6. Roof_semi-d(idp)
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Transcript of 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
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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
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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
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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
(on slope) = 0.596 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)
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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
(on slope) = 0.111 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
Thus, design strenght y= 275 N/mm2
= (y/275) = 1
Table 11 2. Web of a channel d/t = 2.4 < 40 = 40
Thus, overall class is class 1.
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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
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 = 80
Thus, overall class is class 1.
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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Semi-detached Calculations
(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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Semi-detached Calculations
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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Semi-detached Calculations
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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Semi-detached Calculations
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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Semi-detached Calculations
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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Semi-detached Calculations
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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Semi-detached Calculations
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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Semi-detached Calculations
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
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Semi-detached Calculations
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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Semi-detached Calculations
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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Semi-detached Calculations
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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Semi-detached Calculations
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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Semi-detached Calculations
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
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Semi-detached Calculations
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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Semi-detached Calculations
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.
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Detailing
6965
1915
Figure 7: Detailing for RC Flat Roof
T10-300
T10-300 mm
mm
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Bar diameter 12 mm
No. of bars 3
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Bar diameter 12 mm
No. of bars 2
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Semi-detached Calculations
Bsx= 0.098
lx= 1915 mmn= 7.4 kN/m
Bsy= 0.045
lx= 1915 mm
n= 7.4 kN/m
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Semi-detached Calculations
Bsx= 0.074
lx= 1915 mm
n= 7.4 kN/m
Bsy= 0.034
lx= 1915 mmn= 7.4 kN/m
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Semi-detached Calculations
Bvx = 0.626
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Semi-detached Calculations
Bvy= 0.418
Bvx = 0.626
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Semi-detached Calculations
Bvy= 0.26
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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
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= 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
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-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
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(-) 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
Nominal cover, c = 25 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
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M-Mu
.95fy(d-d')
= 86.531 mm2
Provide
ovide 2T12bars. (Area prov: 226 mm2) 2T12 Bar
N
= 123.53
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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
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Second Mid Span
Beam dimension
Width, b = 180 mm
Depth, h = 200 mm
Nominal cover, c = 25 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 (
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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
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diameter 12 mm
. of bars = 2
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diameter 12 mm
. of bars = 2
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diameter 12
. of bars = 2
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