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Beam Design

rns

Beam Design

General Presentation

The longitudinal and transversal beam computation will be performed

according to STAS 10107/90.

- finding the optimum reinforcement area - from the bending moment

diagram;

- stirrups computation, necessary section and distance between - from the

shear force diagram;

- torsion moment computation and design of necessary reinforcement for

torsion efforts.

Used materials: (according to STAS 10107/90)

Concrete: BC20 - Rc = 12.5 N/mm2 concrete compression strength

- Ra = 0,95 N/ mm2 concrete tension strength

Steel: PC52 - Ra = 300 N/ mm2 tension strength

-OB37- Ra = 210 N/ mm2 tension strength

For on bearing design a rectangular section is to be considered, the

compressed area being at the bottom of the section and the necessary

reinforcement area at the tensioned zone, which is at the top:

where:

ab-distance between reinforcement and the end of the section (concrete

cover);

b - width of the beam element; b=25cm

hp- slab height

h - height of the element; h=40cm

h0 - height where the reinforcement is placed;

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Beam Design

x - height of the compressed area.

=0F a

ca

R

bxRA =

x=*ho

ho=h-ab=40-2.5=37.5cm

co Rhb

MB

** 2= = 0041.0

125000*375.0*25.0

68.172

=

= B211 =0.0041

== Ra

RchbAoa

*** 2.28 cm

2

For Aa=2.283 cm2

For on field design section the compressed area being at the top of the

section and the necessary reinforcement area at the tensioned zone, which is at

the bottom:

where:

bp-active width of the slab;

bp=2*b+b

where b:

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Beam Design

005,0

*31,005,0

*61.0

=

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Beam Design

Column Design:

General Presentation

The design of columns should be made in special group of forces, taking

into account the maximum values of sectional efforts.

The design values of bending moment for columns are evaluated using the

formula:

column

beam

beam

cap

designM

M

McM

=//

*

where:

-Mcolumn is the value of bending moment in the column in special group of forces;

- //beam

capM is the sum of the absolute capable bending moment from the

extremities of the beam at the considered level, with the same rotation sign;- beamM is the algebraic summation of the values of the bending moment in thesame section in the special groups of forces;

- c coefficient corresponding to the seismic calculus zone, max 1.5 from pct.

3.1.2 STAS 10107/0-90

The design of columns are made taking into account the special

prescriptions from STAS 10107/0-90 from point 6.4.1 for columns with

important axial efforts:

= 05,0

cbhR

Nn

Used materials(according to STAS 10107/90):

Concrete: BC20 - Rc = 12.5 N/mm2 concrete compression strength

- Ra = 0,95 N/ mm2 concrete tension strength

Steel: PC52 - Ra = 300 N/ mm2 tension strength

-OB37- Ra = 210 N/ mm2 tension strength

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Beam Design

4.2.2 Column Checking:

The listing of ROBOT computation program provides us data for necessary

computation:

-2.0

-2.0

-1.0

-1.0

0.0

0.0

1.0

1.0

2.0

2.0

3.0

3.0

4.0

4.0

5.0

5.0

6.0

6.0

7.0

7.0

8.0

8.0

9.0

9.0

10.0

10.0

11.0

11.0

12.0

12.0

0.

00.0

1.0

1.0

2.0

2.0

3.0

3.0

4.

04.0

5.0

5.0

6.0

6.0

XY

Z

Node X (m) Z (m) Support code Support

1 2.60 0.0 xxx Fixed

2 2.60 3.20

3 2.60 6.00

4 5.20 0.0 xxx Fixed

5 5.20 3.206 5.20 3.00

de 7 5.20 6.00

8 7.80 0.0 xxx Fixed

9 7.80 3.20

10 7.80 3.00

11 7.80 6.00

12 1.30 3.20

13 0.0 3.20 xxf Pinned

14 3.90 3.20

15 6.50 3.20

16 10.00 3.20 xxf Pinned

17 1.30 6.00

18 0.0 6.00 xxf Pinned

19 3.90 6.00

20 6.50 6.00

21 10.00 6.00 xxf Pinned

22 8.90 3.20

23 8.90 6.00

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Beam Design

Node X (m) Z (m) Support code Support

1 2.60 0.0 xxx Fixed

2 2.60 3.20

3 2.60 6.00

4 5.20 0.0 xxx Fixed

5 5.20 3.206 5.20 3.00

de 7 5.20 6.00

8 7.80 0.0 xxx Fixed

9 7.80 3.20

10 7.80 3.00

11 7.80 6.00

12 1.30 3.20

13 0.0 3.20 xxf Pinned

14 3.90 3.20

15 6.50 3.20

16 10.00 3.20 xxf Pinned

17 1.30 6.00

18 0.0 6.00 xxf Pinned19 3.90 6.00

20 6.50 6.00

21 10.00 6.00 xxf Pinned

22 8.90 3.20

23 8.90 6.00

Section name Bar list AX

(cm^2)

AY

(cm^2)

AZ

(cm^2)

IX

(cm^4)

IY

(cm^4)

IZ

(cm^4)

C R30x30 1 2 5 24to26 900.000 750.000 750.000 113872.

301

67500.0

00

67500.0

00B R15x30 7to12 14to23 450.000 375.000 375.000 23154.3

27

33750.0

00

8437.50

0

Cas

e

1 self-weight 1 2 57to12

14to23

PZ Negative

PZ=-13.30(kN/m)

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Beam Design

Node/Case/Mode FX (kN) FZ (kN) MY (kNm)

1/ 1/ -0.44 97.06 -0.48

1/ 2/ -0.14 27.12 -0.15

1/ 4/ SRSS 0.04 1.03 0.05

1/ 5 (K)/ -0.70 146.87 -0.75

1/ 6 (K) (CQC)/ -0.51 117.30 -0.544/ 1/ 0.00 74.55 -0.00

4/ 2/ 0.00 24.00 0.00

4/ 4/ SRSS 0.06 1.63 0.08

4/ 5 (K)/ 0.01 116.93 0.00

4/ 6 (K) (CQC)/ 0.07 92.34 0.08

8/ 1/ 0.01 83.41 0.01

8/ 2/ 0.00 24.68 0.00

8/ 4/ SRSS 0.05 1.48 0.06

8/ 5 (K)/ 0.02 128.00 0.02

8/ 6 (K) (CQC)/ 0.06 102.26 0.07

13/ 1/ -0.68 14.40 -0.00

13/ 2/ -0.21 4.64 0.0

13/ 4/ SRSS 1.70 0.14 0.0013/ 5 (K)/ -1.06 22.59 -0.00

13/ 6 (K) (CQC)/ 0.99 17.74 -0.00

16/ 1/ -0.24 12.16 0.00

16/ 2/ -0.07 3.92 -0.00

16/ 4/ SRSS 1.80 0.07 0.00

16/ 5 (K)/ -0.37 19.08 -0.00

16/ 6 (K) (CQC)/ 1.69 14.96 -0.00

18/ 1/ 1.01 14.57 0.00

18/ 2/ 0.32 4.69 -0.00

18/ 4/ SRSS 1.05 0.12 0.00

18/ 5 (K)/ 1.57 22.86 0.00

18/ 6 (K) (CQC)/ 2.28 18.01 0.00

21/ 1/ 0.35 12.24 -0.00

21/ 2/ 0.11 3.95 -0.0021/ 4/ SRSS 1.08 0.09 0.00

21/ 5 (K)/ 0.54 19.21 -0.00

21/ 6 (K) (CQC)/ 1.50 15.05 -0.00

Case DL1

Mode

Sum of val. 0.00 308.39 -0.47

Sum of reac. 0.00 308.39 -1529.93

Sum of forc. 0.0 -308.39 1529.93

Check val. 0.00 -0.00 0.00

Precision 5.24171e-017

2.08440e-031

Case LL1

Mode

Sum of val. 0.00 93.00 -0.15

Sum of reac. 0.00 93.00 -465.00

Sum of forc. 0.0 -93.00 465.00

Check val. 0.00 -0.00 0.00

Precision 5.03042e-

017

1.41025e-

031

Case Seismic

P100-92

Sum of val. 5.79 4.56 0.19

Sum of reac. 4.31 3.40 25.76

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Beam DesignSum of forc. 4.31 3.40 25.76

Check val. 8.63 6.79 51.53

Precision 8.70319e-004

1.45882e-005

Case COMB1

Mode

Sum of val. 0.00 475.55 -0.73

Sum of reac. 0.00 475.55 -2363.92Sum of forc. 0.0 -475.55 2363.92

Check val. 0.00 -0.00 0.00

Precision 1.25675e-

016

4.23038e-

031

Case COMB2

Mode

Sum of val. 6.07 377.66 -0.39

Sum of reac. 4.39 375.26 -1827.80

Sum of forc. 4.39 -371.72 1883.06

Check val. 8.79 3.54 55.27

Precision 1.25471e-003

1.51845e-005

Node/Case/Mode UX (cm) UZ (cm) RY (Rad)

1/ 1/ 0.0 0.0 0.0

1/ 2/ 0.0 0.0 0.0

1/ 4/ SRSS 0.0 0.0 0.0

1/ 5 (K)/ 0.0 0.0 0.0

1/ 6 (K) (CQC)/ 0.0 0.0 0.0

2/ 1/ 0.0001 -0.0088 -0.000

2/ 2/ 0.0000 -0.0025 -0.000

2/ 4/ SRSS 0.0003 0.0001 0.000

2/ 5 (K)/ 0.0002 -0.0134 -0.000

2/ 6 (K) (CQC)/ 0.0004 -0.0104 -0.0003/ 1/ -0.0002 -0.0124 -0.000

3/ 2/ -0.0000 -0.0036 -0.000

3/ 4/ SRSS 0.0002 0.0001 0.000

3/ 5 (K)/ -0.0002 -0.0190 -0.000

3/ 6 (K) (CQC)/ -0.0000 -0.0148 -0.000

4/ 1/ 0.0 0.0 0.0

4/ 2/ 0.0 0.0 0.0

4/ 4/ SRSS 0.0 0.0 0.0

4/ 5 (K)/ 0.0 0.0 0.0

4/ 6 (K) (CQC)/ 0.0 0.0 0.0

5/ 1/ 0.0001 -0.0070 0.000

5/ 2/ 0.0000 -0.0022 0.000

5/ 4/ SRSS 0.0004 0.0002 0.0005/ 5 (K)/ 0.0001 -0.0109 0.000

5/ 6 (K) (CQC)/ 0.0004 -0.0085 0.000

6/ 1/ 0.0001 -0.0065 0.000

6/ 2/ 0.0000 -0.0021 0.000

6/ 4/ SRSS 0.0004 0.0001 0.000

6/ 5 (K)/ 0.0001 -0.0103 0.000

6/ 6 (K) (CQC)/ 0.0005 -0.0079 0.000

7/ 1/ -0.0001 -0.0100 0.000

7/ 2/ -0.0000 -0.0032 0.000

7/ 4/ SRSS 0.0002 0.0002 0.000

7/ 5 (K)/ -0.0001 -0.0157 0.000

7/ 6 (K) (CQC)/ 0.0001 -0.0121 0.000

8/ 1/ 0.0 0.0 0.0

8/ 2/ 0.0 0.0 0.0

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Beam Design8/ 4/ SRSS 0.0 0.0 0.0

8/ 5 (K)/ 0.0 0.0 0.0

8/ 6 (K) (CQC)/ 0.0 0.0 0.0

9/ 1/ 0.0000 -0.0075 0.000

9/ 2/ 0.0000 -0.0023 0.000

9/ 4/ SRSS 0.0002 0.0001 0.000

9/ 5 (K)/ 0.0000 -0.0116 0.000

9/ 6 (K) (CQC)/ 0.0003 -0.0089 0.000

10/ 1/ 0.0000 -0.0070 0.00010/ 2/ 0.0000 -0.0022 0.000

10/ 4/ SRSS 0.0002 0.0001 0.000

10/ 5 (K)/ 0.0000 -0.0109 0.000

10/ 6 (K) (CQC)/ 0.0003 -0.0084 0.000

11/ 1/ -0.0000 -0.0106 -0.000

11/ 2/ -0.0000 -0.0033 -0.000

11/ 4/ SRSS 0.0001 0.0002 0.000

11/ 5 (K)/ -0.0001 -0.0165 -0.000

11/ 6 (K) (CQC)/ 0.0001 -0.0127 0.000

12/ 1/ 0.0001 -0.0342 -0.000

12/ 2/ 0.0000 -0.0108 -0.000

12/ 4/ SRSS 0.0001 0.0006 0.000

12/ 5 (K)/ 0.0001 -0.0534 -0.000

12/ 6 (K) (CQC)/ 0.0002 -0.0413 -0.000

13/ 1/ 0.0 0.0 0.000

13/ 2/ 0.0 0.0 0.000

13/ 4/ SRSS 0.0 0.0 0.000

13/ 5 (K)/ 0.0 0.0 0.001

13/ 6 (K) (CQC)/ 0.0 0.0 0.001

14/ 1/ 0.0001 -0.0203 -0.000

14/ 2/ 0.0000 -0.0064 0.000

14/ 4/ SRSS 0.0003 0.0004 0.000

14/ 5 (K)/ 0.0001 -0.0316 -0.000

14/ 6 (K) (CQC)/ 0.0004 -0.0245 -0.000

15/ 1/ 0.0000 -0.0206 0.000

15/ 2/ 0.0000 -0.0066 0.000

15/ 4/ SRSS 0.0003 0.0004 0.00015/ 5 (K)/ 0.0001 -0.0322 0.000

15/ 6 (K) (CQC)/ 0.0004 -0.0248 0.000

16/ 1/ 0.0 0.0 -0.000

16/ 2/ 0.0 0.0 -0.000

16/ 4/ SRSS 0.0 0.0 0.000

16/ 5 (K)/ 0.0 0.0 -0.000

16/ 6 (K) (CQC)/ 0.0 0.0 -0.000

17/ 1/ -0.0001 -0.0375 -0.000

17/ 2/ -0.0000 -0.0118 -0.000

17/ 4/ SRSS 0.0001 0.0006 0.000

17/ 5 (K)/ -0.0001 -0.0584 -0.000

17/ 6 (K) (CQC)/ -0.0000 -0.0449 -0.000

18/ 1/ 0.0 0.0 0.001

18/ 2/ 0.0 0.0 0.000

18/ 4/ SRSS 0.0 0.0 0.000

18/ 5 (K)/ 0.0 0.0 0.001

18/ 6 (K) (CQC)/ 0.0 0.0 0.001

19/ 1/ -0.0001 -0.0230 -0.000

19/ 2/ -0.0000 -0.0072 0.000

19/ 4/ SRSS 0.0002 0.0005 0.000

19/ 5 (K)/ -0.0002 -0.0359 -0.000

19/ 6 (K) (CQC)/ 0.0000 -0.0278 -0.000

20/ 1/ -0.0001 -0.0239 0.000

20/ 2/ -0.0000 -0.0077 0.000

20/ 4/ SRSS 0.0002 0.0008 0.000

20/ 5 (K)/ -0.0001 -0.0374 0.000

20/ 6 (K) (CQC)/ 0.0001 -0.0284 0.000

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Beam Design21/ 1/ 0.0 0.0 -0.000

21/ 2/ 0.0 0.0 -0.000

21/ 4/ SRSS 0.0 0.0 0.000

21/ 5 (K)/ 0.0 0.0 -0.001

21/ 6 (K) (CQC)/ 0.0 0.0 -0.000

22/ 1/ 0.0000 -0.0189 0.000

22/ 2/ 0.0000 -0.0060 0.000

22/ 4/ SRSS 0.0001 0.0003 0.000

22/ 5 (K)/ 0.0000 -0.0295 0.00022/ 6 (K) (CQC)/ 0.0001 -0.0229 0.000

23/ 1/ -0.0000 -0.0209 0.000

23/ 2/ -0.0000 -0.0067 0.000

23/ 4/ SRSS 0.0001 0.0003 0.000

23/ 5 (K)/ -0.0000 -0.0326 0.000

23/ 6 (K) (CQC)/ 0.0000 -0.0254 0.000

Bar FX (kN) FZ (kN) MY (kNm)

1 / MAX 146.87 0.70 1.47

1 / MIN 1.03 0.04 -0.75

2 / MAX 72.87 2.20 3.302 / MIN 0.55 0.08 -2.86

5 / MAX 128.00 0.38 0.02

5 / MIN 1.24 -0.02 -0.07

7 / MAX 1.62 36.19 10.27

7 / MIN -1.06 0.26 -17.68

8 / MAX 1.70 6.80 10.27

8 / MIN -1.06 -22.59 -0.18

9 / MAX 1.16 29.68 6.14

9 / MIN 0.09 0.08 -13.34

10 / MAX 0.94 0.33 6.14

10 / MIN 0.09 -29.10 -12.59

11 / MAX 0.96 29.42 6.37

11 / MIN 0.06 -0.00 -12.78

12 / MAX 1.18 0.17 6.37

12 / MIN 0.06 -29.36 -12.70

14 / MAX 2.20 35.93 10.61

14 / MIN 0.32 0.21 -16.99

15 / MAX 2.28 6.53 10.61

15 / MIN 0.32 -22.86 -0.15

16 / MAX 0.48 29.84 6.00

16 / MIN -0.63 0.11 -13.68

17 / MAX 0.28 0.45 6.00

17 / MIN -0.63 -28.95 -12.53

18 / MAX 0.41 29.46 6.42

18 / MIN -0.48 0.01 -12.78

19 / MAX 0.60 0.37 6.42

19 / MIN -0.48 -29.32 -12.6020 / MAX 2.20 30.66 7.31

20 / MIN 0.07 0.11 -12.73

21 / MAX 2.27 5.79 7.31

21 / MIN 0.07 -19.08 -0.08

22 / MAX 1.01 30.53 7.45

22 / MIN -0.54 0.13 -12.46

23 / MAX 1.08 5.66 7.45

23 / MIN -0.54 -19.21 -0.10

24 / MAX 59.86 0.10 0.14

24 / MIN 0.75 0.01 -0.13

25 / MAX 116.93 0.58 0.00

25 / MIN 1.38 -0.01 -0.08

26 / MAX 58.41 0.07 0.17

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Beam Design26 / MIN 0.86 -0.15 -0.39

S max

(MPa)

S min

(MPa)

S max(My)

(MPa)

S min(My)

(MPa)

Fx/Ax

(MPa)

MAX 7.83 1.47 7.86 0.0 1.63

Bar 7 1 7 8 1Node 2 1 2 13 1

Case 5 (K) 5 (K) 5 (K) 2 5 (K)

Mode

MIN -0.02 -7.88 0.0 -7.86 -0.02

Bar 8 7 8 7 8

Node 13 2 13 2 12

Case 5 (K) 5 (K) 2 5 (K) 5 (K)

Mode

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Beam Design

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Beam Design

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