


depbasic

=
2500
mm

Diameter under slab modified for hardcore;


depslab

=

depbasic

-

h
hcoreslab

=
2350

mm

Diameter under thickenings modi
fied for hardcore;


depthick

=

depbasic

-

h
hcorethick

=
2250

mm

Raft slab definition

Max dimension/max dimension between joints;

l
max

=
10.000

m

Slab thickness;

h
slab

=
250

mm

Concrete strength;

f
cu

=
40

N/mm
2

Poissons ratio of concrete;



=
0.2

Slab mesh reinforcement strength;

f
yslab

=
500

N/mm
2

Partial safety factor for steel reinforcement;


s

=
1.15

From C&CA document ‘Concrete ground floors’ Table 5

Minimum mesh required in top for shrinkage;

A142
;

Actual mesh provided in top;

A393 (A
sslabtop

= 393 mm
2
/m)

Mesh provided in bottom;

A393 (A
sslabbtm

= 393 mm
2
/m)

Top mesh bar diameter;


slabtop

=
10

mm

Bottom mesh bar diameter;


slabbtm

=
10

mm

Cover to top reinforcement;

c
top

=
50

mm

Cover to bottom reinforcement;

c
btm

=
75

mm

Average effective depth of top reinforcement;

d
tslabav

= h
slab

-

c
t
op

-


slabtop

=
190

mm

Average effective depth of bottom reinforcement;

d
bslabav

= h
slab

-

c
btm

-


slabbtm

=
165

mm

Overall average effective depth;

d
slabav

= (d
tslabav

+ d
bslabav
)/2 =
178

mm

Minimum effective depth of top
reinforcement;

d
tslabmin

= d
tslabav

-


slabtop
/2 =
185

mm

Minimum effective depth of bottom reinforcement;

d
bslabmin

= d
bslabav

-


slabbtm
/2 =
160

mm

Edge beam definition

Overall depth;

h
edge

=
500

mm



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rev.



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Calc. by

Kevin Miller

Date

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Chk'd by

Kevin Miller

Date



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Width;

b
edge

=
500

mm

Angle of chamfer to horizontal;


edge

=
60

deg

Strength of main bar reinforcement;

f
y

=
500

N/mm
2

Strength of link
reinforcement;

f
ys

=
500

N/mm
2

Reinforcement provided in top;

2 T20 bars (A
sedgetop

= 628 mm
2
)

Reinforcement provid
ed in bottom;

2 T20 bars (A
sedgebtm

= 628 mm
2
)

Link r
einforcement provided;

2 T10 legs at 250 ctrs (A
sv
/s
v

= 0.628 mm)

Bottom cover to links;

c
beam

=
35

mm

Effective depth of top reinforcement;

d
edgetop

= h
edge

-

c
top

-


slabtop

-

edgelink

-


edgetop
/2 =
420

mm

Effective depth of bottom reinforcement;

d
edgebtm

= h
edge

-

c
beam

-


edgelink

-


edgebtm
/2 =
445

mm

Internal slab design checks

Basic loading

Slab self weight;

w
slab

= 24 kN/m
3



h
slab

=
6.0

kN/m
2

Hardcore;

w
hcoreslab

=

hcore



h
hcoreslab

=
2.9

kN/m
2

Applied loading

Uniformly distributed dead loa
d;

w
Dudl

=
0.0

kN/m
2

Uniformly distributed live load;

w
Ludl

=
0.0

kN/m
2

Slab load number 1

Load type;

Point load

Dead load;

w
D1

=
0.0

kN

Live load;

w
L1

=
75.0

kN

Ultimate load;

w
ult1

= 1.4


w
D1

+ 1.6


w
L1

=
120.0

kN

Load dimension 1;

b
11

=
440

mm

Load dimension 2;

b
21

=
440

mm

Internal slab bearing pressure check

Total uniform load at formation level;

w
udl

= w
slab

+ w
hcoreslab

+ w
Dudl

+ w
Ludl

=
8.9

kN/m
2

Bearing pressure beneath load number 1

Net bearing pressure available to resist point load;

q
net

= q
allow

-

w
udl

=
41.2

kN/m
2

Net
‘ultimate’ bearing pressure available;

q
netult

= q
net



w
ult1
/(w
D1

+ w
L1
) =
65.8

kN/m
2

Loaded area required at formation;

A
req1

= w
ult1
/q
netult

=
1.823

m
2

Length of cantilever projection at formation;

p
1

= max(0 m, [
-
(b
11
+b
21
) +

((b
1
1
+b
21
)
2

-

4

(b
11

b
21

-

A
req1
))]/4)


p
1

=
0.455

m

Length of cantilever projection at u/side slab;

p
eff1

= max(0 m, p
1

-

h
hcoreslab



tan(30)) =
0.368

m

Effective loaded area at u/side slab;

A
eff1

= (b
11

+ 2


p
eff1
)


(b
21

+ 2


p
eff1
)

=
1.385

m
2

Effective net ult bearing pressure at u/side slab;

q
netulteff

= q
netult



A
req1
/A
eff1

=
86.6

kN/m
2

Cantilever bending moment;

M
cant1

= q
netulteff



p
eff1
2
/2 =
5.9

kNm/m

Reinforcement required in bottom

Maximum cantilever moment;

M
cantmax

=
5.9

kNm/m

K factor;

K
slabbp

= M
cantmax
/(f
cu



d
bslabmin
2
) =
0.006

Lever arm;

z
slabbp

= d
bslabmin



min(0.95, 0.5 +

(0.25
-

K
slabbp
/0.9
)) =
152.0

mm

Area of steel required;

A
sslabbpreq

= M
cantmax
/((1.0/

s
)


f
yslab



z
slabbp
) =
89

mm
2
/m

PASS
-

A
sslabbpreq

<= A
sslabbtm

-

Area of reinforcement provided to distribute the loa
d is adequate

The allowable bearing pressure w
ill not be exceeded



Advanced Engineering Solutions
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Job Ref.



Section

Civil Engineering

Sheet no.
/
rev.



3



Calc. by

Kevin Miller

Date

16/05/2008

Chk'd by

Kevin Miller

Date



App'd by



Date




Internal slab bending and shear check

Applied bending moments

Span of slab;

l
slab

=

depslab

+ d
tslabav

=
2540

mm

Ultimate self weight udl;

w
swult

= 1.4


w
slab

=
8.4

kN
/m
2

Self weight moment at centre;

M
csw

= w
swult



l
slab
2



(1 +

) / 64 =
1.0

kNm/m

Self weight moment at edge;

M
esw

= w
swult



l
slab
2

/ 32 =
1.7

kNm/m

Self weight shear force at edge;

V
sw

= w
swult



l
slab

/ 4 =
5.3

kN/m

Moments due to applied uniformly distributed loads

Ultimate applied udl;

w
udlult

= 1.4


w
Dudl

+ 1.6


w
Ludl

=
0.0

kN/m
2

Moment at centre;

M
cudl

= w
udlult



l
slab
2



(1 +

) / 64 =
0.0

kNm/m

Mo
ment at edge;

M
eudl

= w
udlult



l
slab
2

/ 32 =
0.0

kNm/m

Shear force at edge;

V
udl

= w
udlult



l
slab
/ 4 =
0.0

kN/m

Moment due to load number 1

Moment at centre;

M
c1

= w
ult1
/(4


)


(1+

)


ln(l
slab
/min(b
11
, b
21
)) =
20.1

kNm/m

Moment at edge;

M
e1

= w
ult1
/(4


) =
9.5

kNm/m

Minimum dispersal width for shear;

b
v1

= min(b
11

+ 2

b
21
, b
21

+ 2

b
11
) =
1320.0

mm

Approximate shear force;

V
1

= w
ult1

/ b
v1

=
90.9

kN/m

Resultant moments and shears

Total moment at edge;

M

e

=
11.2

kNm/m

Total moment at centre;

M

c

=
21.1

kNm/m

Total shear force;

V


=
96.2

kN/m

Reinforcement required in top

K factor;

K
slabtop

= M

e
/(f
cu



d
tslabav
2
) =
0.008

Lever arm;

z
slabtop

= d
tslabav



min(0.95, 0.5 +

(0.25
-

K
slabtop
/0.9)) =
180.5

mm

Area of steel required for bending
;

A
sslabtopbend

= M

e
/((1.0/

s
)


f
yslab



z
slabtop
) =
143

mm
2
/m

Minimum area of steel required;

A
sslabmin

= 0.0013


h
slab

=
325

mm
2
/m

Area of steel required;

A
sslabtopreq

= max(A
sslabtopbend
, A
sslabmin
) =
325

mm
2
/m

PASS
-

A
sslabtopreq

<= A
sslabtop

-

Area of reinforcement provided in top to span local depressions is adequate

Reinforcement required in bottom

K factor;

K
slabbtm

= M

c
/(f
cu



d
bslabav
2
) =
0.019

Lever arm;

z
slabbtm

= d
bslabav



min(0.95, 0.5 +

(0.25
-

K
slabbtm
/0.9)) =
156.7

mm

Area of steel required for bending;

A
sslabbtmbend

= M

c
/((1.0/

s
)


f
yslab



z
slabbtm
) =
310

mm
2
/m

Area of steel required;

A
sslabbtmreq

= max(A
sslabbtmbend
, A
sslabmin
) =
325

mm
2
/m

PASS
-

A
sslabbtmreq

<= A
sslabbtm

-

Area of reinforceme
nt provided in bottom to span local depressions is adequate

Shear check

Applied shear stress;

v = V

/d
tslabmin

=
0.520

N/mm
2

Tension steel ratio;



= 100


A
sslabtop
/d
tslabmin

=
0.212

From BS8110
-
1:1997
-

Table 3.8
;

Desig
n concrete shear strength;

v
c

=
0.535

N/mm
2

PASS
-

v <= v
c

-

Shear capaci
ty of the slab is adequate

Internal slab deflection check

Basic allowable span to depth ratio;

Ratio
basic

=
26.0

Moment factor;

M
factor

= M

c
/d
bslabav
2

=
0.775

N/mm
2

Steel service stress;

f
s

= 2/3


f
yslab



A
sslabbtmbend
/A
sslabbtm

=
262.667

N/mm
2



Advanced Engineering Solutions
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Project



Job Ref.



Section

Civil Engineering

Sheet no.
/
rev.



4



Calc. by

Kevin Miller

Date

16/05/2008

Chk'd by

Kevin Miller

Date



App'd by



Date




Modification factor;

MF
slab

= min(2.0, 0.55 + [(477N/mm
2

-

f
s
)/(120


(0.9N/mm
2

+ M
factor
))])


MF
slab

=
1.616

Modi
fied allowable span to depth ratio;

Ratio
allow

= Ratio
basic



MF
slab

=
42.021

Actual span to depth ratio;

Ratio
actual

= l
slab
/ d
bslabav

=
15.394

PASS
-

Ratio
actual

<= Ratio
allow

-

Slab span to depth ratio is adequate

Edge beam design checks

Basic loading

Hardcore;

w
hcorethick

=

hcore



h
hcorethick

=
4.8

kN/m
2

Edge beam

Rectangular beam

element;

w
beam

= 24 kN/m
3



h
edge



b
edge

=
6.0

kN/m

Chamfer element;

w
chamfer

= 24 kN/m
3



(h
edge

-

h
slab
)
2
/(2


tan(

edge
)) =
0.4

kN/m

Slab element;

w
slabelmt

= 24 kN/m
3



h
slab



(h
edge

-

h
slab
)/tan(

edge
) =
0.9

kN/m

Ed
ge beam self weight;

w
edge

= w
beam

+ w
chamfer

+ w
slabelmt

=
7.3

kN/m

Edge load number 1

Load type;

Longitudinal line load

Dead load;

w
Dedge1

=
4.0

kN/m

Live load;

w
Ledge1

=
0.0

kN/m

Ultimate load;

w
ultedge1

= 1.4


w
Dedg
e1

+ 1.6


w
Ledge1

=
5.6

kN/m

Longitudinal line load width;

b
edge1

=
140

mm

Centroid of load from outside face of raft;

x
edge1

=
0

mm

Edge beam bearing pressure check

Effective bearing width of edge beam;

b
bearing

= b
edge

+ (h
edge

-

h
slab
)/tan(

edge
) =
644

mm

Total uniform load at formation level;

w
udledge

= w
Dudl
+w
Ludl
+w
edge
/b
bearing
+w
hcorethick

=
16.1

kN/m
2

Centroid of longitudinal and equiv
alent line loads from outside face of raft

Load x distance for edge load 1
;

Moment
1

= w
ultedge1



x
edge1

=
0.0

kN

Sum of ultimate longitud’l and equivalent line loads;


UDL =
5.6

kN/m

Sum of load x distances;


Moment =
0.0

kN

Centroid of loads;

x
bar

=

Moment/

UDL =
0

mm

Initially assume no moment transferred into slab due to load/reaction eccentricity

Sum of unfactored longitud’l and eff
’tive line loads;


UDLsls =
4.0

kN/m

Allowable bearing width;

b
allow

= 2


x
bar

+ 2


h
hcoreslab



tan(30) =
173

mm

Bearing pressure due to line/point loa
ds;

q
linepoint

=

UDLsls/ b
allow

=
23.1

kN/m
2

Total applied bearing pressure;

q
edge

= q
linepoint

+ w
udledge

=
39.2

kN/m
2

PASS
-

q
edge

<= q
allow

-

Allowable bearing pressure is not exceeded

Edge beam bending check

Divider for

moments due to udl’s;


udl

=
10.0

Applied bending moments

Span of edge beam;

l
edge

=

depthick

+ d
edgetop

=
2670

mm

Ultimate self weight udl;

w
edgeult

= 1.4


w
edge

=
10.2

kN/m

Ultimate slab udl (approx);

w
edgeslab

= max(0 kN/m,1.4

w
slab

((

depthick
/2

3/4)
-
(b
edge
+(h
edge
-
h
slab
)/tan(

edge
))))


w
edgeslab

=
1.7

kN/m

Self weight and slab bending moment;

M
edgesw

= (w
edgeult

+ w
edgeslab
)


l
edge
2
/

udl

=
8.5

kNm

Self

weight shear force;

V
edgesw

= (w
edgeult

+ w
edgeslab
)


l
edge
/2 =
15.9

kN



Advanced Engineering Solutions
Ltd







Project



Job Ref.



Section

Civil Engineering

Sheet no.
/
rev.



5



Calc. by

Kevin Miller

Date

16/05/2008

Chk'd by

Kevin Miller

Date



App'd by



Date




Moments due to applied uniformly distributed loads

Ultimate udl (approx);

w
edgeudl

= w
udlult




depthick
/2


3/4 =
0.0

kN/m

Bending moment;

M
edgeudl

= w
edgeudl



l
edge
2
/

udl

=
0.0

kNm

Shear force;

V
edgeudl

= w
edgeudl



l
edge
/2 =
0.0

kN

Moment and shear due to load number 1

Bending moment;

M
edge1

= w
ultedge1



l
edge
2
/

udl

=
4.0

kNm

Shear force;

V
edge1

= w
ultedge1



l
edge
/2 =
7.5

kN

Resultant moments and
shears

Total moment (hogging and sagging);

M

edge

=
12.5

kNm

Maximum shear force;

V

edge

=
23.4

kN

Reinforcement required in top

Width of section in compression zone;

b
edgetop

= b
edge

=
500

mm

Average web width;

b
w

= b
edge

+ (h
edge
/tan(

edge
))/2 =
644

mm

K factor;

K
edgetop

= M

edge
/(f
cu



b
edgetop



d
edgetop
2
) =
0.004

Lever arm;

z
edgetop

= d
edgetop



min(0.95, 0.5 +

(0.25
-

K
edgetop
/0.9)) =
399

mm

Area of steel required for bending;

A
sedgetopbend

= M

edge
/((1.0/

s
)


f
y



z
edgetop
) =
72

mm
2

Minimum area of steel required;

A
sedgetopmin

= 0.0013


1.0


b
w



h
edge

=
419

mm
2

Area of steel required;

A
sedgetopreq

= max(A
sedgetopbend
, A
sedgetopmin
) =
419

mm
2

PASS
-

A
sedgetopreq

<= A
sedgetop

-

Area of reinforcement provided in top of edge beams is adequate

Reinforcement required in bottom

Width of section in compression zone;

b
edgebtm

= b
edge

+ (h
edge

-

h
slab
)/tan(

edge
) + 0.1


l
edge

=
911

mm

K factor;

K
edgebtm

= M

edge
/(f
cu



b
edgebtm



d
edgebtm
2
) =
0.002

Lever arm;

z
edgebtm

= d
edgebtm



min(0.95, 0.5 +

(0.25
-

K
edgebtm
/0.9))

=
423

mm

Area of steel required for bending;

A
sedgebtmbend

= M

edge
/((1.0/

s
)


f
y



z
edgebtm
) =
68

mm
2

Minimum area of steel required;

A
sedgebtmmin

= 0.0013


1.0


b
w



h
edge

=
419

mm
2

Area of steel required;

A
sedgebtmreq

= max(A
sedgebtmbend
, A
sedgebtmmin
) =
419

mm
2

PASS
-

A
sedgebtmreq

<= A
sedgebtm

-

Area
of reinforcement provided in bottom of edge beams is adequate

Edge beam shear check

Applied shear stress;

v
edge

= V

edge
/(b
w



d
edgetop
) =
0.086

N/mm
2

Tension steel ratio;


edge

= 100


A
sedgetop
/(b
w



d
edgeto
p
) =
0.232

From BS8
110
-
1:1997
-

Table 3.8

Design concrete shear strength;

v
cedge

=
0.454

N/mm
2

v
edge

<= v
cedge

+ 0.4
N/mm
2

-

Therefore minimum links required

Link area to spacing ratio required;

A
sv
_upon_s
vreqedge

= 0.4N/mm
2



b
w
/((1.0/

s
)


f
ys
) =
0.593

mm

Link area to spacing ratio provided;

A
sv
_upon_s
vprovedge

= N
edgelink




edgelink
2
/(4

s
vedge
) =
0.628

mm

PASS
-

A
sv
_upon_s
vreqedge

<= A
sv
_up
on_s
vprovedge

-

Shear reinforcement provided in edge beams is adequate

Corner design checks

Basic loading

Corner load number 1

L
oad type;

Line load in x direction

Dead load;

w
Dcorner1

=
4.0

kN/m

Live load;

w
Lcorner1

=
0.0

kN/m

Ultimate load;

w
ultcorner1

= 1.4


w
Dcorner1

+ 1.6


w
Lcorner1

=
5.6

kN/m

Centroid of load from outside face of raft;

y
corne
r1

=
0

mm

Corner load number 2



Advanced Engineering Solutions
Ltd







Project



Job Ref.



Section

Civil Engineering

Sheet no.
/
rev.



6



Calc. by

Kevin Miller

Date

16/05/2008

Chk'd by

Kevin Miller

Date



App'd by



Date




Load type;

Line load in y direction

Dead load;

w
Dcorner2

=
4.0

kN/m

Live load;

w
Lcorner2

=
0.0

kN/m

Ultimate load;

w
ultcorner2

= 1.4


w
Dcorner2

+ 1.6


w
Lcorner2

=
5.6

kN/m

Centroid of load from outside face of raft;

x
corner2

=
0

mm

Corner bearing pressure check

Total uniform load at formation level;

w
udlcorner

= w
Dudl
+w
Ludl
+w
edge
/b
bearing
+w
hcorethick

=
16.1

kN/m
2

Net bearing press avail to resist line/point loads;

q
netcorner

= q
allow

-

w
udlcorner

=
33.9

kN/m
2

Total line/point loads

Total unfactored line load in x direction;

w

linex

=
4.0

kN/m

Total ultimate line load in x direction;

w

ultlinex

=
5.6

kN/m

Total unfactor
ed line load in y direction;

w

liney

=
4.0

kN/m

Total ultimate line load in y direction;

w

ultliney

=
5.6

kN/m

Total unfactored point load;

w

point

=
0.0

kN

Total ultimate point load;

w

ultpoint

=
0.0

kN

Length o
f side of sq reqd to resist line/point loads;

p
corner

=[w

linex
+w

liney
+

((w

linex
+w

liney
)
2
+4

q
netcorner

w

point
)]/(2

q
netcorner
)


p
corner

=
236

mm

Bending moment about x
-
axis due to load/reaction eccentricity

Moment due to load 1 (x line)
;

M
x1

= w
ultcorner1



p
corner



(p
corner
/2
-

y
corner1
) =
0.2

kNm

Total moment

about x axis;

M

x

=
0.2

kNm

Bending moment about y
-
axis due to load/reaction eccentricity

Moment due to load 2 (y line)
;

M
y2

= w
ultco
rner2



p
corner



(p
corner
/2
-

x
corner2
) =
0.2

kNm

Total moment about y axis;

M

y

=
0.2

kNm

Check top reinforcement in edge beams for load/reaction eccentric moment

Max moment due to load/reaction ecc
entricity;

M


= max(M

x
, M

y
) =
0.2

kNm

Assume all of this moment is resisted by edge beam

From edge beam design checks away from corners

Moment due to edge beam spanning depression;

M

edge

=
12.5

kNm

Total moment to be resisted;

M

co
rnerbp

= M


+ M

edge

=
12.6

kNm

Width of section in compression zone;

b
edgetop

= b
edge

=
500

mm

K factor;

K
cornerbp

= M

cornerbp
/(f
cu



b
edgetop



d
edgetop
2
) =
0.004

Lever arm;

z
cornerbp

= d
edgetop



min(0.95, 0.5 +

(0.25
-

K
cornerbp
/0.9)) =
399

mm

Total area of top steel required;

A
scornerbp

= M

cornerbp

/((1.0/

s
)


f
y



z
co
rnerbp
) =
73

mm
2

PASS
-

A
scornerbp

<= A
sedgetop

-

Area of reinforcement provided to resist eccentric moment is adequate

The allowable bearing pressure at the corner will not be exceeded

Corn
er beam bending check

Cantilever span of edge beam;

l
corner

=

depthick
/

(2) + d
edgetop
/2 =
1801

mm

Moment and shear due to self weight

Ultimate self weight udl;

w
edgeult

= 1.4


w
edge

=
10.2

kN/m

Average ultimate slab udl (approx); w
cornerslab

= max(0 kN/m,1.4

w
slab

(

depthick
/(

(2)

2)
-
(b
edge
+(h
edge
-
h
slab
)/tan(

edge
))))


w
cornerslab

=
1.3

kN/m

Self weight and slab bending moment;

M
cornersw

= (w
edgeult

+ w
cornerslab
)


l
corner
2
/2 =
18.6

kNm

Self weight and slab shear force;

V
cornersw

= (w
edgeult

+ w
cornerslab
)


l
corner

=
20.7

kN



Advanced Engineering Solutions
Ltd







Project



Job Ref.



Section

Civil Engineering

Sheet no.
/
rev.



7



Calc. by

Kevin Miller

Date

16/05/2008

Chk'd by

Kevin Miller

Date



App'd by



Date




Moment and shear due to udls

Maximum ultimate udl;

w
cornerudl

= ((1.4

w
Dudl
)+(1.6

w
Ludl
))



depthick
/

(2) =
0.0

kN/m

Bending moment;

M
cornerudl

= w
cornerudl



l
corner
2
/6 =
0.0

kNm

Shear force;

V
cornerudl

=

w
cornerudl



l
corner
/2 =
0.0

kN

Moment and shear due to line loads in x direction

Bending moment;

M
cornerlinex

= w

ultlinex



l
corner
2
/2 =
9.1

kNm

Shear force;

V
cornerlinex

= w

ultlinex



l
co
rner

=
10.1

kN

Moment and shear due to line loads in y direction

Bending moment;

M
cornerliney

= w

ultliney



l
corner
2
/2 =
9.1

kNm

Shear force;

V
cornerliney

= w

ultliney



l
corner

=
10.1

kN

Total moments and shears due to point loads

Bending moment about x axis;

M
cornerpointx

=
0.0

kNm

Bending moment about y axis;

M
cornerpointy

=
0.0

kNm

Shear force;

V
cornerpoint

=
0.0

kN

Resultant moments and shears

To
tal moment about x axis;

M

cornerx

= M
cornersw
+ M
cornerudl
+ M
cornerliney
+ M
cornerpointx

=
27.7

kNm

Total shear force about x axis;

V

cornerx

= V
cornersw
+ V
cornerudl
+ V
cornerliney

+ V
cornerpoint

=
30.8

kN

Total moment about y axis;

M

cornery

= M
cornersw
+ M
corne
rudl
+ M
cornerlinex
+ M
cornerpointy

=
27.7

kNm

Total shear force about y axis;

V

cornery

= V
cornersw
+ V
cornerudl
+ V
cornerlinex

+ V
cornerpoint

=
30.8

kN

Deflection of both edge beams at corner will be the same therefore design for averag
e of these moments and shears

Design bending moment;

M

corner

= (M

cornerx

+ M

cornery
)/2 =
27.7

kNm

Design shear force;

V

corner

= (V

cornerx

+ V

cornery
)/2 =
30.8

kN

Reinforcement required
in top of edge beam

K factor;

K
corner

= M

corner
/(f
cu



b
edgetop



d
edgetop
2
) =
0.008

Lever arm;

z
corner

= d
edgetop



min(0.95, 0.5 +

(0.25
-

K
corner
/0.9)) =
399

mm

Area of stee
l required for bending;

A
scornerbend

= M

corner
/((1.0/

s
)


f
y



z
corner
) =
160

mm
2

Minimum area of steel required;

A
scornermin

= A
sedgetopmin

=
419

mm
2

Area of steel required;

A
scorner

= max(A
scornerbend
, A
scornermin
) =
419

mm
2

PASS
-

A
scorner

<= A
sedgetop

-

Area of reinforcement provided in top of edge beams at corners is adequate

Corner beam shear check

Average web width;

b
w

= b
edge

+ (h
edge
/tan(

edge
))/2 =
644

mm

Applied shear stress;

v
corner

= V

corner
/(b
w



d
edgetop
) =
0.114

N/mm
2

Tension steel ratio;


corner

= 100


A
sedgetop
/(b
w



d
ed
getop
) =
0.232

From BS8110
-
1:1997
-

Table 3.8

Design concrete shear strength;

v
ccorner

=
0.449

N/mm
2

v
co
rner

<= v
ccorner

+ 0.4N/mm
2

-

Therefore minimum links required

Link area to spacing ratio required;

A
sv
_upon_s
vreqcorner

= 0.4N/mm
2



b
w
/((1.0/

s
)


f
ys
) =
0.593

mm

Link area to spacing ratio provided;

A
sv
_upon_s
vprovedge

= N
edgelink




edgelink
2
/(4

s
vedge
) =
0.628

mm

PASS
-

A
sv
_upon_s
vreqcorner

<= A
sv
_upon_s
vprovedge

-

Shear reinforcement provided in edge beams at corners is
adequate

Corner beam deflection check

Basic allowable span to depth ratio;

Ratio
basiccorner

=
7.0

Moment factor;

M
factorcorner

= M

corner
/(b
edgetop



d
edgetop
2
) =
0.314

N/mm
2

Steel service stress;

f
scorner

= 2/3


f
y



A
scornerbend
/A
sedgetop

=
84.751

N/mm
2

Modification factor; MF
corner
=min(2.0,0.5
5+[(477N/mm
2
-
f
scorner
)/(120

(0.9N/mm
2
+M
factorcorner
))])



Advanced Engineering Solutions
Ltd







Project



Job Ref.



Section

Civil Engineering

Sheet no.
/
rev.



8



Calc. by

Kevin Miller

Date

16/05/2008

Chk'd by

Kevin Miller

Date



App'd by



Date





MF
corner

=
2.000

Modified allowable span to depth ratio;

Ratio
allowcorner

= Ratio
basiccorner



MF
corner

=
14.000

Actual span to depth ratio;

Ratio
actualcorner

= l
corner
/ d
edgeto
p

=
4.288

PASS
-

Ratio
actualcorner

<= Ratio
allowcorner

-

Edge beam span to depth ratio is adequate