3. PERIPHERAL BEAM DEFLECTION CALCULATION
361 of 392
LARSEN & TOUBRO LIMITEDECC Division - GES
The vertical deflections of beams is calculated as per Euro Code-2. The
Vertical deflection of edge beam is calculated for the most unfavourable serviceability load
case. Edge Beams in five faces of clinic building is checked for deflection. i.e. north face,
east face,south face, west face curved portion and west face as shown previously.
The following pages shows the vertical deflection calculation of edge beams
in second mezzanine floor level ( since the loading is more in this floor due to presence of
mechanical rooms).Vertical deflection calculation for the beam which has maximum
deflection on that face is shown here.
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 30/01/09
TITLE: Clinic Building - Vertical Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
362 of 392
3.1. NORTH FACE
363 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
Deflection calculation (North Face) (Between grid 2-3) :-(Edge Beam 600X600)
Moment at critical section MQP = kN.m
From concrete properties (From table 1)
fctm = N/mm2
Ec28 = N/mm2
Creep�coeffiecient = (From figure 4)
Elastic�modulus�for�reinforcement Es = N/mm2
Ec28
Long term elastic modulus Eeff = ------------------- = ------------------------- = N/mm2
[ 1 + Ø (�,to) 1 +
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO
3700024666.67
0.5
DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
295
3.51
37000
0.5
200000
Es
Effective modular ratio �e = --------------- = ------------------------- =Eeff
Area of Tension reinforcement As = mm2
Area of Compression reinforcement As2 = mm2
Depth of beam h = mm Breadth b = mm
Clear cover = mm
Effective depth to tension reinf. d = mm
Depth to Compression reinf. d2 = mm
b.h2
------ + ( �e - 1) (As. d + As2. d2)2
Xu = -------------------------------------------------b.h + ( �e - 1) (As + As2)
x x----------------------------------- + ( - 1 ) x ( x + x 50 )
2= --------------------------------------------------------------------------------------------------------------------------------------------
x + ( - 1 ) x ( + )
2000008.11
24666.67
2130
521
600 600
40
540
50
600 600 6008.11 2130 540 521
600 600 8.11 2130 521
364 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
= mm
b . h3 h 2Iu = ------- + b. h { --- - Xu } + ( �e - 1) (As.( d - Xu)2+ As2.(Xu- d2)
2)12 2
x x x= ------------------------------------------------- + x { - }2 +
( - 1 ) x { x ( - )2 + ( - )2 }
= + +
= mm4
12 2
307.15
600 600 600 600 600
521 307.15
600 600 ----- 307.15
50
1.1E+10 1.8E+07 1.07E+09
1.2E+10
8.11 2130 540 307.15
Cracking moment
0.9. fctm. Iu x xMcr = ----------------- = ------------------------------------------ = kN.m
h - Xu -
Mcr < MQP Cracked Section, So again calculate Ic & Xc.
� = 1 - 0.5 (Mcr/MQP)
= 1 - x ( / )2
=
{ [ ( As. �e�+�As2.�(�e���1)2�+�2b�(�As.�d.��e�+As2.�d2�(�e���1))]0.5���(As.��e�+�As2.�(�e���1)�)}�
Xc = --------------------------------------------------------------------------------------------------------------------b
{ x + x ( - 1 )2
+ 2 x x ( x x + x x ( - 1 ) ) }0.5
- x + ( - 1 )= -----------------------------------------------------------------------------------------------------------------------------------------------
0.9 3.51 1.2E+10128.19
600 307.15
0.5 128.19 295.00
0.906
2130 8.11 521 8.11
600 2130 540 8.11 521 50 8.11
2130 8.11 521 8.11
600
365 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
= ( + )0.5 -------------------------------------------------------------------------------
Xc = mm
b . Xc3
Ic = ------- + ( �e .As.( d - Xc)2+( �e-1)As2.(d2-Xc)2)3
x 3
= -------------------------- + x x ( - )2 + ( - 1 ) x3
x ( - )2
= + +
4.399E+08 1.14E+10 2.10E+04
600
146.50
600 146.58.11 2130 540 146.5 8.11
521 50 146.50
6.3E+08 2.7E+09 3.4E+07
= mm4
Flexural curvature
1 MQP MQP
------ = � ----------------- + ( 1 - � ) ------------rn Eeff x Ic Eeff x Iu
= x -------------------------------------- + ( 1 - ) x -----------------------------------------x x
= +1
---- =rn
Total strinkage strain
� cd = Kh .�cd,0 = Drying shrinkage strain
Kh = Coefficient based on notional size, see Table 2. =
�cd,0 = Nominal unrestrained drying shrinkage, see Table 1. =
� cd =
� ca = Micro strain From Table 1
3.3E+09
2.95E+08 3E+080.906 0.906
24666.67 3.3E+09 24666.67 1.2E+10
3.2E-06 9.5E-08
3.3E-06
0.75
598
449
75
366 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
� cs = � cd + � ca
= +
=
1 Su Sc
------ = � �cs.��e.� ----- + ( 1 - �) �cs.��e.� ------rcs Iu Ic
Su = As (d-Xu) - As2 (Xu - d2)
= x ( - ) - ( - )
= mm3
Sc = As (d-Xc) - As2 (Xc - d2)
( ) ( )
449 75
5.24E-04
2130 540 307.15 521 307.15 50
3.6E+05
2130 540 146 50 521 146 50 50= x ( - ) - ( - )
= mm3
1------ = x x x ------------------ + ( 1 - ) x xrcs
x x -------------------
1------ =rcs
1 1 1------ = ------ + ----- = + =rt,QP rn rcs
Total deflection1
QP = K. L2. -------------------rt,QP
K = 0.104 x ( 1 - (/10))
2130 540 146.50 521 146.50 50
7.9E+05
3.62E+050.91 5.2E-04 8.11 0.91 5.24E-04
1.19E+107.88E+05
8.113.34E+09
2.12E-07
3.34E-06 2.12E-07 3.55E-06
367 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
Edge Beam :-
Bending moment
Span of beam, L = m
Negative moment at the continous edge MA = (From ETABS Model)
Negative moment at the continous edge MB = (From ETABS Model)
Positive moment at midspan MC = (From ETABS Model)
MA + MB + = --------------- = ---------------------------- =
Mc
K = x ( 1 - --------- )
10.8
397.00
472.00
295.00
397.000 472.0002.95
295.000
2.950.104
10
K =
QP = x x x
QP = mm < = mm----------10800
250
43.230.39 Hence Safe
10
0.0734
0.0734 10800 10800 3.55E-06
368 of 392
3.2. EAST FACE
369 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
Deflection calculation (East face) (Between grid B-C) :-(Edge Beam 600x600)
Moment at critical section MQP = kN.m
From concrete properties (From table 1)
fctm = N/mm2
Ec28 = N/mm2
Creep�coeffiecient = (From figure 4)
Elastic�modulus�for�reinforcement Es = N/mm2
Ec28
Long term elastic modulus Eeff = ------------------- = ------------------------- = N/mm2
[ 1 + Ø (�,to) 1 +
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO
3700024666.67
0.5
DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
342
3.51
37000
0.5
200000
Es
Effective modular ratio �e = --------------- = ------------------------- =Eeff
Area of Tension reinforcement As = mm2
Area of Compression reinforcement As2 = mm2
Depth of beam h = mm Breadth b = mm
Clear cover = mm
Effective depth to tension reinf. d = mm
Depth to Compression reinf. d2 = mm
b.h2
------ + ( �e - 1) (As. d + As2. d2)2
Xu = -------------------------------------------------b.h + ( �e - 1) (As + As2)
x x----------------------------------- + ( - 1 ) x ( x + x 63 )
2= --------------------------------------------------------------------------------------------------------------------------------------------
x + ( - 1 ) x ( + )
2000008.11
24666.67
2500
521
600 600
40
540
62.5
600 600 6008.11 2500 540 521
600 600 8.11 2500 521
370 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
= mm
b . h3 h 2Iu = ------- + b. h { --- - Xu } + ( �e - 1) (As.( d - Xu)2+ As2.(Xu- d2)
2)12 2
x x x= ------------------------------------------------- + x { - }2 +
( - 1 ) x { x ( - )2 + ( - )2 }
= + +
= mm4
12 2
308.87
600 600 600 600 600
521 308.87
600 600 ----- 308.87
62.5
1.1E+10 2.8E+07 1.17E+09
1.2E+10
8.11 2500 540 308.87
Cracking moment
0.9. fctm. Iu x xMcr = ----------------- = ------------------------------------------ = kN.m
h - Xu -
Mcr < MQP Cracked Section, So again calculate Ic & Xc.
� = 1 - 0.5 (Mcr/MQP)
= 1 - x ( / )2
=
{ [ ( As. �e�+�As2.�(�e���1)2�+�2b�(�As.�d.��e�+As2.�d2�(�e���1))]0.5���(As.��e�+�As2.�(�e���1)�)}�
Xc = --------------------------------------------------------------------------------------------------------------------b
{ x + x ( - 1 )2
+ 2 x x ( x x + x x ( - 1 ) ) }0.5
- x + ( - 1 )= -----------------------------------------------------------------------------------------------------------------------------------------------
0.9 3.51 1.2E+10130.24
600 308.87
0.5 130.24 342.00
0.927
2500 8.11 521 8.11
600 2500 540 8.11 521 62.5 8.11
2500 8.11 521 8.11
600
371 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
= ( + )0.5 -------------------------------------------------------------------------------
Xc = mm
b . Xc3
Ic = ------- + ( �e .As.( d - Xc)2+( �e-1)As2.(d2-Xc)2)3
x 3
= -------------------------- + x x ( - )2 + ( - 1 ) x3
x ( - )2
= + +
5.747E+08 1.34E+10 2.40E+04
600
157.16
600 157.28.11 2500 540 157.2 8.11
521 62.5 157.16
7.8E+08 3E+09 3.3E+07
= mm4
Flexural curvature
1 MQP MQP
------ = � ----------------- + ( 1 - � ) ------------rn Eeff x Ic Eeff x Iu
= x -------------------------------------- + ( 1 - ) x -----------------------------------------x x
= +1
---- =rn
Total strinkage strain
� cd = Kh .�cd,0 = Drying shrinkage strain
Kh = Coefficient based on notional size, see Table 2. =
�cd,0 = Nominal unrestrained drying shrinkage, see Table 1. =
� cd =
� ca = Micro strain From Table 1
3.8E+09
3.42E+08 3.4E+080.927 0.927
24666.67 3.8E+09 24666.67 1.2E+10
3.4E-06 8.4E-08
3.5E-06
0.75
598
449
75
372 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
� cs = � cd + � ca
= +
=
1 Su Sc
------ = � �cs.��e.� ----- + ( 1 - �) �cs.��e.� ------rcs Iu Ic
Su = As (d-Xu) - As2 (Xu - d2)
= x ( - ) - ( - )
= mm3
Sc = As (d-Xc) - As2 (Xc - d2)
( ) ( )
449 75
5.24E-04
2500 540 308.87 521 308.87 63
4.5E+05
2500 540 157 16 521 157 16 63= x ( - ) - ( - )
= mm3
1------ = x x x ----------------- + ( 1 - ) x xrcs
x x -------------------
1------ =rcs
1 1 1------ = ------ + ----- = + =rt,QP rn rcs
Total deflection1
QP = K. L2. -------------------rt,QP
K = 0.104 x ( 1 - (/10))
2500 540 157.16 521 157.16 63
9.1E+05
4.49E+050.93 5.2E-04 8.11 0.93 5.24E-04
1.20E+109.08E+05
8.113.78E+09
2.21E-07
3.49E-06 2.21E-07 3.71E-06
373 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
Edge Beam :-
Bending moment
Span of beam, L = m
Negative moment at the continous edge MA = (From ETABS Model)
Negative moment at the continous edge MB = (From ETABS Model)
Positive moment at midspan MC = (From ETABS Model)
MA + MB + = --------------- = ---------------------------- =
Mc
K = x ( 1 - --------- )
10.8
480.00
542.00
342.00
480.000 542.0002.99
342.000
2.990.104
10
K =
QP = x x x
QP = mm < = mm----------
Hence Safe
250
43.231.53
10
0.0729
0.0729 10800 10800 3.71E-06
10800
374 of 392
3.3. SOUTH FACE
375 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
Deflection calculation (South face) (Between grid 7-8) :-(Edge Beam 600x600)
Moment at critical section MQP = kN.m
From concrete properties (From table 1)
fctm = N/mm2
Ec28 = N/mm2
Creep�coeffiecient = (From figure 4)
Elastic�modulus�for�reinforcement Es = N/mm2
Ec28
Long term elastic modulus Eeff = ------------------- = ------------------------- = N/mm2
[ 1 + Ø (�,to) 1 +
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO
3700024666.67
0.5
DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
112
3.51
37000
0.5
200000
Es
Effective modular ratio �e = --------------- = ------------------------- =Eeff
Area of Tension reinforcement As = mm2
Area of Compression reinforcement As2 = mm2
Depth of beam h = mm Breadth b = mm
Clear cover = mm
Effective depth to tension reinf. d = mm
Depth to Compression reinf. d2 = mm
b.h2
------ + ( �e - 1) (As. d + As2. d2)2
Xu = -------------------------------------------------b.h + ( �e - 1) (As + As2)
x x----------------------------------- + ( - 1 ) x ( x + x 63 )
2= --------------------------------------------------------------------------------------------------------------------------------------------
x + ( - 1 ) x ( + )
2000008.11
24666.67
1000
521
600 600
40
540
62.5
600 600 6008.11 1000 540 521
600 600 8.11 1000 521
376 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
= mm
b . h3 h 2Iu = ------- + b. h { --- - Xu } + ( �e - 1) (As.( d - Xu)2+ As2.(Xu- d2)
2)12 2
x x x= ------------------------------------------------- + x { - }2 +
( - 1 ) x { x ( - )2 + ( - )2 }
= + +
= mm4
12 2
302.23
600 600 600 600 600
521 302.23
600 600 ----- 302.23
62.5
1.1E+10 1788066 6.15E+08
1.1E+10
8.11 1000 540 302.23
Cracking moment
0.9. fctm. Iu x xMcr = ----------------- = ------------------------------------------ = kN.m
h - Xu -
Mcr > MQP Un-cracked section
� = 1 - 0.5 (Mcr/MQP)
= 1 - x ( / )2
=
{ [ ( As. �e�+�As2.�(�e���1)2�+�2b�(�As.�d.��e�+As2.�d2�(�e���1))]0.5���(As.��e�+�As2.�(�e���1)�)}�
Xc = --------------------------------------------------------------------------------------------------------------------b
{ x + x ( - 1 )2
+ 2 x x ( x x + x x ( - 1 ) ) }0.5
- x + ( - 1 )= -----------------------------------------------------------------------------------------------------------------------------------------------
0.9 3.51 1.1E+10121.12
600 302.23
0.5 121.12 112.00
0.415
1000 8.11 521 8.11
600 1000 540 8.11 521 62.5 8.11
1000 8.11 521 8.11
600
377 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
= ( + )0.5 -------------------------------------------------------------------------------
Xc = mm
b . Xc3
Ic = ------- + ( �e .As.( d - Xc)2+( �e-1)As2.(d2-Xc)2)3
x 3
= -------------------------- + x x ( - )2 + ( - 1 ) x3
x ( - )2
= + +
1.395E+08 5.53E+09 1.18E+04
600
105.83
600 105.88.11 1000 540 105.8 8.11
521 62.5 105.83
2.4E+08 1.5E+09 7.0E+06
= mm4
Flexural curvature
1 MQP MQP
------ = � ----------------- + ( 1 - � ) ------------rn Eeff x Ic Eeff x Iu
= x -------------------------------------- + ( 1 - ) x -----------------------------------------x x
= +1
---- =rn
Total strinkage strain
� cd = Kh .�cd,0 = Drying shrinkage strain
Kh = Coefficient based on notional size, see Table 2. =
�cd,0 = Nominal unrestrained drying shrinkage, see Table 1. =
� cd =
� ca = Micro strain From Table 1
1.8E+09
1.12E+08 1.1E+080.415 0.415
24666.67 1.8E+09 24666.67 1.1E+10
1.1E-06 2.3E-07
1.3E-06
0.75
598
449
75
378 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
� cs = � cd + � ca
= +
=
1 Su Sc
------ = � �cs.��e.� ----- + ( 1 - �) �cs.��e.� ------rcs Iu Ic
Su = As (d-Xu) - As2 (Xu - d2)
= x ( - ) - ( - )
= mm3
Sc = As (d-Xc) - As2 (Xc - d2)
( ) ( )
449 75
5.24E-04
1000 540 302.23 521 302.23 63
1.1E+05
1000 540 105 83 521 105 83 63= x ( - ) - ( - )
= mm3
1------ = x x x ----------------- + ( 1 - ) x xrcs
x x -------------------
1------ =rcs
1 1 1------ = ------ + ----- = + =rt,QP rn rcs
Total deflection1
QP = K. L2. -------------------rt,QP
K = 0.104 x ( 1 - (/10))
1000 540 105.83 521 105.83 63
4.1E+05
1.13E+050.42 5.2E-04 8.11 0.42 5.24E-04
1.14E+104.12E+05
8.111.77E+09
5.94E-07
1.30E-06 5.94E-07 1.89E-06
379 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
Edge Beam :-
Bending moment
Span of beam, L = m
Negative moment at the continous edge MA = (From ETABS Model)
Negative moment at the continous edge MB = (From ETABS Model)
Positive moment at midspan MC = (From ETABS Model)
MA + MB + = --------------- = ---------------------------- =
Mc
K = x ( 1 - --------- )
6.65
10.00
305.00
112.00
10.000 305.0002.81
112.000
2.810.104
10
K =
QP = x x x
QP = mm < = mm----------
Hence Safe
250
26.66.25
10
0.0748
0.0748 6650 6650 1.89E-06
6650
380 of 392
3.4. WEST FACE CURVED PORTION
381 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
Deflection calculation (West Face curved portion) (Between grids 5.2-6) :-(Edge beam 600x600)
Moment at critical section MQP = kN.m
From concrete properties (From table 1)
fctm = N/mm2
Ec28 = N/mm2
Creep�coeffiecient = (From figure 4)
Elastic�modulus�for�reinforcement Es = N/mm2
Ec28
Long term elastic modulus Eeff = ------------------- = ------------------------- = N/mm2
[ 1 + Ø (�,to) 1 +
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO
3700024666.67
0.5
DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
478
3.51
37000
0.5
200000
Es
Effective modular ratio �e = --------------- = ------------------------- =Eeff
Area of Tension reinforcement As = mm2
Area of Compression reinforcement As2 = mm2
Depth of beam h = mm Breadth b = mm
Clear cover = mm
Effective depth to tension reinf. d = mm
Depth to Compression reinf. d2 = mm
b.h2
------ + ( �e - 1) (As. d + As2. d2)2
Xu = -------------------------------------------------b.h + ( �e - 1) (As + As2)
x x----------------------------------- + ( - 1 ) x ( x + x 63 )
2= --------------------------------------------------------------------------------------------------------------------------------------------
x + ( - 1 ) x ( + )
2000008.11
24666.67
4500
521
600 600
40
540
62.5
600 600 6008.11 4500 540 521
600 600 8.11 4500 521
382 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
= mm
b . h3 h 2Iu = ------- + b. h { --- - Xu } + ( �e - 1) (As.( d - Xu)2+ As2.(Xu- d2)
2)12 2
x x x= ------------------------------------------------- + x { - }2 +
( - 1 ) x { x ( - )2 + ( - )2 }
= + +
= mm4
12 2
317.18
600 600 600 600 600
521 317.18
600 600 ----- 317.18
62.5
1.1E+10 1.1E+08 1.83E+09
1.3E+10
8.11 4500 540 317.18
Cracking moment
0.9. fctm. Iu x xMcr = ----------------- = ------------------------------------------ = kN.m
h - Xu -
Mcr < MQP Cracked Section, So again calculate Ic & Xc.
� = 1 - 0.5 (Mcr/MQP)
= 1 - x ( / )2
=
{ [ ( As. �e�+�As2.�(�e���1)2�+�2b�(�As.�d.��e�+As2.�d2�(�e���1))]0.5���(As.��e�+�As2.�(�e���1)�)}�
Xc = --------------------------------------------------------------------------------------------------------------------b
{ x + x ( - 1 )2
+ 2 x x ( x x + x x ( - 1 ) ) }0.5
- x + ( - 1 )= -----------------------------------------------------------------------------------------------------------------------------------------------
0.9 3.51 1.3E+10142.24
600 317.18
0.5 142.24 478.00
0.956
4500 8.11 521 8.11
600 4500 540 8.11 521 62.5 8.11
4500 8.11 521 8.11
600
383 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
= ( + )0.5 -------------------------------------------------------------------------------
Xc = mm
b . Xc3
Ic = ------- + ( �e .As.( d - Xc)2+( �e-1)As2.(d2-Xc)2)3
x 3
= -------------------------- + x x ( - )2 + ( - 1 ) x3
x ( - )2
= + +
1.615E+09 2.39E+10 4.02E+04
600
199.35
600 199.48.11 4500 540 199.4 8.11
521 62.5 199.35
1.6E+09 4.2E+09 6.9E+07
= mm4
Flexural curvature
1 MQP MQP
------ = � ----------------- + ( 1 - � ) ------------rn Eeff x Ic Eeff x Iu
= x -------------------------------------- + ( 1 - ) x -----------------------------------------x x
= +1
---- =rn
Total strinkage strain
� cd = Kh .�cd,0 = Drying shrinkage strain
Kh = Coefficient based on notional size, see Table 2. =
�cd,0 = Nominal unrestrained drying shrinkage, see Table 1. =
� cd =
� ca = Micro strain From Table 1
5.9E+09
4.78E+08 4.8E+080.956 0.956
24666.67 5.9E+09 24666.67 1.3E+10
3.1E-06 6.7E-08
3.2E-06
0.75
598
449
75
384 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
� cs = � cd + � ca
= +
=
1 Su Sc
------ = � �cs.��e.� ----- + ( 1 - �) �cs.��e.� ------rcs Iu Ic
Su = As (d-Xu) - As2 (Xu - d2)
= x ( - ) - ( - )
= mm3
Sc = As (d-Xc) - As2 (Xc - d2)
( ) ( )
449 75
5.24E-04
4500 540 317.18 521 317.18 63
8.7E+05
4500 540 199 35 521 199 35 63= x ( - ) - ( - )
= mm3
1------ = x x x ----------------- + ( 1 - ) x xrcs
x x -------------------
1------ =rcs
1 1 1------ = ------ + ----- = + =rt,QP rn rcs
Total deflection1
QP = K. L2. -------------------rt,QP
K = 0.104 x ( 1 - (/10))
4500 540 199.35 521 199.35 63
1.5E+06
8.70E+050.96 5.2E-04 8.11 0.96 5.24E-04
1.27E+101.46E+06
8.115.89E+09
3.24E-07
3.21E-06 3.24E-07 3.54E-06
385 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
Edge Beam :-
Bending moment
Span of beam, L = m
Negative moment at the continous edge MA = (From ETABS Model)
Negative moment at the continous edge MB = (From ETABS Model)
Positive moment at midspan MC = (From ETABS Model)
MA + MB + = --------------- = ---------------------------- =
Mc
K = x ( 1 - --------- )
14.28
850.00
326.00
478.00
850.000 326.0002.46
478.000
2.460.104
10
K =
QP = x x x
QP = mm < = mm----------
57.1 Hence Safe
250
56.55
10
0.0784
0.0784 14280 14280 3.54E-06
14280
386 of 392
3.5. WEST FACE
387 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
Deflection calculation (West Face) (Between grids H & J) :-(Edge beam 600x600)
Moment at critical section MQP = kN.m
From concrete properties (From table 1)
fctm = N/mm2
Ec28 = N/mm2
Creep�coeffiecient = (From figure 4)
Elastic�modulus�for�reinforcement Es = N/mm2
Ec28
Long term elastic modulus Eeff = ------------------- = ------------------------- = N/mm2
[ 1 + Ø (�,to) 1 +
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO
3700024666.67
0.5
DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
315
3.51
37000
0.5
200000
Es
Effective modular ratio �e = --------------- = ------------------------- =Eeff
Area of Tension reinforcement As = mm2
Area of Compression reinforcement As2 = mm2
Depth of beam h = mm Breadth b = mm
Clear cover = mm
Effective depth to tension reinf. d = mm
Depth to Compression reinf. d2 = mm
b.h2
------ + ( �e - 1) (As. d + As2. d2)2
Xu = -------------------------------------------------b.h + ( �e - 1) (As + As2)
x x----------------------------------- + ( - 1 ) x ( x + x 63 )
2= --------------------------------------------------------------------------------------------------------------------------------------------
x + ( - 1 ) x ( + )
2000008.11
24666.67
2300
521
600 600
40
540
62.5
600 600 6008.11 2300 540 521
600 600 8.11 2300 521
388 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
= mm
b . h3 h 2Iu = ------- + b. h { --- - Xu } + ( �e - 1) (As.( d - Xu)2+ As2.(Xu- d2)
2)12 2
x x x= ------------------------------------------------- + x { - }2 +
( - 1 ) x { x ( - )2 + ( - )2 }
= + +
= mm4
12 2
308.01
600 600 600 600 600
521 308.01
600 600 ----- 308.01
62.5
1.1E+10 2.3E+07 1.1E+09
1.2E+10
8.11 2300 540 308.01
Cracking moment
0.9. fctm. Iu x xMcr = ----------------- = ------------------------------------------ = kN.m
h - Xu -
Mcr < MQP Cracked Section, So again calculate Ic & Xc.
� = 1 - 0.5 (Mcr/MQP)
= 1 - x ( / )2
=
{ [ ( As. �e�+�As2.�(�e���1)2�+�2b�(�As.�d.��e�+As2.�d2�(�e���1))]0.5���(As.��e�+�As2.�(�e���1)�)}�
Xc = --------------------------------------------------------------------------------------------------------------------b
{ x + x ( - 1 )2
+ 2 x x ( x x + x x ( - 1 ) ) }0.5
- x + ( - 1 )= -----------------------------------------------------------------------------------------------------------------------------------------------
0.9 3.51 1.2E+10129.03
600 308.01
0.5 129.03 315.00
0.916
2300 8.11 521 8.11
600 2300 540 8.11 521 62.5 8.11
2300 8.11 521 8.11
600
389 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
= ( + )0.5 -------------------------------------------------------------------------------
Xc = mm
b . Xc3
Ic = ------- + ( �e .As.( d - Xc)2+( �e-1)As2.(d2-Xc)2)3
x 3
= -------------------------- + x x ( - )2 + ( - 1 ) x3
x ( - )2
= + +
4.996E+08 1.24E+10 2.24E+04
600
151.76
600 151.88.11 2300 540 151.8 8.11
521 62.5 151.76
7E+08 2.8E+09 3.0E+07
= mm4
Flexural curvature
1 MQP MQP
------ = � ----------------- + ( 1 - � ) ------------rn Eeff x Ic Eeff x Iu
= x -------------------------------------- + ( 1 - ) x -----------------------------------------x x
= +1
---- =rn
Total strinkage strain
� cd = Kh .�cd,0 = Drying shrinkage strain
Kh = Coefficient based on notional size, see Table 2. =
�cd,0 = Nominal unrestrained drying shrinkage, see Table 1. =
� cd =
� ca = Micro strain From Table 1
3.5E+09
3.15E+08 3.2E+080.916 0.916
24666.67 3.5E+09 24666.67 1.2E+10
3.3E-06 9.0E-08
3.4E-06
0.75
598
449
75
390 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
� cs = � cd + � ca
= +
=
1 Su Sc
------ = � �cs.��e.� ----- + ( 1 - �) �cs.��e.� ------rcs Iu Ic
Su = As (d-Xu) - As2 (Xu - d2)
= x ( - ) - ( - )
= mm3
Sc = As (d-Xc) - As2 (Xc - d2)
( ) ( )
449 75
5.24E-04
2300 540 308.01 521 308.01 63
4.1E+05
2300 540 151 76 521 151 76 63= x ( - ) - ( - )
= mm3
1------ = x x x ----------------- + ( 1 - ) x xrcs
x x -------------------
1------ =rcs
1 1 1------ = ------ + ----- = + =rt,QP rn rcs
Total deflection1
QP = K. L2. -------------------rt,QP
K = 0.104 x ( 1 - (/10))
2300 540 151.76 521 151.76 63
8.5E+05
4.06E+050.92 5.2E-04 8.11 0.92 5.24E-04
1.19E+108.46E+05
8.113.54E+09
2.17E-07
3.40E-06 2.17E-07 3.61E-06
391 of 392
LARSEN & TOUBRO LIMITED ECC Division - GES
PROJECT: SIDRA MEDICAL & RESEARCH CENTER, DOHADOCUMENT NO DATE
1861B-CS-05-002-03 1/30/2009
TITLE: Clinic Building - Deflection CalculationDESIGNED CHECKED SHEET
RR JSB/MDS
Edge Beam :-
Bending moment
Span of beam, L = m
Negative moment at the continous edge MA = (From ETABS Model)
Negative moment at the continous edge MB = (From ETABS Model)
Positive moment at midspan MC = (From ETABS Model)
MA + MB + = --------------- = ---------------------------- =
Mc
K = x ( 1 - --------- )
10.83
422.00
530.00
315.00
422.000 530.0003.02
315.000
3.020.104
10
K =
QP = x x x
QP = mm < = mm----------
43.3 Hence Safe
250
30.75
10
0.0726
0.0726 10830 10830 3.61E-06
10830
392 of 392