6. Roof_semi-d(idp)

8/12/2019 6. Roof_semi-d(idp)

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Semi-detached Calculations

Roof Calculator - Semi-detached

Roof Dimension

Roof Number 1:

Dimension of roof

(on plan) b = 4700 mm

l = 8752 mm

Distance between roof and structure= 1075 mm

(on slope) b = 4700 mm

l = 8817.7 mm

Purlin

Length of purlin = 4700.0 mm

Number of space between purlin = 4

Number of purlin = 5

Spacing of purlin = 2204 mm

Rafter

Length of rafter = 8817.7 mm

Number of space between rafter = 3Number of rafter = 4

Spacing of rafter = (4700-1075)/3 mm

= 1208 mm

Roof 1


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Roof Number 2:

Dimension of roof

(on plan) b = 6627 mm

l = 3100 mm

Distance between roof and structure= 1075 mm

(on slope) b = 6627 mm

l = 3123.3 mm

Purlin

Length of purlin = 6627.0 mm

Number of space between purlin = 6

Number of purlin = 7

Spacing of purlin = 521 mm

Rafter

Length of rafter = 3123.3 mm

Number of space between rafter = 3

Number of rafter = 4

Spacing of rafter = (6627-1075)/3

= 1851 mm

Roof 2


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Steel Section

Purlin: C-channel 150x75x18

Self-weight = 17.9 kg/m

Width = 75 mm

Depth of section, h = 150 mm

Thickness of flange = 10 mm

(b/t)flange = 7.5 mm

(d/t)web = 19.3 mm

ry= 2.4 cm

u = 0.946

x = 13.1

I = 861 cm4

Plastic modulus, Sx= 132 cm3

Elastic modulus, Zx= 115 cm3

Elastic modulus, Zy= 26.6 cm3

Rafer : I-beam 305x165x54

Self-weight = 54 kg/m

Width = 166.9 mm

Depth of section, h = 310.4 mm

Thickness of flange = 13.7 mm

(b/t)flange = 6.09 mm

(d/t)web = 33.6 mmry= 3.93 cm

u = 0.889

x = 23.6

I = 11700 cm4

Plastic modulus, Sx= 846 cm3

Elastic modulus, Zx= 754 cm3

Roof 5


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# Building size: Class A

Table 3 H (m) S2

10 0.78

10.556 0.791

15 0.88

Thus, S2is 0.791

Clause 5.6 For completed structure; Factor S3= 1

Clause 5.1 Design Wind Speed, Vs= VxS1xS2xS3

= 27.69 m/s

Clause 6 Dynamic Pressure, q = k*(Vs^2)

k = 0.613 (in SI unit)

Thus, q = 469.98 N/m2

= 0.47 kN/m2

Table 9 Most critical wind load occurs at wind angle 90.

Roof angle, Wind angle 905 -1.0

7 -1.0

10 -1.0

Appendix E Conditition Cpi

a) wind normal to permeable face 0.2

b) wind normal to impermeable face -0.3

CpeCpe

CpiCpi

H side

L side

Cp =(Cpe- Cpi)Cp=(Cpe- Cpi)

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Worst case scenario at wind angle, 90 with;

Cp= -1.2

Therefore, the worst case pressure coefficient, Cp is -1.2

Clause 7.2 Pressure on roof, P = Cp*q= (-1.2)(0.47)

= -0.564 kN/m2

Wind load, F

a) Internal Node = -1.502 kN

b) End Node = -0.751 kN

Figure 1: Loads Transferred to Purlin

BS 5950: 1 (i) Purlin Design

Loads acting on purlin

1. Zinc + Insulation load

(on plan) = 0.112 kN/m2

(on slope) = 0.111 kN/m2

2. Purlin self-weight = 0.179 kN/m

Total load on node, Wp= (0.111 x 2.132 x 1.828)+(0.179 x 1.828)

= 0.51 kN

Table 27 Section modulus, Zp =

=

= 0.34 cm3

Purlin

Rafter

2.132m

2.132m

1.828m1.828m

W L

1800

0.93 x 1828

1800

Roof 8


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D = L/45

= 1828/45

= 27 mm

B = L/60

= 1828/60

= 20 mm

Try C-channel of section 150x75x18.

Treated as simply supported;

loads on purlin = 3.132 kN/m

reaction = 1.892 kN

maximum moment = 0.572 kN.m

3.132 kN/m

1.208 m

1.892 kN 1.892 kN

V(kN)

1.892

- 1.892

M(kN.m)

0.572 kN.m

Figure 2: Shear and Moment Diagram for Purlin

Checking:

Table 9 1. Thickness of flange, t = 10 mm < 16mm

Thus, design strenght y= 275 N/mm2 = (y/275) = 1

Tabele 11 2. Web of a channel d/t = 2.4 < 40 = 40

Thus, overall class is class 1.

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3. Biaxial Bending

Segment length, LLT= 1.208 m

Table 13 Effective length, LE= 1.2LLT+2D

= 1.750 m

Clause 4.3.6.7 Slenderness, = LE/ry= 72.92

/x = 5.57

Table 19 /x v7.50 0.720

5.57 0.797

8.00 0.700

Clause 4.3.6.9 Class 1 - plastic: Bw = 1

Clause 4.3.6.7 Equivalent slenderness, LT = uv Bw= 55.00

Table 16 LT y = 275 N/mm2

b65.0 201.0

55.0 227.0

70.0 188.0

Bending strength, b= 227.0 N/mm2

Clause 4.3.6.4 Class 1-plastic: Mb= bSx= 29.96 kN.m > Mmax 0.572 kN.m

# Thus, ok

Table 26 Equivalent uniform moment factor for = 0.95

flexural buckling, m

Table 18 Equivalent uniform moment factor for = 0.925

lateral-torsional buckling, mLT

Roof 10


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Biaxial checking formula:

1

Mx=

0.572 kN.mMy = 0.07 kN.m

=

= 0.026


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(ii) Rafter Design

Figure 3: Loads Transferred to Rafter

Loadings:

Try I-beam section 305x165x54 for rafter.

Dead Load:

Transferred from purlin = 0.51 kN

Rafter self-weight = 0.540 kN/m

Imposed Load:

Qk(on slope) = 0.596 kN/m2

= 0.720 kN/m

Wind Load:

Wk= 0.47 kN/m2

= 0.568 kN/m

Purlin

Rafter

2.132m

2.132m

1.828m1.828m0.60m 1.828m 0.60m

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Load combinations (on internal node as shown in red dot in Figure 2):

Case 1:

Dead + Imposed load = 1.4Gk+1.6Qk

= 1.4[0.93+(0.54x(2.132)]+1.6(1.327x2.123)

= 4.922 kN

Case 2:

Dead + Wind load = 1.0Gk+1.4Wk

= 1.0[0.93+(0.54x(2.132)]+1.4(-1.047x2.123)

= -0.050 kN

Case 3:

Dead + Imposed + 1.2 (Gk+Qk+Wk)

Wind load =

= 1.2[(0.93+(0.54x(2.132))+(1.327x2.123)+(-1.047x2.123)]

= 2.445 kN

Case 1 is used in rafter design because it is the most critical among the three load

combinations.

Loads acting on (not including self-weight of rafter):

a) Internal node = 1.4[(0.111 x 2.132 x 1.828)+(0.179 x 1.828)]+

1.6[0.596x2.132x1.828]

= 3.255 kN

b) End node = 1.4[(0.111 x (2.132/2) x 1.828)+(0.179 x 1.828))]+

1.6[0.596x(2.132/2)x1.828]

= 1.779 kN

1.779 3.255 3.255 3.255 1.779

0.756 kN/m

2.204 2.204 2.204 0.704 1.500

7.95 12.04

Figure 4: Loads Acted on Rafter

MA= [RB(2.132+2.132+2.132+0.632)]-[5.825 = 0

x(2.132+(2.132x2)+(2.132x3)]+(-3.192x8.528) -

(0.54x(8.5282/2))

RB= 12.04 kN

RA= RB

=kN kN

Roof 13


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MB= [-RA(2.132+2.132+2.132+0.632)]+[5.825 = 0

x((2.132+2.132+0.632)+(2.132+0.632)+0.632]+

(-3.192x1.5)+(3.192x7.028)

RA= 7.95 kN

V(kN)

6.17 4.50

2.91

1.25 1.78

-0.42

-3.68

-5.34

-8.60 -9.13

M(kN.m)

3.54

0

-11.76 -2.70

-12.82 -12.64

Figure 5: Shear and Moment Diagram for Rafter

BS5950 Checking:

Table 9 1. Thickness of flange, t = 13.7 mm < 16mm

Thus, design strenght y= 275 N/mm2

= (y/275) = 1

Table 11 Flange b/t = 6.09 < 40 = 40

Web d/t = 33.6 < 80 = 80Thus, overall class is class 1.

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2. Section selection

Mmax= 12.82 kN.m

M = ySxRearranging; Sx = M/y

= 46624.15 mm3

= 46.62 cm3

Try section 305x165x54.

Sx= 846 cm3

Mdesign= ySx

= 275x(846x103)

= 232.65 kN.m > Mmax 12.82 kN.m

Thus, ok

3. Shear Capacity Check

Fmax= 9.13 kN

Pv= 0.6yAv

= 701.66 kN > Fmax 9.13 kN

Thus, section is adequate in term of shear capacity.

Web d/t = 33.6 < 70 = 70Thus, it is not required to check for shear buckling.

4. Moment Capacity Check

0.6 Pv= 421.00 kN

Fv= 9.13 kN < 0.6 Pv (421 kN)

Therefore, it is low shear.

Thus, Class 1: Mc = ySx= 232.65 kN.m > Mmax 12.82 kN.m

Thus, this section is adequate in term of moment capacity.

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5. Deflection Check

Point load from purlin;

a) Internal node = 0.596x2.132x1.828

= 1.586 kN

b) End node = 0.596x(2.132/2)x1.828

= 0.793 kN

Young's Modulus, E = 2.05E+05 N/mm2

Moment of Inertia, I = 11700 cm4

Distance between the end and nodes:

a1= 0 mm

a2 = 2204.4 mm

a3 = 4408.9 mm

a4 = 6613.3 mm

a5 = 8817.7 mm

Deflection, =

=

= 0.563 mm

Table 8 /span = 6.3792E-08 < 1/360

Therefore, the I-beam of section 305x165x54 is adequate in terms of deflection.

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Task Design Roof for Semi-detached Unit Roof 2

Reference Calculation

Loadings

Dead Load

Structural Self-weight of purlin = 0.179 kN/m

Sections: to Self-weight of rafter = 0.540 kN/m

BS4: Part 1 and

BS 4848:Part 4

BS 648 Zinc sheeting (0.041in.) = 7.8 kg/m2

= 0.078 kN/m2

Insulation (aluminium = 3.4 kg/m2

sheet 0.048 in.) 0.034 kN/m2

BS6399 Imposed Load

: Part 3

Clause 4.3.1.(c) (on plan) = 0.6 kN/m2


CP3: Chapter Wind Load

V-2: 1972= 7 degree

H = 9.133 m

h = 8.3 m

w = 7.7 m

h/w = 1.08 < 2

Thus, value of Table 9 from CP3: Chapter V-2: 1972 can be used.

Basic Wind Speed, V = 35 m/s

Clause 5.4 Topographic Factor, S1= 1

Clause 5.5.2 Ground roughness, building size and height above ground factor

# Ground roughness: (3) Country with many windbreakers: small towns

, outskirts of large cities

h

Hw

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# Building size: Class A

Table 3 H (m) S2

10 0.78

9.133 0.763

15 0.88

Thus, S2is 0.791

Clause 5.6 For completed structure; Factor S3 1

Clause 5.1 Design Wind Speed, Vs= VxS1xS2xS3

= 26.69 m/s

Clause 6 Dynamic Pressure, q = k*(Vs^2)

k = 0.613 (in SI unit)

Thus, q = 436.78 N/m2

= 0.44 kN/m2

Table 9 Most critical wind load occurs at wind angle 90.

Roof angle, Wind angle 90

5 -1.07 -1.0

10 -1.0

Appendix E Conditition Cpi

a) wind normal to permeable face 0.2

b) wind normal to impermeable face -0.3

CpeCpe

CpiCpi

H side

L side

Cp =(Cpe- Cpi)

Cp=(Cpe- Cpi)

Roof 45


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Worst case scenario at wind angle, 90with;

Cp= -1.2

Therefore, the worst case pressure coefficient, Cp is -1.2

Clause 7.2 Pressure on roof, P = Cp*q

= (-1.2)(0.47)= -0.524 kN/m

2

Wind load, F

a) Internal Node = -0.505 kN

b) End Node = -0.252 kN

Figure 1: Loads Transferred to Purlin

BS 5950: 1 (i) Purlin Design

Loads acting on purlin

1. Zinc + Insulation load

(on plan) = 0.112 kN/m2


2. Purlin self-weight = 0.179 kN/m

Total load on node, Wp= (0.111 x 1.033x 2.167)+(0.179 x 2.167)

= 0.44 kN

Table 27Section modulus, Zp =

=

= 0.45 cm3

Purlin

Rafter

1.033m

1.033m

2.167m2.167m

W L

1800

1.13 x 2167

1800

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D = L/45

= 2167/45

= 27 mm

B = L/60

= 2167/60

= 31 mm

Try C-channel of section 150x75x18.

Treated as simply supported;

loads on purlin = 1.250 kN/m

reaction = 1.156 kN

maximum moment = 0.535 kN.m

1.250 kN/m

1.851 m

1.156 kN 1.156 kN

V(kN)

1.156

- 1.156

M(kN.m)

0.535 kN.m

Figure 2: Shear and Moment Diagram for Purlin

Checking:

Table 9 1. Thickness of flange, t = 10 mm < 16mm


= (y/275) = 1

Table 11 2. Web of a channel d/t = 2.4 < 40 = 40


Roof 47


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Biaxial checking formula:

1

Mx= 0.535 kN.m

My = 0.07 kN.m

=

= 0.025


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(ii) Rafter Design

Figure 3: Loads Transferred to Rafter

Loadings:

Try I-beam section 305x165x54 for rafter.

Dead Load:

Transferred from purlin = 0.44 kN

Rafter self-weight = 0.540 kN/m

Imposed Load:

Qk(on slope) = 0.596 kN/m2

= 1.102 kN/m

Wind Load:

Wk= 0.44 kN/m2

= 0.808 kN/m

Purlin

Rafter

1.033m

1.033m

2.167m2.167m0.60m

1.033m

1.033m

2.167m 0.60m

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Load combinations (on internal node as shown in red dot in Figure 2):

Case 1:

Dead + Imposed load = 1.4Gk+1.6Qk

= 1.4[0.75+(0.54x(1.033)]+1.6(1.529x1.033)

= 1.925 kN

Case 2:

Dead + Wind load = 1.0Gk+1.4Wk

= 1.0[0.75+(0.54x(1.033)]+1.4(-1.121x1.033)

= 0.130 kN

Case 3:

Dead + Imposed 1.2 (Gk+Qk+Wk)

+ Wind load =

= 1.2[(0.75+(0.54x(1.033))+(1.529x1.033)+(-1.121x1.033)]

= 1.047 kN

Case 1 is used in rafter design because it is the most critical among the three load

combinations.

Loads acting on (not including self-weight of rafter):

a) Internal node = 1.4[(0.111 x 1.033 x 2.167)+(0.179 x 2.167)]+

1.6[0.596x1.033x2.167]

= 1.532 kN

b) End node = 1.4[(0.111 x (1.033/2) x 2.228)+(0.179 x 2.167))]+

1.6[0.596x(1.033/2)x2.167]

= 0.998 kN

0.998 1.532 1.532 1.532 0.998

0.756 kN/m

0.521 0.521 0.521 -0.129 0.650

2.23 5.93

Figure 4: Loads Acted on Rafter

MA= [RB(1.033+1.033+1.033+0.383)]-[5.825 = 0

x(1.033+(1.033x2)+ (1.033x3)]+(-2.112x4.131) -

(0.54x(4.1312/2))

RB= 5.93 kN

RA= R

B=kN kN

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MB= [-RA(1.033+1.033+1.033+0.383)]+[5.825x = 0

((1.033+1.033+0.383)+(1.033+0.383)+0.383]+

(-2.112x0.65)+(2.112x3.482)

RA= 2.23 kN

V(kN)

1.23 0.84

1.49

-0.69 1.00

-1.09

-2.62 -3.01

-4.54 -4.45

M(kN.m)

1.40

1

-0.54 0.51 1.98

0.05

Figure 5: Shear and Moment Diagram for Rafter

BS5950 Checking:

Table 9 1. Thickness of fla 13.7 mm < 16mm


= (y/275) = 1

Table 11 Flange b/t = 6.09 < 40 = 40

Web d/t = 33.6 < 80 = 80


2. Section selection

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Mmax= -0.05 kN.m

M = ySxRearranging; Sx = M/y

= -192.77 mm3

= -0.19 cm3

Try section 305x165x54.

Sx= 846 cm3

Mdesign= ySx

= 275x(846x103)

= 232.65 kN.m > Mmax -0.05 kN.m

Thus, ok

3. Shear Capacity Check

Fmax= 4.45 kN

Pv= 0.6yAv

= 701.66 kN > Fmax 4.45 kN

Thus, section is adequate in term of shear capacity.

Web d/t = 33.6 < 70 = 70Thus, it is not required to check for shear buckling.

4. Moment Capacity Check

0.6 Pv= 421.00 kN

Fv= 4.45 kN < 0.6 Pv (421 kN)

Therefore, it is low shear.

Class 1: Mc = ySx= 232.65 kN.m > Mmax -0.05 kN.m

Thus, this section is adequate in term of moment capacity.

5. Deflection Check

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Point load from purlin;

a) Internal node = 0.596x1.033x2.167

= 0.574 kN

b) End node = 0.596x(1.033/2)x2.167

= 0.287 kN

Young's Modulus, E = 2.05E+05 N/mm2

Moment of Inertia, I = 11700 cm4

Distance between the end and nodes:

a1= 0 mm

a2 = 520.55 mm

a3 = 1041.09 mm

a4 = 1561.64 mm

a5 = 2082.19 mm

Deflection, =

=

= 1 mm

Table 8 /span = 3.20176E-07 < 1/360

Therefore, the I-beam of section 305x165x54 is adequate in terms of deflection.

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(iii) Roof Beam Design

The roof beam selected for design the beam sustain most critical load from the roof.

Most critical roof beam for semi-detached unit is roof 1 with dimension on plan of

6685 x 8465mm.

Figure 1: Roof Beam Position for Roof 1

Details:

Concrete unit weight = 24 kN/m3

Beam breath = 0.18 m

Beam depth = 0.2 m

Loadings:

Self-weight of beam = 0.864 kN/m

The most critical load is chosen for design:

At point C from Roof 1 with load of 12.04

Load from roof = 15.79 x cos5

= 11.95 kN

2.208m2.208m 2.208m

Purlin

Rafter

Roof Beam6.965

1.50m

3.850m 1.635m

0.60m 0.60m

kN

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11.95 11.95 11.95 11.95

1.208 1.208 -0.427 1.635

0.864 kN/m

3.850 1.635

Figure 2: Loadings Acted on Roof Beam

Stiffness,

KAB= 4EI/L KBC= 4EI/L

= 4EI/3.850 = 4EI/1.635

= 1.04EI = 2.45EI

Distribution Factor,

DFAB= KAB/KAB DFBA= KBA/(KAB+KBC)

= 1.04EI/1.04EI = 1.04EI/(1.04EI + 2.45EI)

= 1 = 0.3

DFBC= KBC/(KAB+KBC) DFCB= KBC/KBC

= 2.45EI/(1.04EI + 2.45EI) = 2.45EI/2.45EI

= 0.7 = 1

Fixed End Moment,

FEMAB= (Pb2a)/(l

2)+(Pb

2a)/(l

2)+(wl

2/12)+(Pb

2a)/(l2)

= {-[(15.67x2.0212x1.828)/(3.85

2)]+[(0.864x3.85

2)/12]+

[(15.67x0.1932

x3.656)/(3.852

)]}= -2.02 kN.m

FEMBA= (Pa2b)/(l

2)+(Pa

2b)/(l

2)+(wl

2/12)

= [(15.67x1.8282x2.021)/(3.85

2)]+[(0.864x3.85

2)/12]+

[(15.67x3.6562x0.193)/(3.85

2)]

= -0.02 kN.m

FEMBC= (wl2/12)+(Pa

2b)/(l2)

= {-[(0.864x3.3052

)/12]+0}= -0.19 kN.m

FEMCB= (wl2/12)

= [(0.864x3.3052)/12]+0

= 0.19 kN.m

kN kN kN kN

m m m

mm

A B C

m

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Joint A C

Member AB BA BC CB

DF 1 0.3 0.7 1

FEM -2.017 -0.022 -0.192 0.192

Dist. 2.017 0.064 0.150 -0.192

0.032 1.009 -0.096 0.075

-0.032 -0.274 -0.639 -0.075

-0.137 -0.016 -0.038 -0.319

0.137 0.016 0.038 0.319

0.008 0.068 0.160 0.019

-0.008 -0.068 -0.160 -0.019

M 0.000 0.777 -0.777 0.000

11.954 11.95 11.95

0.864 kN/m

0.777 kN.m

1.208 1.208 -0.427

RA= [-10.937+(0.8640x(3.852/2))+(15.67x2.021)+(15.67x0.193)+

(15.67x3.85)]/3.85

= 14.56 kN

RB= [10.937+(0.8640x(3.852/2))+(15.67x1.828)+(15.67x3.656)]/3.850

= 23.03 kN

11.95 kN

0.864 kN/m

0.777

kN.m

1.635

RB= [10.937-(0.8640x(1.6352/2))]/1.635

= 1.18 kN

RC= [-10.937+(0.8640x(1.6352/2))+(15.67x1.635)]/1.635

= 12.19 kN

RA= 14.56 kN

RB= 24.21 kN

RC= 12.19 kN

B

B C

RB RC

kN

m

RB

A B

RA

kNkN

m m m

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V(kN)

(+)

2.60 1.18

1.56 -0.23

-10.40

-11.44 -12.19

(-)

-23.40

-23.03

M(kN.m)

(-) 2.51

4.7E-15

-10.68

(+)

-0.78

Figure 3: Shear and Moment Diagram for Roof Beam Supporting the Rafter and Purlin

Task Design Roof Beam for Supporting Roof

Reference Output

BS8110:

Part 1 Design Parameter:

fcu= 25 N/mm2

fy= 460 N/mm2

b

fyv= 250 N/mm2

Beam dimension lWidth, b = 180 mm

Table 3.3 Depth, h = 200 mm

Nominal cover, c = 25 mm

Main bar diameter, = 12 mmLink diameter, ' = 8 mm

Calculation

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Bending Moment

Mid Span

Assume 12mm diameter main bar and 8mm diameter link.

d= h - c - /2 - '= 200 - 25 - 12/2 - 8

= 161 mm

Moment = 2.51 kN.m

M

fcubd

= (12.89x106) /(25x180x161)

= 0.022 (


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Shear Reinforcement

Mid Span

Vmax= 23.40 kN

v = Vbd

= 26.66x103/(180x161)

= 0.807 N/mm

0.8fcu= 0.8*(25^0.5)= 4 N/mm v


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First Interior Support

Vmax= 23.03 kN

v = V

bd

= 26.83x103

/(180x161)= 3.906 N/mm

0.8fcu= 0.8*(25^0.5)= 4 N/mm v


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Deflection Check

Mid Span (Most Critical)

M = 2.51 kN.m

M/bd2= (12.89x10

6)/(150x161

2)

= 0.54

Table 3.10 fs= 2fyAs req

3As prov

= 2x460x192.8

3x339

= 49.68 N/mm2

Modification factor=

= 0.55+ {(477-290.1)/[120X(0.9+2.76)]}

= 3.025

Table 3.9 Basic span/d ratio = 26

span/d allowable = 0.975x26

= 78.66

span/dactual = 3.395/(161/1000)

= 23.913

The span is the most critical span in this beam.Therefore, the beam is satisfactory with respect to deflection.

Crack Control

Check for longest span as more steel reinforcement are provided on

that span.

Clear Spacing= b-2(cover)-2(link diameter)-no.of bars x bar diameter

no. of bars -1

= 39 mm

Minimum size of coarse agg = 25 mm

Minimum distanc between bar = hagg + 5mm

= 30 mm

Minimum distance between bars(30mm) < Clear Spacing. ok

Roof 87


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BS8110: Bending Moment

Part 1

Table 3.14 Slab condition: Two adjacent adge discontinuous

Figure 5: Bending Moment Coefficient

Design for the most critical slab: 4260mm x 1915mm

Continuous Edges

Short Span

Effective depth of outer layer:

d= 150-25-5= 120 mm

Msx = Bsxnlx2

= 0.098 x 7.4 x 1.9152

= 2.66 kN.m

Clause K= M

3.4.4.4 fcubd

= 2.66x106/ 25x1000x120

= 0.007 (


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As= M

0.95fyz

= 2.66x106/0.95x460x114

= 53.38 mm


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Provide 10mm diamerter bars at 250mm centres. Provide

(Asprovided = 262 mm Per m) T10@300

Mid Span

Short Span

Effective depth of outer layer:

d= 150-25-5

= 120 mm

Mx = Bxnlx2

= 0.074 x 7.4 x 1.9152

= 2.01 kN.m

Clause K= M

3.4.4.4 fcubd

= 17x106/ 25x1000x119

= 0.006 (


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Long Span

Effective depth of inner layer:

d= 150-25-10-5

= 110 mm

Msy = Bsynlx2

= 0.034 x 7.4 x 1.9152

= 0.92 kN.m

Clause K= M

3.4.4.4 fcubd

= 0.92x106/ 25x1000x110

= 0.003 (


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Shear

Table 3.15 Slab condition: Two adjacent edges discontinuous

Figure 6: Shear Force Coefficient

Cotinuous Edge

Short Span

Vsx = Bvxnlx

= 0.626 x 7.4 x 1.915

= 8.87 kN

d= 120 mm

Clause V

3.5.5.2 bd

= 8.87x103/(1000x120)

= 0.074

100As= 100(53.38)

bd 1000x120

= 0.015 1 ok

Table 3.8 v c = 0.79{100As/(bd)} (400/d)/ m

= 0.79(0.328)1/3

(1.826)1/4

/ 1.25

= 0.213

v


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Long Span

Vsx = Bvxnlx

= 0.418 x 7.4 x 1.915

= 5.92 kN

d= 110 mm

Clause V

3.5.5.2 bd

= 0.57x103/(1000x110)

= 0.054

100As= 100(18.52)

bd 1000x110

= 0.022 1 ok

Table 3.8 v c = 0.79{100As/(bd)}1/3

(400/d)1/4 / m

= 0.79(0.022)1/3

(3.636)1/4

/ 1.25

= 0.246

v


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Table 3.8 v c = 0.79{100As/(bd)}1/3

(400/d)1/4 / m

= 0.79(0.034)1/3

(3.333)1/4

/ 1.25

= 0.276

v


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Deflection

Check using steel at short span of midspan.

M/bd2= (2.01x10

6)/(1000x120

2)

= 0.139

fs= 2fyAs req3As prov

= 2x460x40.31

3x262

= 5.48 N/mm

Modification factor=

= 0.55+ {(477-5.48)/[120 x (0.9+0.139)]}

= 4.330

Table 3.9 basic (span/d) ratio = 26

(span/d)allowable= 4.33x26

= 112.586

(span/d)actual= 6965/120

= 35.500

(span/d)allowable> (span/d)actual ok

The slab is satisfactory with respect to deflection. Deflection

ok.

Torsion Steel

Extend 1/5 x Shorter Span = 1/5 x 1915

= 383 mm

Corner X: As = 3/4 x 383 Provide

= 287 mm2per m T10@250

Corner Y: As = 1/2 x 383 Provide

= 144 mm2per m T10@250

Cracking

Clause The bar spacing is less than 3d (637.5mm) and for grade of 460 N/mm2steel Cracking

3.12.11.2.7 reinforcement, with slab depth is less than 200mm, no further cracking ok.

check is required.

Roof 96


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Detailing

6965

1915

Figure 7: Detailing for RC Flat Roof

T10-300

T10-300 mm

mm

Roof 97


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Roof 98


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Roof 99


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Roof 100


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Roof 101


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Roof 102


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Roof 103


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Roof 104


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Roof 105


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Roof 106


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Roof 107


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Roof 108


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Roof 109


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Bar diameter 12 mm

No. of bars 3

Roof 110


85/117


Bar diameter 12 mm

No. of bars 2

Roof 111


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Roof 112


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Roof 113


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Roof 114


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Bsx= 0.098

lx= 1915 mmn= 7.4 kN/m

Bsy= 0.045

lx= 1915 mm

n= 7.4 kN/m

Roof 116


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92/117


Bsx= 0.074

lx= 1915 mm

n= 7.4 kN/m

Bsy= 0.034

lx= 1915 mmn= 7.4 kN/m

Roof 118


93/117


Roof 119


94/117


Bvx = 0.626

Roof 120


95/117


Bvy= 0.418

Bvx = 0.626

Roof 121


96/117


Bvy= 0.26

Roof 122


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Task Design of Roof Beam to Support RC Flat Roof

(v) Roof Beam Supporting RC Flat Roof

The beam chosen for design is supporting the most critical load.

2705

4260

1915 1915

Figure 1: Location of Critical Beam

Details:

Concrete 24 kN/m3

Beam breath = 0.15 m

Beam depth = 0.2 m

Loadings:

Self-weig 0.72 kN/m

Loads from slab = 7.40 kN/m2

Loading, w = [(10.24 x 1.915) x 2]+0.864

= 14.89 kN/m

14.89 kN/m

4.26 2.705

Stiffness,

KAB= 4EI/L KBC= 4EI/L

= 4EI/4.26 = 4EI/2.705

m mA B C

m

m

mm


98/117

= 0.94EI = 1.48EI

Distribution Factor,

DFAB= KAB/KAB DFBA= KBA/(KAB+KBC)

= 0.94EI/0.94EI = 0.94EI/(0.94EI + 1.48EI)

= 1 = 0.39

DFBC= KBC/(KAB+KBC) DFCB= KBC/KBC

= 1.48EI/(0.94EI + 1.4 = 1.48EI/1.48EI

= 0.61 = 1

Fixed End Moment,

FEMAB= (wl2/12)

= [(0.72x3.85^2)/12]= -22.52 kN.m

FEMBA= (wl2/12)

= [(0.72x3.3952)/12]

= 22.52 kN.m

FEMBC= (wl2/12)

= (0.72x3.3052)/12

= -9.08 kN.m

FEMCB= (wl2/12)

= (0.72x3.3052)/12

= 9.08 kN.m

Joint A C

Member AB BA BC CB

DF 1.000 0.390 0.610 1.000FEM -22.520 22.520 -9.080 9.080

Dist. 22.520 -5.242 -8.198 -9.080

-2.621 11.260 -4.540 -4.099

2.621 -2.621 -4.099 4.099

-1.310 1.310 2.050 -2.050

1.310 -1.310 -2.050 2.050

-0.655 0.655 1.025 -1.025

0.655 -0.655 -1.025 1.025

B


99/117

-0.328 0.328 0.512 -0.512

0.328 -0.328 -0.512 0.512

-0.164 0.164 0.256 -0.256

0.164 -0.164 -0.256 0.256

M 0.000 25.917 -25.917 0.000

14.89 kN/m25.917 kN.m

4.26

RA= [-50.581+(0.720x(3.852/2))+(15.79x2.021)+(15.79x0.193)+

(15.79x3.85)]/3.85

= 25.63 kN

RB= [69.513+(39.94x(4.26 /2))]/4.26

= 37.80 kN

14.89 kN/m

25.917

kN.m

2.705 m

RB= [69.513+(39.94x(2.7052/2))]/2.705

= 29.72 kN

RC= [-69.513+(39.94x(2.7052/2))]/2.705

= 10.56 kN

V(kN)

(+) 29.72

25.63 2.539

1.721 -10.56

(-)

-37.80

M(kN.m)

B C

R RC

RB

A B

RA

m

m

m


100/117

(-) 22.06

0.0

(+)

-25.93

Reference Output

BS8110:

Part 1 Design Parameter: b

fcu= 25 N/mm

fy= 460 N/mm2

l

fyv= 250 N/mm

2

First Mid Span

Beam dimension

Width, b = 180 mm

Table 3.3 epth, h = 200 mm


Top bar diameter, = 20 mmression bar diameter = 12 mm

Link diameter, ' = 10 mm

d= h - c - /2 - '= 200 - 25 - 12/2 - 10

= 159 mm

Moment = 22.06 kN.m

M

fcubd

= (22.06x106)/(25x180x159)

= 0.194 (>0.156) K>K'

K' = 0.156

d' = c + /2+ '= 25+6+10

= 45.0 mm

K=

Calculation


101/117

M-Mu

.95fy(d-d')

= 86.531 mm2

Provide

ovide 2T12bars. (Area prov: 226 mm2) 2T12 Bar

N

= 123.53


102/117

Moment = 25.93 kN.m

M

fcubd

= (25.93x106)/(25x180x159)

= 0.228 (>0.156) K>K'

K' = 0.156

d' = c + /2+ '= 45.0 mm

M-Mu

.95fy(d-d')

= 164.276 mm

2

Provideovide 2T12bars. (Area prov: 226 mm

2) 2T12 Bar

N

= 123.53


103/117

Second Mid Span

Beam dimension

Width, b = 180 mm

Depth, h = 200 mm


ain bar diameter, = 12 mm

Link diameter, ' = 10 mm

d= h - c - /2 - '= 200 - 25 - 12/2 - 10

= 159 mm

Moment = 4.50 kN.m

M

fcubd

= (4.5x106)/(25x180x159)

= 0.040 (


104/117

Shear Reinforcement

First Mid Span

V = 25.63 kN

Clause v = V

3.4.5.2 bd

= 25.63x103/(180x159)

= 0.896 N/mm

0.8fcu= 0.8*(25^0.5)= 4 N/mm v


105/117


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109/117

diameter 12 mm

. of bars = 2


110/117

diameter 12 mm

. of bars = 2


111/117

diameter 12

. of bars = 2


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6. Roof_semi-d(idp)

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