3. Design Assumption and Beam Analysis

8/11/2019 3. Design Assumption and Beam Analysis

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REINFORCED CONCRETE

STRUCTURE I

Design AssumptionRevised : 17-September-2013

1

CIVIL ENGINEERING DEPARTMENT

FACULTY OF CIVIL ENGINEERING AND PLANNING

INSTITUT TEKNOLOGI SEPULUH NOPEMBER

SURABAYA

Prepared By : LB3


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Design Assumptions

1. Strain in reinforcement and concrete shall be assumed directly

proportional to the distance from the neutral axis.

2. Strain in steel and surrounding concrete is the same prior to

cracking of the concrete or yielding of the steel.

3. Tensile Strength of Concrete shall be neglected in flexural

calculation of reinforced concrete.

2Prepared By : LB3.


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3

Design Assumptions

4. Maximum usable strain at extreme concrete compression fiber

shall be assumed equal to u = 0.003.

5. Stress in reinforcement fs below the yield strength fy shall be

taken as Es times the steel strain s . For strains greater than

fy/Es, stress in reinforcement shall be considered independent

of strain and equal to fy.

6. Relationship between concrete compressive stress distribution

and concrete strain shall be assumed to be rectangular.


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Design Assumption #1

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6Prepared By : LB3

Parabolic Stress-Strain distribution in concrete may be considered satisfied by

an equivalent rectangular concrete stress distribution.

30MPa 58MPa

65.005.07

30'85.01

cf

SNI-03-2847-2002, pasal 12.2.7.3


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7Prepared By : LB3

Relationship between concrete compressive stress distribution and concrete

strain shall be assumed to be rectangular, trapezoidal, parabolic, or any othershape that results in prediction of strength in substantial agreement with results

of comprehensive tests.


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REINFORCED CONCRETE

STRUCTURE

Analysis and Design of Single RC Beam

Revised : 17-September-2013

9

CIVIL ENGINEERING DEPARTMENT

FACULTY OF CIVIL ENGINEERING AND PLANNING

INSTITUT TEKNOLOGI SEPULUH NOPEMBER

SURABAYA

Prepared By : LB3


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Balanced Strain Condition

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Condition where the yield of steel reinforcement and the crushing of outer concrete

compressive fiber occur at the same time.

Or condition when ultimate strain of concrete occur the same time as steel yield strain


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Strain linear relationship :

From force equilibrium :

11Prepared By : LB3

yu

ub

d

c

fyfyyu

u

600

600

200000/003.0

003.0

ybbc

ysbbc

bb

bdfcbf

fAbaf

TC

1

'

'

85.0

85.0

yy

cb

b

y

cb

ff

f

dc

ff

600

60085.0

85.0

'

1

'

1


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To ensure the structure is under reinforced condition :

Minimum reinforcement for flexural member :

12Prepared By : LB3

yy

cb

ff

f

600

60085.075.075.0

'

1max

db

f

db

f

fAs w

y

w

y

c 4.13 '

min


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Design of Reinforced Concrete Beam

Design of reinforced concrete beam is used to design the beam dimension with

only known moment forces. Other rules in RC design can also be based on ACI

318-99 or SNI 2847-2002.

13Prepared By : LB3


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Force Equilibrium :

Moment Equilibrium :

A nominal strength coefficient of resistance (Rn) is obtained when both sides of

Eq. above are divided by bd2:

14Prepared By : LB3

''

'

85.085.0

85.0

c

y

c

ys

yysc

f

df

bf

fAa

bdffAbaf

TC

'85.0

5.0

2

c

y

yn

n

f

fddbdfM

adTorCM

'285.0

5.01

c

y

yn

nf

ff

bd

MR


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When b and d are preset (determined), is obtained by solving the quadratic

equation for Rn :

Equation above can be used to determine the steel ratio given Mu or vice-versa

if the section properties b and q are known. Substituting Mn = Mu/ into

Equation above and divided each side by fc:

15Prepared By : LB3

'

'

1

2

'

2

85.0

2

11

85.0

085.0

5.0

c

n

y

c

c

y

f

R

f

f

Rnfyf

f

59.01

;85.0

5.01

2

'

'''2'

bdf

M

f

f

f

f

f

f

bdf

MR

c

u

c

y

c

y

c

y

c

un


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Example of design using graphics guide of single RC beam in flexure.

16Prepared By : LB3

Home Work :

1. Create a graphics for single

reinforced concrete beam with

various fcand fy.

2. Use the constraint of fy in onegraphics for example fy : 240

MPa, 300 MPa, 320 MPa, 350

MPa, 400 MPa.

3. Use several fc in one graphics

for example fc : 20 MPa, 25MPa, 30 MPa, 35 MPa, 40 MPa,

45 Mpa, 50 MPa.


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Example Design [1]

Example Design :

Design the concrete section of the beam, which is simple supported and are

loaded as below : [fc= 35 MPa, fy = 400 MPa].

17Prepared By : LB3

L=6m

Ql=1.5t/m;Qd=1t/m

kNmMMM

kNmtmlqM

kNmtmlqM

ldu

ll

dd

76.15815.666.11.442.16.12.1

15.6675.665.18

1

8

1

1.445.4618

1

8

1

22

22


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Example Design [1]

#1 Determine maximum reinforcement ration (max) for material strength fc=

35 MPa and fy = 400 MPa.

18Prepared By : LB3

65.0814.01

65.005.07

303585.01

65.005.07

30'85.01

cf

Calculating 1

Calculating max:

0272.0

400600

600

400

35814.085.075.0

600

60085.075.075.0

max

max

'

1max

fyfy

fcba l


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Example Design [1]

#2 Compute bd2required :

#3 Determine Size member so that bd2> bd2required :

Minimum Beam Depth (h) = d + cover + dh + db/2

Minimum Beam Depth (h) = 303.37 + 40 +10 + 8 = 361.37 mm 400 mm

d = h cover dh db/2 = 342 mm

19Prepared By : LB3

32

'22

23008696625.88.0

100000076.158

625.83585.0

4000272.05.014000272.0

85.0

5.01

mmRMbd

MPaR

f

ff

bd

M

bd

MR

n

u

n

c

y

yun

n

mmd

mmb

37.303250

23008696

250


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Example Design [1]

#4 Using the 400 mm beam depth (h), compute a revised value of :

20Prepared By : LB3

MPabd

MR

bd

MR

un

un

786.63422508.0

100000076.15822

2

0035.00196.00272.0

400

4.14.1

3585.0

786.6211

400

3585.00272.0

4.185.021185.0

minmax

minmax

min'

'

max

fy

fyfR

ff

c

n

y

c


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Example Design [1]

#5 Compute As Required :

As = x b x d

As = 0.0196 x 250 x 342

As = 1675.80 mm2

Use 6 D19 (As=1701 mm2)

#6 CrossCheck The Moment Nominal with Moment Ultimate :

21Prepared By : LB3

kNmMkNmM

kNm

a

dfAM

nu

ysn

26.16176.158

26.1612

48.91

34240017018.02

mmbf

fAa

c

ys48.91

2503585.0

4001701

85.0 '


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Example Analysis [2]

Example Analysis :

Analyze the Moment Nominal Capacity (Mn) of the beam below : [fc = 35MPa, fy = 400 MPa].

22Prepared By : LB3

d=350mm h=400mm

b=250mm

Cover+dh+db/2=50mm

3D19


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Example Analysis [2]

Example Analysis :

Analyze the Moment Nominal Capacity (Mn) of the beam below : [fc = 35MPa, fy = 400 MPa].

23Prepared By : LB3

T

C

d

a

d-a/2

228501925.03 mmAs

mmbf

fAa

c

ys71.45

2503585.0

400850

85.0 '

kNmM

MM

kNmM

M

adfAM

n

nu

n

n

ysn

983.88229.1118.0

229.1112

71.45350400850

2


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24

0

1

2

3

4

5

6

7

8

9

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Mn/bd2

= As/bd

Example Design 1 :

Calculate the lateral reinforcement requirement for beam size of

150x350mm which supported nominal moment load of 110kN-m,with fc=30 Mpa, fy=300 Mpa.

Solution:

From Rn chart we get:

98.5350.150

10.1102

6

2

bd

Mn

023.0

2

2

1256.64D20use

5.1207

350*150*023.0

mm

mmAs

bdAs


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Home Work:

2. Solve Problem 5.1

3. By using your own graph, Solve Problem 5.5.a

Documents

3. Design Assumption and Beam Analysis