DESIGN OF BEAMS

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1. The design of beams is using core program listed below:

BEAM DESIGN PROGRAM (BEAM-2013) Version 5.0
The core program had been approved by BD. The BD reference number is S0919.

2. The bending moments and shears of continuous beams are calculated by

stiffness method.

3. The design data:

Main bars -- High tensile steel, fy = 500.0 N/mm2
Stirrup -- High tensile steel, fy = 500.0 N/mm2
Minimum reinforcement ratio = 0.20%
Maximum redistribution factor:
Hogging moment : 0%
Sagging moment : 0%
Designed support moments are taken at 0.500 B, where B is the width of
column support

4. The load combinations and values of partial safety factors for ULS:
Dead Load Imposed Load Earth &
Load Combination Adverse Beneficial Adverse Beneficial Water Wind
D.L.+L.L.+EARTH 1.40 1.00 1.60 0.00 1.40 ----
D.L.+EARTH+WIND 1.40 1.00 ---- ---- 1.40 1.40
D.L.+L.L.+EARTH+WIND 1.20 1.00 1.20 0.00 1.20 1.20

5. The load combinations and values of partial safety factors for FLS:
The load combination factors for fire limit state:
Dead load 1.00
Permanent live load, escape stairs and lobbies 1.00
Non-ermanent live load in other area 0.80
Lateral soil load 0.80
Lateral wind load 0.33
The partial safety factors for fire limit state:
For concrete (flexure) 1.100
For concrete (shear) 1.100
For steel bars 1.000

6. The load combinations for Serviceability Limit State:

All factors are 1.0.

7. The following loading types are available: Point load in kN, concentrated
moment in kN-M and other distributed load in kN/M.

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 [1] Concentrated load. [2] Uniformly dist. load.

a a b
[3] Triangular dist. load. [4] Trapezoidal Dist. load.

c c
a b a b
[5] Tri. dist. load (LHS). [6] Tri. dist. load (RHS).

a b a b
[7] Concentrated moment.

8. The reinforcement of beam section is calculated accordance with CP-2013.

When exposure class of beam to be classified as "0.1mm", "0.2mm" or "0.3mm",
the reinforced bars of beam are calculated accordance with BS-8007.

9. The calculation options are listed as below.

(1) The requirements of PNAP173 are included.
(2) The requirements of detailing of ductility are included.

10. The notations in program output are described as below:

(1) Fire Limit State data:
Design Temperature : The temperature for designing Fire Limit State.
Reduction : Strength reduction factors for concrete and steel bar taken
from Table 3.5 and 3.6 in Clause 3.6 of CoP 2013.
(2) Beam data:
L : Span of beam, unit: M.
Sec. : Size of beam section, unit: mm.

(3) Load data:

Type : Description of loading type.
D.L. : Value of dead load, unit: kN or kN/M.
LL(N) : Value of non-permanent imposed load, unit: kN or kN/M.
LL(P) : Value of permanent imposed load, unit: kN or kN/M.
Vehi : Optional output of vehicular traffic load.
Dyna : Optional output of vertical dynamic load.
Own W : Optional output of own weight load.
Uplift: Optional output of uplift load.
a : Position of concentrated load or the beginning position of
distributed load, unit: M.
b : Length of distributed load, unit: M.
c : Length of triangular part in load type 4, unit: M.

Concentrated Qk: The minimum concentrated load, unit: kN.

(4) Support data:

No. : Sequential numbers of supports.
Mark : Identification labels of supports.
Type : Type of support: Col., Beam, Hinge Wall and Fixed End.
Angle : The angle of local X axis of column.

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 B(Upper): Size of upper column perpendicular to beam span, unit: mm.
D(Upper): Size of upper column parallel to beam span, unit: mm.
H(Upper): Height of upper column, unit: M.
B(Lower): Size of Lower column perpendicular to beam span, unit: mm.
D(Lower): Size of lower column parallel to beam span, unit: mm.
H(Lower): Height of lower column, unit: M.

(5) Transferred shears and moments of beams:

Mark: Marks of beams.
Type: Type of load:
D.L. - dead load;
L.L.(N) - non-permanent imposed load;
L.L.(P) - permanent imposed load;
Vehi - vehicular traffic load;
H.A. - HA knife loading;
Dyna - vertical dynamic load;
O.W. - own weight load;
U.L. - uplift load.
FIXED END MOMENTS: Fixed end moments at both ends of beams.
HOGGING MOMENTS: Hogging moments at both ends of beams.
TRANSFERRED SHEARS: Reactions at both ends of beams.

(6) To Beam-column Joint:

Mark : Column mark that the BC joint is located.
Load Case : The load case that the load combunation factors is used.
DL+LL: All moments are applied with ULS dead and imposed load
combination factors.
D+L(W): All moments are applied with ULS dead, imposed and wind load
combination factors.
DL ONLY: All moments are applied with ULS dead load only combination
factors.
D+L(FLS): All moments are applied with FLS dead and imposed load
combination factors.
D ONLY(FLS): All moments are applied with FLS dead load only
combination factors.
Mlmin: The maximum hogging moment at LHS of joint, unit: kN-M.
Vcl : The column shear in anti-clockwise case, unit: kN.
Mrmax: The maximum sagging or minimum hogging moment at RHS of joint,
unit: kN-M.
Mlmax: The maximum sagging or minimum sagging moment at LHS of joint,
unit: kN-M.
Vcl : The column shear in clockwise case, unit: kN.
Mrmin: The maximum hogging moment at right end of beam, unit: kN-M.
(\) : The joint is in anti-clockwise case.
(/) : The joint is in clockwise case.

(7) Lateral loads:

Dirc. : The direction of the soil load.
Ms(LHS): Bending moments at left end of beams which is taken from
soil load. It will not be printed when there is no soil
load, unit: kN-M.
Ms(RHS): Bending moments at right end of beams which is taken from
soil load. It will not be printed when there is no soil
load, unit: kN-M.
Vs : Shears of beams which is taken from imported soil load.
Dirc. : The direction of wind load.
Mw(LHS): Bending moments at left end of beams which is taken from

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 wind load. It will not be printed when there is no wind
load, unit: kN-M.
Mw(RHS): Bending moments at right end of beams which is taken from
wind load. It will not be printed when there is no wind
load, unit: M.
Vw : Shears of beams which is taken from imported wind load.
Dirc. : The direction of dynamic load.
Mn(LHS): Bending moments at left end of beams which is taken from
dynamic bent. It will not be printed when there is no
dynamic load, unit: kN-M.
Mn(RHS): Bending moments at right end of beams which is taken from
dynamic bent. It will not be printed when there is no
dynamic load, unit: kN-M.
Vn : Shears of beams which is taken from imported dynamic load.
Note:
The bending moments and shears are printed at the edge of support.

(8) Crack checking:

Crack Width Limit: The maximum width of carck at concrete surface.
Checking position: Both faces contact with water.
Upper face contacts with water.
Lower face contacts with water.

(9) Calculation result:

Dist.(M): Distances between the center of left support to divided
points, unit: M.
-Mmax: Maximum hogging moments at divided points, unit: kN-M.
+Mmax: Maximum sagging moments at divided points, unit: kN-M.
: Redistribution ratio.
At(Top): The required area of tension bars at the top of beam, unit:
mm2.
Ac(Top): The required area of compressive bars at the top of beam,
unit: mm2.
d2(Top): Distance between the center of tension bars and top of beam,
unit: mm.
At(Bot): The required area of tension bars at the bottom of beam,
unit: mm2.
Ac(Bot): The required area of compression bars at the bottom of beam,
unit: mm2.
d2(Bot): Distance between the center of tension bars and bottom of
beam, unit: mm.
Vmax(kN): The maximum shear at divided points, unit: kN.
Av/s: The required area of stirrup per meter, unit: mm2/M.
Fmax(mm): The deflexion calculated by curvature method.

Span-Effective Depth Ratio: Calculated by effective depth span ratio.

Actual: The actual span-effectice depth ratio.
Allowable: The calculation result from Clause 7.3.4 of CP-2013.

Note: The output of hogging and sagging moment with bold font indicates
the section is controlled by Fire Limit State, with under line
indicates the section is controlled by crack checking, otherwise
with regular font indicates the section is controlled by Ultimate
Limit State.

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BEAM DESIGN PROGRAM (BEAM-2013) Version 5.0 BD Ref. No.: S0919
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CONTINUOUS BEAM :
Concrete : C45 fcu = 45
Main Bars: 500B fy = 500
Stirrup : 500B fyv = 500
Maximum Redistribution Factors: Hogging Moment = 0%, Sagging Moment = 0%
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* RB25 * L = 3.750 Sec.= 250x600
ST 150BW
RS13
Own W.

3.750

Type D.L. LL(N) LL(P) a b c

Own W. Uniform 3.675 0.000 0.000 0.000 3.750
RS13 Trapez. 7.520 8.813 0.000 0.000 3.750 0.500
ST Uniform 33.500 0.000 0.000 0.000 1.075
150BW Uniform 12.000 0.000 0.000 1.075 2.675
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SUPPORT OF BEAMS :
No. Mark Type Angle B D H B D H
-----------------------------------( Upper )------------( Lower )-----
1 X250 Col. 0.0 250 250 4.000 250 250 2.900
2 X250 Col. 0.0 250 250 4.000 250 250 2.900
----------------------------------------------------------------------

TRANSFERRED SHEARS AND MOMENTS OF BEAMS :

Mark Type FIXED END MOMENTS TRANSFERRED SHEARS
------------------------(LHS)--------(RHS)--------(LHS)--------(RHS)-
RB25 D.L. 35.074 28.753 61.570 44.764
L.L.(N) 9.984 9.984 14.320 14.320
L.L.(P) 0.000 0.000 0.000 0.000
---------------------------------------------------------------------

TO BEAM-COLUMN JOINT :
Mark Load Case Mlmin Vcl Mrmax Mlmax Vcl Mrmin
-------------------------------------(\)---------------------------(/)----------
X250 DL+LL 0.000 -2.592 -0.517 0.000 -1.349 -1.682
D+L(W) 0.000 -2.146 -0.517 0.000 -1.349 -1.339
DL ONLY 0.000 -1.889 -0.517 0.000 -1.349 -0.723
D+L(FLS) 0.000 -1.788 -0.517 0.000 -1.349 -1.473
D ONLY(FLS) 0.000 -1.349 -0.517 0.000 -1.349 -0.517
X250 DL+LL -3.550 -2.592 0.000 -1.851 -1.349 0.000
D+L(W) -2.940 -2.146 0.000 -1.851 -1.349 0.000
DL ONLY -2.592 -1.889 0.000 -1.851 -1.349 0.000
D+L(FLS) -2.807 -1.788 0.000 -1.851 -1.349 0.000
D ONLY(FLS) -1.851 -1.349 0.000 -1.851 -1.349 0.000
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FLOOR MARK : RF/F

* RB25 * L = 3.750 Sec.= 250x600

Wind Load: Dirc. Mw(LHS) Mw(RHS) Vw
A-A -1.000 1.800 -0.700
B-B 0.500 -1.000 0.400
C-C 1.100 -2.200 0.900
D-D 2.600 -5.100 2.000

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BEAM DESIGN PROGRAM (BEAM-2013) Version 5.0 BD Ref. No.: S0919
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E-E -0.700 1.200 -0.500
F-F 2.000 -3.900 1.600
G-G 0.500 -1.000 0.400
H-H 3.200 -6.200 2.500
I-I -1.300 2.400 -1.000
J-J 0.200 -0.400 0.200
K-K 0.800 -1.600 0.600
L-L 2.300 -4.500 1.800
M-M -1.000 1.900 -0.800
N-N 1.700 -3.300 1.300
O-O 0.200 -0.400 0.100
P-P 2.900 -5.500 2.200
Q-Q -0.400 0.700 -0.300
R-R 1.100 -2.100 0.900
S-S 0.800 -1.500 0.600
T-T 2.200 -4.400 1.800
U-U -1.000 1.900 -0.800
V-V 0.500 -1.000 0.400
W-W 0.200 -0.400 0.100
X-X 1.600 -3.200 1.300
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Dist.(M) 0.125 0.563 1.000 1.438 1.875 2.313 2.750 3.188 3.625
-Mmax -5.20 -11.27
Beta 1.000 1.000
+Mmax 3.96 36.78 61.01 72.53 75.06 68.67 53.37 30.13 6.83
Beta 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

Top : At 23 0 0 0 0 0 0 0 49
Ac 0 0 0 0 0 0 0 0 0
d2 48.0 48.0 48.0 48.0 48.0 48.0 48.0 48.0 48.0
......................................................................
Bot.: At 17 162 268 319 330 302 235 133 30
Ac 0 0 0 0 0 0 0 0 0
d2 50.0 50.0 50.0 50.0 50.0 50.0 50.0 50.0 50.0

Vmax(kN) 103.53 73.45 39.90 17.27 -7.91 -24.79 -45.17 -65.54 -82.45
Av/s 500 500 500 500 500 500 500 500 500

Span-Effective Depth Ratio : Actual = 6.818 < Allowable = 47.055 O.K.

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3T16 2T16 3T16

1.11 1.11

2T20

8T10 T10 8T10

DS.@150 DS.@225 DS.@150
RB25 (250x600)

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