Analysis and Design of Roof Beams

39
A B C ANALYSIS AND DESIGN OF BEAMS Roof beam Roof beam: RB 1 and RB2 BS 8110 Referenc e Calculations Output Table 3.3 Specification: Self weight of concrete = 24 KN/m 3 f cu = 30mm f y = 460 N/mm 2 Fire resistance = 1 hours Concrete exposure = mild Cover = 25mm Ceiling = 0.10KN/m 2 Roof = 0.75 KN/m 2 Tension φ = 12mm Link φ = 8mm f yv = 250 N/mm 2 Case 1 : Adverse + adverse 2m 4m

Transcript of Analysis and Design of Roof Beams

Page 1: Analysis and Design of Roof Beams

A B C

ANALYSIS AND DESIGN OF BEAMS

Roof beam

Roof beam: RB 1 and RB2

BS 8110 Reference

Calculations Output

Table 3.3

Specification:

Self weight of concrete = 24 KN/m3

f cu = 30mm

f y = 460 N/mm2

Fire resistance = 1 hours

Concrete exposure = mild

Cover = 25mm

Ceiling = 0.10KN/m2

Roof = 0.75 KN/m2

Tension φ = 12mm

Link φ = 8mm

f yv = 250 N/mm2

Case 1 : Adverse + adverse

2m 4m

Self weight of the concrete = 24 × 0.3 × 0.2 = 1.44KN/m

Dead load of roof + ceiling = (0.75 + 0.1 ) × 1m width = 0.85 KN/m

Live load = (0.5KN/m/m) 1m width = 0.5 KN/m

Page 2: Analysis and Design of Roof Beams

A AB C

Design load = 1.4Gk+1.6Qk

= 1.4( 1.44 + 0.85) + 1.6( 0.5) = 4.00KN/m

Gk= 0.85 KN/mQk= 0.5 KN/m

Design load= 4.00kN/m

4 KN/m

2m 4m

i) Fixed end momentFEMAB = FEMCB = 0

FEMBA = wL2

8 =

(4.00 )(2)2

8 = 2.00KN. m

FEMBC = -wL2

8 = -

(4.00 )(2)2

8 = - 8.00KN.m

ii) Stiffness factor for each member (K)

Kab = Kba = 3EIL

= 3EI

2 = 1.5EI

Kbc = Kcb = 3EIL

= 3EI

4 = 0.75EI

iii) Joint stiffness factor (∑K)∑ Kb = Kba + Kbc

= 1.5EI + 0.75EI = 2.25EI

iv) Distribution factor, DF = K∑K

DFab = 1

DFba = 1.5EI

2.25EI = o.67

DFbc = 0.75 EI2.25 EI

= 0.33

DFcb = 1

v) Carry over

0.5 0 0 0.5

Page 3: Analysis and Design of Roof Beams

A

2m 4m

Calculations

vi) Moment distribution table

Joint a COF b COF cSpan ab ba bc cbDF 1 0.67 0.33 1

FEM 0 2.00 -8.00 0Balance 0 6.00 6.00 0

Distribution 0 4.02 1.98 0Carry over 0 0 0 0

Final moment

0 6.02 -6.02 0

For span RB1(A-B)

4 KN/m 6.02 KN

B (L)

4 KN/m

A B C

2m 4m

6.02 KN 8kN

B

Page 4: Analysis and Design of Roof Beams

Taking moment at BL

+ MB = 0-2Vab + 8.00 – 6.02 = 0 VA = 0.99KN VB (L) = 7.01 KN

VA = 0.99KNVB (L) = 7.01 KN

Shear diagram

0.99x

= 7.012−x

1.98 – 0.99 x = 7.01x x = 0.2475

For left hand sideMax. moment when V = 0

+ Mmax. - 0.99 ( 0.2475 ) + 4 (0.2475)2

2 = 0

Mmax. = 0.1225KN.m

Mmax. = 0.1225KN.m

For right hand side

+ Mmax + 6.02 + 7.01( 1.7525

2 ) – 1.7525 ( 7.01 ) = 0

Mmax = 0.1225KN.m

0.99

2 - x

7.01

7.01KN

1.7525 m

Page 5: Analysis and Design of Roof Beams

For span RB2 ( B-C)

Taking moment at BR

+ MB (R) = 0-6.02 + 16(2) – 4Vc = 0 Vc = 6.495 KN VB (R) = 9.505 KN

Vc = 6.495 KN

VB (R) = 9.505 KN

9.505x

= 6.4954−x

38.02 – 9.505x = 6.495x x = 2.376m

4 m

16 KN

6.02KN.m

VB (R) Vc

4 KN/m

9.505

x

6.495

4 - x

Page 6: Analysis and Design of Roof Beams

+ Mmax + 6.02 + 9.504 (2.376

2) – 9.505 (2.376) = 0

Mmax = 5.273 KN.mMmax = 5.273 KN.m

+ Mmax + 6.496 (1.624

2) + 6.495 (1.624) = 0

Mmax = 5.273 KN.m

9.504 KN

2.376 m

6.02 KN.

Mmax

9.505

4 KN/m

6.496 KN

1.624 m

6.495 KN

4 KN/m

Mmax

Page 7: Analysis and Design of Roof Beams

Case 2 : For adverse + Beneficial

h = 300mb = 200m

Self weight of the concrete = 24 × 0.3 × 0.2 = 1.44 KN/m Gk = 0.85 KN/m

Qk =0.5 KN/mDead load of root + ceiling = (0.75 + 0.1) 1m width = 0.85 KN/m Live load = 0.5KN/m/m width = 0.5 ×1 m = 0.5 KN/m

Design load for span RB1( A – B) ( adverse )Design load = 1.4Gk+1.6Qk

= 1.4( 1.44 + 0.85) + 1.6( 0.5) = 4.00KN/m

Design load for span RB2(B – C) ( Beneficial )Design load = 1.0 Gk + 0 Qk

= 1.0 Gk

= 1.0 ( 1.44 + 0.85 ) = 2.29 KN/m

2m

w = 2.29 KN/mBeneficial

w = 4.00KN/m

4m CBA

Adverse

Page 8: Analysis and Design of Roof Beams

i) Fixed end momentFEMAB = FEMCB = 0

FEMBA = wL2

8 =

(4.00 )(2)2

8 = 2.00KN. m

FEMBC = -wL2

8 = -

(2.29 )(4 )2

8 = - 4.58KN. m

ii) Stiffness factor for each member (K)

Kab = Kba = 3EIL

= 3EI

2 = 1.5EI

Kbc = Kcb = 3EIL

= 3EI

4 = 0.75EI

iii) Joint stiffness factor (∑K)∑ Kb = Kba + Kbc

= 1.5EI + 0.75EI = 2.25EI

iv) Distribution factor, DF = K∑K

DFab = 1

DFba = 1.5EI

2.25EI = o.67

DFbc = 0.75 EI2.25 EI

= 0.33

DFcb = 1

v) Carry over

0.5 0 0 0.5

4m2m

A B C

4.00 KN/m 2.29 KN/m

Page 9: Analysis and Design of Roof Beams

vi) Moment distribution table

Joint a COF b COF cSpan ab ba bc cbDF 1 0.67 0.33 1FEM 0 2.00 -4.58 0Balance 0 2.58 2.58 0Distribution 0 1.729 0.851 0Carry over 0 0 0 0Final moment

0 3.729 -3.729 0

For span RB1 (A – B)

Taking moment at B1L

4m2m

8.00 KN

2 m

Mmax

VA

4 KN/m

BL

VB1(L)

3.729 KN

Page 10: Analysis and Design of Roof Beams

+ Mmax = 0-VA(2) + 8.00 – 3.729 = 0VA = 2.136 KNVB(L) = 5.864 KN

VA = 2.136 KNVB(L) = 5.864 KN

2.136x = 5.864

2−x

4.272 – 2.316x = 5.864x x = 0.534m

For left hand side

Max. moment

2.136

x

5.864

2 – x = 1.4762m

5.864 KN

1.466 m

5.864 KN

Mmax

3.729 KN.m

Page 11: Analysis and Design of Roof Beams

+ Mmax – 2.136 ( 0.534 ) + 4.0(0.534)2

2 = 0

Mmax = 0.57 KN.m

+ Mmax + 5.864 ( 1.466

2) – 5.864 (1.466) + 3.729 = 0

Mmax = 0.57 KN.m

Mmax = 0.57 KN.m

For span RB2(BR – C)

Taking moment at BR

+ MB (R) = 03.729 – 9.16 (2) +Vc1 = 3.65 KNVB (R) = 5.51 KN

VB (R) = 5.51 KN

5.51x

= 3.654−x

22.04 – 5.51x= 3.65x x = 2.406m

Right hand side

4 m

9.16 KN

3.729 KN.m

VB (R) Vc

2.29 KN/m

CBR

5.51

x

3.65

4 – x

Page 12: Analysis and Design of Roof Beams

+ Mmax – 3.65( 1.594

2 ) + 3.65 ( 1.594 ) = 0

Mmax = 2.90 KN.m

Mmax = 2.90 KN.m

Left hand side

+ Mmax + 3.729 + (5.51)(2.406

2) – (5.51)(2.406) = 0

Mmax = 2.90 KN.m

Case 3:For Beneficial + adverse

h = 300mb = 200m

Self weight of the concrete = 24 × 0.3 × 0.2 = 1.44 KN/m

Dead load of root + ceiling = 0.75 + 0.1 = 0.85KN/m/m width = 0.85× 1m = 0.85 KN/m

3.65 KN

1.594 m

3.65 KN

2.29 KN/mMmax

5.51 KN

2.406 m

Mmax

5.51 KN

2.29 KN/m3.729KNm

2m

Beneficial

4m CBA

adverse

Page 13: Analysis and Design of Roof Beams

Live load = 0.5KN/m/m width = 0.5 ×1 m = 0.5 KN/m Gk=0.85 KN/m

Qk=0.5 KN/mDesign load for span AB (Beneficial) Design load = 1.0 Gk + 0 Qk

= 1.0 Gk

= 1.0 ( 1.44 + 0.85 ) = 2.29 KN/m

Design load for span BC (Adverse)Design load = 1.4Gk+1.6Qk

= 1.4( 1.44 + 0.85) + 1.6( 0.5) = 4.00KN/m

i) Fixed end momentFEMAB = FEMCB = 0

FEMBA = wL2

8 =

(2.29 )(2)2

8 = 1.145 KN. m

FEMBC = -wL2

8 = -

(4.00 )(4)2

8 = - 8.00 KN. m

ii) Stiffness factor for each member (K)

Kab = Kba = 3EIL

= 3EI

2 = 1.5EI

Kbc = Kcb = 3EIL

= 3EI

4 = 0.75EI

iii) Joint stiffness factor (∑K)∑ Kb = Kba + Kbc

= 1.5EI + 0.75EI = 2.25EI

4m2m

CBA

4.00 KN/m2.29 KN/m

Page 14: Analysis and Design of Roof Beams

iv) Distribution factor, DF = K∑K

DFab = 1

DFba = 1.5EI

2.25EI = o.67

DFbc = 0.75 EI2.25 EI

= 0.33

DFcb = 1

vii) Carry over

0.5 0 0 0.5

v) Moment distribution tableJoint a COF b COF cSpan ab ba bc cbDF 1 0.67 0.33 1FEM 0 1.145 -8.00 0Balance 0 6.855 6.855 0Distribution 0 4.593 2.262 0Carry over 0 0 0 0Final moment

0 5.738 -5.738 0

For span RB1(A- BL)

4m2m

A B C

5.738 KN

Page 15: Analysis and Design of Roof Beams

Taking moment at B1L = 0+ MBL = 04.58(1) – 2VA1 – 5.738 = 0VA = -0.579 KNVBL = 5.159 KN

VA = -0.579 KNVBL = 5.159 KN

0.579x

= −5.159

2−x1.158 – 0.579x = 5.159xx = 0.2018Left Hand Side

VA 4.58 KN

2.29 KN/m

VB1(L)

2 m BL

5.159

2 - x

x

0.579

M = 0

0.462 KN

0.2018 m

Mmax

0.579 KN

2.29 KN/m

Page 16: Analysis and Design of Roof Beams

+ Mmax + 0.579(0.2018) + 0.462( 0.2018

2) = 0

Mmax = - 0.163 KN.mMmax = - 0.163 KN.m

Right Hand Side

+ Mmax + 4.118(1.7982

2) + 5.738 – 5.159(1.7982) = 0

Mmax = - 0.163KN.m

For span RB2(BR – C)

Taking moment at C + MC = 016(2) + 5.738 – 4VB1(R) = 0VB (R) = 9.435 KNVC = 6.565 KN

4.118 KN

1.7982 m

5.159 KN

2.29 KN/m

Mmax

5.738

4 m

16 KN

5.738 KN.m

VB(R) Vc

4.0 KN/m

CBR

Page 17: Analysis and Design of Roof Beams

9.435x

= 6.5654−x

37.74 – 9.435x = 6.565xx = 2.359 m

Left Hand Side

+ Mmax + 9.436( 2.359

2 ) – 9.435( 2.35 ) = 0

Mmax = 5.39 KN.m

Right Hand Side

Mmax + 6.564 ( 1.641

2 ) – 6.565 ( 1.641 ) = 0

Mmax = 5.39 KN.m

9.435

x

6.565

4 – x

6.565

9.436 KN

2.359 m

Mmax

9.435

5.738 KN.m

VB1(L)

4.0 KN/m

4 KN/m

1.641 m

6.565 KN6.564 KN

Mmax

Page 18: Analysis and Design of Roof Beams

2.90

5.273

Shear force envelope diagram

Moment force envelope diagram

Maximum shear diagram

Maximum moment diagram

Reinforced designFor sagging at B

3.729

9.505

7.01

0.99

6.565

0.579

5.8646.495

6.02

5.738

5.5193.65

0.57

5.51

0.1225

9.4352.136

5.39

Page 19: Analysis and Design of Roof Beams

Check xd

K = Mf cu bd2

= 6.02×106

(30 )(200)(261)2

= 0.0147< 0.156 ok

Clause 3.4.4.4

z = 261[ 0.5 + ¿ ] = 256.66 > 0.95d = (247.95) use 0.95d

ASreq = 6.02×106

(0.95 ) (460 )(247.95) = 55.58 mm2

Aprov = 226 mm2 2T12, Asprov = 226mm2

For span A – B Hogging

Check xd

K = Mf cu bd2

= 0.57×106

(30 )(200)(261)2

= 0.00139

K < K’( = 0.00139 ) okSo the compression reinforcement is not required

Find zClause 3.4.4.4 z = d [ 0.5 + √0.25− K

0.9 ]

= 261 [ 0.5 + √0.25−0.001390.9

]

= 260.60mm > ( 0.95d = 247.95mm )

>0.95d, so use 0.95d

Find AS

M = 0.95fyAsz

ASreq = 0.57×106

0.95 (460 )(247.95) = 5.26mm2

AS prov = 226mm2

2T12

For span B – C (Hogging)

Check xd

K = Mf cu bd2

K < K’( = 0.0129 ) okSo the compression reinforcement is not required

Page 20: Analysis and Design of Roof Beams

= 5.39×106

(30 )(200)(261)2

= 0.0132

Find zClause 3.4.4.4 z = d [ 0.5 + √0.25− K

0.9 ]

= 261 [ 0.5 + √0.25−0.01320.9

]

= 257.11mm > ( 0.95d = 247.95mm )

>0.95d, so use 0.95d

Find AS

M = 0.95fyAsz

ASreq = 5.273×106

0.95 (460 )(247.95) = 48.66mm2

As prov = 226mm2

2T12

Check max. & min. As

Table 3.25Min. As =

0.13bh100

= 0.13100

(200 )(300) = 78mm2

Max. As = 4

100bh =

4100

(200)(300) = 2400mm2

As min = 78 mm2

As max = 2400 mm2

Check deflectionFor span A – B ( Hogging )

( Ld

)basic = 26 ( For continues beam )

d = 261mmM

bd2 = 0.57×106

(200 )(261)2

= 0.04184

fs = 2 f y A s req

3 A s prov

= 2(460)(5.26)

3(226) = 7.137

Table 3.10 The modification factor for tension steelMFT > 2, so use 2

2T12

C1B1A1

Page 21: Analysis and Design of Roof Beams

= 0.55 +

477−f s

120(0.9+ Mbd2 )

= 0.55 + 477−7.137

120(0.9+0.04184 )= 4.707 > 2

( Ld

)allowable

= 26 × 2

= 52

( Ld

)actual

= ( 2000261

)

= 7.663

( Ld

)allowable

> (Ld

)actual

ok

For span B – CTable 3.10

( Ld

)basic = 26 ( For continues beam )

d = 261mmM

bd2 = 5.39×106

(200 )(261)2

= 0.3956

fs = 2 f y A s req

3 A s prov

= 2(460)(48.60)

3 (226) = 65.95 N/mm2

The modification factor for tension steel

= 0.55 +

477−f s

120(0.9+ Mbd2 )

= 0.55 + 477−65.9

120(0.9+0.3956)= 3.1939 > 2

More than 2, use 2

( Ld

)allowable

= 26 × 2

= 52

( Ld

)actual

= ( 4000261

)

= 15.33

( Ld

)allowable

> (Ld

)actual

ok

Check shearAt support AAs prov = 226mm2

Page 22: Analysis and Design of Roof Beams

Table 3.8 100 A s

bd =

100 (226)(200 )(261)

= 0.433 < 3

( 400d

)14 = ( 400

261)

14

= 1.1126 > 1

3√ f cu25 = 3√ 30

25 = 1.06

Vc = 0.79× 3√ 100 As

bd× 4√ 400

3√ f cu25Υ m

= 0.79× 3√0.433×1.1126×1.06

1.25= 0.5639 N/mm2

ok

ok

Table 3.7V =

vbd

= 2.136×103

(200 )(261)= 0.0409 N/mm2

0.5Vc = 0.282N/mm2

0.5Vc >V, minimum shear is provided

At support BTake 9.05 KN to calculate the shear

V = vbd

= 9.505×103

(200 )(261) = 0.1820.5Vc > V

At support CTake 6.565 KN to calculate the shear

V = vbd

= 6.565×103

(200 )(261) = 0.1260.5Vc > V

Hence, for the beam RB1 and RB2. Minimum link should be provided in all beams of structural

Page 23: Analysis and Design of Roof Beams

importance, it will be satisfactory to omit them in members of minor structural importance such as lintels or where the maximum design shear stress is less than half Vc.

Table 3.7 A s

Sv =

0.4 bv0.9 f yv

Let link = 8 mmArea = 101 mm ( for 2 leg )101Sv

= 0.4(200)

0.95(250)

Sv = 299.84 mmMax. spacing = 0.75d = 195.75 mm

Hence use R8@175mm c/c

Crack checking [ only consider tension reinforcement]

Clear spacing = 200−2 (25 )−2 (8 )−2(12)

1 = 110 mm

Clear spacing ≤ 47000f s

≤ 300

4700065.95

= 7126.6 ≤ 300

Actual spacing ( = 110mm ) ≤ max. Spacing

Use type deformation type 2 (460) Use for round cross section with rip

Ka= 40( Tension)

Length of anchorgeL= Ka x bar sizeL= 40 x 12 = 480mm

So, we use max. 300 mm

CBA

Page 24: Analysis and Design of Roof Beams

Roof Beam: RB3 and RB 4

REFERENCES: Figure 9 (Appendix)

BS 8110 Reference

Calculations Output

Table 3.15

Specification:

Self weight of concrete = 24 KN/m3

f cu = 30mm

f y = 460 N/mm2

Fire resistance = 1 hours

Concrete exposure = mild

Cover = 25mm

Ceiling = 0.10KN/m2

Roof = 0.75 KN/m2

Tension φ = 12mm

Link φ = 8mm

f yv = 250 N/mm2

Table 3.9Estimation thickness of slab, h

With refer to beam RB3

( Ld

) = 20 ( For simply support)

d min = L

20×MF (Assume, MF = 0.80)

= 4000

20×0.80

= 250mm

25mm

8mm

110mm

4T12

Page 25: Analysis and Design of Roof Beams

Take d = 250mm,

Assume tension steel = 12mm

Link = 8mm

Cover = 25mm

h = 289mm

So, h = 300mm

b = 200mm

Loading

Self-weight of the concrete = 24 × 0.3 × 0.2 × 1.4

= 2.016KN/m

Dead load of roof + ceiling = 0.75 + 0.1

= 0.85KN/m/m width × 1m

= 0.85 KN/m width

Live load = 0.5KN/m/m width

Design load = 1.4(0.85) + 1.6(0.5)

= 1.99KN/m/m width

Point load of roofing + ceiling = 1.99 × 3.5 ×1

= 6.965KN

Page 26: Analysis and Design of Roof Beams

Taking moment at Vab = 0

MA1 = 0,

-6.965(1) - 6.965(2) – 6.965(3) + 4 VA2 – 2(8.064) =0

V A2 = 14.48KN

V A1 = 14.48KN

+ F y = 0; 14.48 – 2.016 - V aL = 0

VA1 VA2

1m 1m 1m 1m

6.965KN 6.965KN 6.965KN

8.064KN

+

14.48KN

1m 1m 1m 1m

8.064KNA2

6.965KN

ca

A1

b

6.965KN 6.965KN

D

Page 27: Analysis and Design of Roof Beams

V aL = 12.464KN

+ F y = 0; 14.48 – 2.016 – 6.695 – V aR =0

V aR = 5.499KN

+ F y = 0; 14.48 – 4.032 – 6.695 – V DL =0

V DL = 3.483KN

+ F y = 0; 14.48 – 4.032 – 6.965 – 6.965 - V DR = 0

V DR = -3.482KN

+ F y = 0; 14.48 – 6.048 – 6.695 – 6.695 - V CL =0

V CL = -5.498KN

+ F y = 0; 14.48 – 6.048 – 6.965(3) - V CR = 0

V CR = -12.463KN

+ F y = 0; 14.48 – 8.064 – 3(6.965) – V A2L =0

V A2L = -14.48KN

Shear Diagram:

Bending moment diagram

14.48

12.464

5.4993.483

-3.482

-5.498

-14.48

Page 28: Analysis and Design of Roof Beams

Hence maximum moment = 17.963 KNm

Check xd

K = M

f cub d2

= 17.963×106

(30 )(200)(261)2

= 0.0439

d = h – 25 – 8 – 6

= 300 – 25 – 8 – 6

= 261 mm

K ¿ K’ ( = 0.156 ) -ok-xd≤ 0.5 -ok-

So, the compression reinforcement is not required.

Find z

z = d [ 0.5 + √0.25− K0.9

]

= 261 [ 0.5 +√0.25−0.04390.9

]

= 247.58 mm ¿ 0.95d = 247.95 mm

¿ 0.95d, Use z = 247.58 mm

Find As :

M = 0,95 f y A s Z

A s req = M

0.95 fy Z

A s prov = 226 mm2

2T12

13.472

17.963

13.473

0

Page 29: Analysis and Design of Roof Beams

= 17.963×10 6

0.95(460)(247.58)

= 166.03 mm2

Check max and min:

Min As = 0.13100

× b × h

¿0.13100

× 200 × 300

= 78 mm2

Min As = 4

100 × b × h

¿4

100 × 200 × 300

= 2400 mm2

Check deflection:

( Ld ) basic = 20 ( for beam simply supported)

( Ld

) actual = Ld

= 4000261

= 15.326 d = 261 mm

( Mbd2

) = 17.963×10 6(200 ) (261 ) 2

= 1.318

f s = 2 f y A sreq3 As prov

= 2(460)(166.03)

3(226)

As min = 78.0 mm2

As max = 2400 mm2

-ok-

Page 30: Analysis and Design of Roof Beams

= 225.29 N/mm2

The modification factor for tension steel

= 0.55 +

477−f s

120(0.9+ Mbd 2 )

= 0.55 + 477−225.29

120 (0.9+1.318 )

= 1.4957 < 2

( Ld ) allowable = 20× 1.4957

= 29.914

( Ld ) actual =

4000261 = 15.326

Check Shear:

As = 226mm2

100 A sbd

= 100(226)200(261)

= 0.433 < 3

(400d ) ¼ = (

400261 ) ¼

= 1.1126 ¿ 1

3√ f y25 = 3√ 30

25 = 1.06

v c = 0.79×

3√ 100 Asbd

×4√ 400d

×3√ f cu25

γm

( Ld ) all ¿ (

Ld ) actual

-ok-

-ok-

-ok-Ok for not greater than 40 N/mm2

Page 31: Analysis and Design of Roof Beams

= 0.79×√0.433×1.1126×1.06

1.25 = 0.5639 N/mm2

v = Vbd

V = 15.49 KN

= 14.48×103(200 )(261)

= 0.2774 N/mm2

0.5Vc = 0.282 N/mm2

Note 1 : Minimum links should be provided in all beams of structural importance, it will be satisfactory to omit them in members of minor structural importance such as lintels or where the maximum design shear stress is less than half Vc . A sSv

= 0.4bv

0.95 fyv

Assume link = 8mm,

Area = 101 mm2 ( for 2 legs )

101Sv

= 0.4(200)

0.95(250)

S v = 299.84 mm

Hence, max spacing = 0.75 d

= 195.75mm

Apply the max R8 @175mm c/c

0.5Vc ¿ V

R8 @175mm c/c

Page 32: Analysis and Design of Roof Beams

Crack checking ( only consider tension reinforcement )

Clear spacing = 200−2 (25 )−2 (8 )−2(12)

1 = 110 mm

Clear spacing ≤ 47000f s

≤ 300

47000225.29

(¿208.62 )≤ 300

actual spacing ≤ max. spacing 110mm = 208.62mm

-ok-

2T12

Use type deformation type 2 (460) Use for round cross section with rip

Ka= 40( Tension)

Length of anchorgeL= Ka x bar sizeL= 40 x 12 = 480mm

8 mm25 mm

110 mm