4.5.3.3.9Combined roofs

NBC 2016 (SP 7:2016) Volume 1

2016 · PDF page 449

Hover any section to copy its link or text, ask Copilot about it, or bookmark it.

The average external pressure coefficients for combined roofs are shown in Table 24.

Roof Angle α Degree	Solidity Ratio Φ	Maximum (Largest + ve) and Minimum (Largest - ve) Pressure Coefficients
Roof Angle α Degree	Solidity Ratio Φ	Overall Coefficients	Local Coefficients
0	All values of Φ	+ 0.2	+ 0.5	+ 1.8	+ 1.1
5		+ 0.4	+ 0.8	+ 2.1	+ 1.3
10		+ 0.5	+ 1.2	+ 2.4	+ 1.6
15		+ 0.7	+ 1.4	+ 2.7	+ 1.8
20		+ 0.8	+ 1.7	+ 2.9	+ 2.1
25		+ 1.0	+ 2.0	+ 3.1	+ 2.3
30		+ 1.2	+ 2.2	+ 3.2	+ 2.4
0	Φ = 0	- 0.5	- 0.6	- 1.3	- 1.4
0	Φ = 1	- 1.0	- 1.2	- 1.8	- 1.9
5	Φ = 0	- 0.7	- 1.1	- 1.7	- 1.8
5	Φ = 1	- 1.1	- 1.6	- 2.2	- 2.3
10	Φ = 0	- 0.9	- 1.5	- 2.0	- 2.1
10	Φ = 1	- 1.3	- 2.1	- 2.6	- 2.7
15	Φ = 0	- 1.1	- 1.8	- 2.4	- 2.5
15	Φ = 1	- 1.4	- 2.3	- 2.9	- 3.0
20	Φ = 0	- 1.3	- 2.2	- 2.8	- 2.9
20	Φ = 1	- 1.5	- 2.6	- 3.1	- 3.2
25	Φ = 0	- 1.6	- 2.6	- 3.2	- 3.2
25	Φ = 1	- 1.7	- 2.8	- 3.5	- 3.5
30	Φ = 0	- 1.8	- 3.0	- 3.8	- 3.6
30	Φ = 1	- 1.8	- 3.0	- 3.8	- 3.6

1 For monopitch canopies the centre of pressure should be taken to act at $0.3w$ from the windward edge.

2 $W$ and $L$ are overall width and length including overhangs.

PART 6 STRUCTURAL DESIGN — SECTION 1 LOADS, FORCES AND EFFECTS

NOTE—W and L are overall width and length including overhangs.

Table 12 Pressure Coefficients for Free Standing Double Sloped Roofs (Clause 4.5.3.3.3)

ve ROOF ANGLE

KEY PLAN

Roof Angle α Degree	Solidity Ratio Φ	Maximum (Largest + ve) and Minimum (Largest - ve) Pressure Coefficients
Roof Angle α Degree	Solidity Ratio Φ	Overall Coefficients	Local Coefficients
-20	All values of Φ
-15		+0.7	+0.8	+1.6	+0.6	+1.7
-10		+0.5	+0.6	+1.5	+0.7	+1.4
-5		+0.4	+0.6	+1.4	+0.8	+1.1
+5		+0.3	+0.5	+1.5	+0.8	+0.8
+10		+0.3	+0.6	+1.8	+1.3	+0.4
+15		+0.4	+0.7	+1.8	+1.4	+0.4
+20		+0.4	+0.9	+1.9	+1.4	+0.4
+25		+0.6	+1.1	+1.9	+1.5	+0.4
+30		+0.7	+1.2	+1.9	+1.6	+0.5
		+0.9	+1.3	+1.9	+1.6	+0.7
-20	Φ=0	-0.7	-0.9	-1.3	-1.6	-0.6
-20	Φ=1	-0.9	-1.2	-1.7	-1.9	-1.2
-15	Φ=0	-0.6	-0.8	-1.3	-1.6	-0.6
-15	Φ=1	-0.8	-1.1	-1.7	-1.9	-1.2
-10	Φ=0	-0.6	-0.8	-1.3	-1.5	-0.6
-10	Φ=1	-0.8	-1.1	-1.7	-1.9	-1.3
-5	Φ=0	-0.5	-0.7	-1.3	-1.6	-0.6
-5	Φ=1	-0.8	-1.5	-1.7	-1.9	-1.4
+5	Φ=0	-0.6	-0.6	-1.4	-1.4	-1.1
+5	Φ=1	-0.9	-1.3	-1.8	-1.8	-2.1
+10	Φ=0	-0.7	-0.7	-1.5	-1.4	-1.4
+10	Φ=1	-1.1	-1.4	-2.0	-1.8	-2.4
+15	Φ=0	-0.8	-0.9	-1.7	-1.4	-1.8
+15	Φ=1	-1.2	-1.5	-2.2	-1.9	-2.8
+20	Φ=0	-0.9	-1.2	-1.8	-1.4	-2.0
+20	Φ=1	-1.3	-1.7	-2.3	-1.9	-3.0
+25	Φ=0	-1.0	-1.4	-1.9	-1.4	-2.0
+25	Φ=1	-1.4	-1.9	-2.4	-2.1	-3.0
+30	Φ=0	-1.0	-1.4	-1.9	-1.4	-2.0
+30	Φ=1	-1.4	-2.1	-2.6	-2.2	-3.0

Each slope of a duopitch canopy should be able to withstand forces using both the maximum and the minimum coefficients, and the whole canopy should be able to support forces using one slope at the maximum coefficient with the other slope at the minimum coefficient. For duopitch canopies the centre of pressure should be taken to act at the centre of each slope.

Table 13 Pressure Coefficients (Top and Bottom) for Pitched Roofs, Roof Slope, $\alpha = 30^{\circ}$ (Clause 4.5.3.3.3)

Roof slope $\alpha = 30^{\circ}$

$\theta = 0^{\circ} - 45^{\circ}, D, D', E, E'$ full length.

$\theta = 90^{\circ},D,D^{\prime},E,E^{\prime}$ part length

$b^{\prime}$ , thereafter $\mathrm{C_p} = 0$

Wind Angle θ	Pressure Coefficients, $C_p$
	D	$D'$	E	$E'$	End Surfaces
	D	$D'$	E	$E'$	C	$C'$	G	$G'$
0°	+ 0.6	- 1.0	- 0.5	- 0.9
45°	+ 0.1	- 0.3	- 0.6	- 0.3
90°	- 0.3	- 0.4	- 0.3	- 0.4	- 0.3	+ 0.8	+ 0.3	- 0.4
For all value of θ	For J : $C_pTop = 1.0$ , $C_pbottom = - 0.2$ Tangentially acting friction : $R_{90^\circ} = 0.05 p_d bd$

PART 6 STRUCTURAL DESIGN — SECTION 1 LOADS, FORCES AND EFFECTS

Table 14 Pressure Coefficients (Top and Bottom) for Pitched Free Roofs, $\alpha = 30^{\circ}$ With Effects of Train or Stored Material (Clause 4.5.3.3.3)

Roof slope $\alpha = 30^{\circ}$

Effects of trains or stored materials.

$\theta = 0^{\circ} - 45^{\circ}$ , or $135^{\circ} - 180^{\circ}$ , $D, D', E, E'$ full length.

$\theta = 90^{\circ},D,D^{\prime},E,E^{\prime}$ part length

$b^{\prime}$ , thereafter $C_p = 0$

Wind Angle θ	Pressure Coefficients, $C_p$
	D	$D'$	E	$E'$	End Surfaces
	D	$D'$	E	$E'$	C	$C'$	G	$G'$
0°	+ 0.1	+ 0.8	- 0.7	+ 0.9
45°	- 0.1	+ 0.5	- 0.8	+ 0.5
90°	- 0.4	- 0.5	- 0.4	- 0.5	- 0.3	+ 0.6	+ 0.3	- 0.4
180°	- 0.3	- 0.6	+ 0.4	- 0.6
For all value of θ	For J : $C_pTop = -1.5$ , $C_p bottom = 0.5$ Tangentially acting friction: $R_{90^\circ} = 0.05 p_d bd$

Table 15 Pressure Coefficients (Top and Bottom) for Pitched Free Roofs, $\alpha = 10^{\circ}$ (Clause 4.5.3.3.3)

Roof slope $\alpha = 10^{\circ}$

$\theta = 0^{\circ} - 45^{\circ}, D, D', E, E'$ full length.

$\theta = 90^{\circ},D,D^{\prime},E,E^{\prime}$ part length

$b^{\prime}$ , thereafter $\mathrm{C_p} = 0$

Wind Angle θ	Pressure Coefficients, $C_p$
	D	$D'$	E	$E'$	End Surfaces
	D	$D'$	E	$E'$	C	$C'$	G	$G'$
0°	-1.0	+0.3	-0.5	+0.2
45°	-0.3	+0.1	-0.3	+0.1
90°	-0.3	0	-0.3	0	-0.4	+0.8	+0.3	-0.6
For all value of θ	For $f: C_pTop = -1.0, C_pbottom = 0.4$ Tangentially acting friction: $R_{90^\circ} = 0.1 p_d bd$

PART 6 STRUCTURAL DESIGN — SECTION 1 LOADS, FORCES AND EFFECTS

Table 16 Pressure Coefficients (Top and Bottom) for Pitched Free Roofs $\alpha = 10^{\circ}$ With Effects of Train or Stored Materials (Clause 4.5.3.3.3)

Roof slope $\alpha = 10^{\circ}$

Effects of trains or stored materials.

$\theta = 0^{\circ} - 45^{\circ}$ or $135^{\circ} - 180^{\circ}, D, D', E, E'$ full length.

$\theta = 90^{\circ}, D, D', E, E'$ part length

$b'$ , thereafter $C_p = 0$ .

Wind Angle θ	Pressure Coefficients, $C_p$
	D	$D'$	E	$E'$	End Surfaces
	D	$D'$	E	$E'$	C	$C'$	G	$G'$
0°	-1.3	+0.8	-0.6	+0.7
45°	-0.5	+0.4	-0.3	+0.3
90°	-0.3	0	-0.3	0	-0.4	+0.8	+0.3	-0.6
180°	-0.4	-0.3	-0.6	-0.3
For all value of θ	For $f: C_p$ Top = -1.6, $C_p$ bottom = -0.9Tangentially acting friction : $R_{90^\circ} = 0.1 p_d$ bd

Table 17 Pressure Coefficients for Troughed Free Roofs, $\alpha = 10^{\circ}$ (Clause 4.5.3.3.3)

Roof slope $\alpha = 10^{\circ}$

$\theta = 0^{\circ} - 45^{\circ}, D, D', E, E'$ full length.

$\theta = 90^{\circ}, D, D', E, E' \text{ part length}$

$b^{\prime}$ , thereafter $\mathrm{C_p} = 0$

Wind Angle $\theta$	Pressure Coefficients, $C_p$
Wind Angle $\theta$	D	$D'$	E	$E'$
$0^\circ$	+ 0.3	- 0.7	+ 0.2	- 0.9
$45^\circ$	0	- 0.2	+ 0.1	- 0.3
$90^\circ$	- 0.1	+ 0.1	- 0.1	+ 0.1
For all value of $\theta$	For $f : C_pTop = 0.4$ , $C_pbottom = -1.5$ Tangentially acting friction: $R_{90^\circ} = 0.1p_d bd$

PART 6 STRUCTURAL DESIGN — SECTION 1 LOADS, FORCES AND EFFECTS

Table 18 Pressure Coefficients (Top and Bottom) for Troughed Free Roofs $\alpha = 10^{\circ}$ with Effects of Train or Stored Materials (Clause 4.5.3.3.3)

Roof slope $\alpha = 10^{\circ}$

Effects of trains or stored materials.

$\theta = 0^{\circ} - 45^{\circ}$ , or $135^{\circ} - 180^{\circ}$ , $D, D', E, E'$ full length.

$\theta = 90^{\circ}$ $D, D', E, E'$ part length

$b'$ , thereafter $C_{p}=0$ .

Wind Angle θ	Pressure Coefficients, $C_p$
Wind Angle θ	D	$D'$	E	$E'$
0°	-0.7	+0.8	-0.6	+0.6
45°	-0.4	+0.3	-0.2	+0.2
90°	-0.1	+0.1	-0.1	+0.1
180°	-0.4	-0.2	-0.6	-0.3
For all value of θ	For $f: C_pTop = -1.1$ , $C_pbottom = 0.9$ Tangentially acting friction: $R_{90^\circ} = 0.1p_d bd$

Roof Angle	Wind Angle	First Span	First Intermediate Span	Other Intermediate Spans	End Span	Local Coefficient
α Degree	θ Degree	a b	c d	m n	x z
5	0	-0.9 - 0.6	-0.4 - 0.3	-0.3 - 0.3	-0.3 - 0.3	-2.0	-1.5
10		-1.1 - 0.6	-0.4 - 0.3	-0.3 - 0.3	-0.3 - 0.4
20		-0.7 - 0.6	-0.4 - 0.3	-0.3 - 0.3	-0.3 - 0.5
30		-0.2 - 0.6	-0.4 - 0.3	-0.2 - 0.3	-0.2 - 0.5
45		+0.3 - 0.6	-0.6 - 0.4	-0.2 - 0.4	-0.2 - 0.5
DISTANCE
Roof Angle α Degrees		Wind Angle θ Degrees	h1	h2	h3
up to 45		90	-0.8	-0.6	-0.2

PART 6 STRUCTURAL DESIGN — SECTION 1 LOADS, FORCES AND EFFECTS

Table 20 External Pressure Coefficients ( $C_{pe}$ ) for Saw Tooth Roofs of Multispan Buildings (All Spans Equal) with h < w' (Clause 4.5.3.3.4)

ROOF PLAN

Wind Angle	First Span	First Intermediate Span		Other Intermediate Spans		End Span	Local Coefficient
θ Degree	a b	c d		m n		x z
0180	+ 0.6 - 0.7- 0.5 - 0.3	- 0.7 - 0.4- 0.3 - 0.3		- 0.3 - 0.2- 0.4 - 0.6		- 0.1 - 0.3- 0.6 - 0.1	- 2.0	- 1.5
DISTANCE
Wind Angleθ Degree	$h_1$		$h_2$		$h_3$
90	- 0.8		- 0.6		- 0.2
270	Similar to 90°, $h_1$ , $h_2$ , $h_3$ , are needed to be reckoned from the windward edge in the same order

Frictional drag : When wing angle $\theta = 0^{\circ}$ , horizontal forces due to frictional drag are allowed for in the above values, and

When wind angle $\theta = 90^{\circ}$ , allow for frictional drag in accordance with 4.5.4.1.

NOTE — Evidence on these buildings is fragmentary and any departure from the cases given should be investigated separately.

Table 21 External Pressure Coefficients ( $C_{pe}$ ) for Curved Roofs (Clause 4.5.3.3.6)

a) ROOF SPRINGING FROM GROUND LEVEL

b) ROOF ON ELEVATED STRUCTURE

c) DOUBLE CURVED ROOFS

VALUES OF $C$ , $C_1$ and $C_2$

H/I	C	$C_1$	$C_2$	$C_2$
0.1	-0.8	+0.1	-0.8	-0.05
0.2	-0.9	+0.3	-0.7	+0.1
0.3	-1.0	+0.4	-0.3	+0.15
0.4	-1.1	+0.6	+0.4	-
0.5	-1.2	+0.7	+0.7	-

NOTE — When the wind is blowing normal to gable ends,

C pe may be taken as equal to -0.7 for the full

width of the roof over a length of //2 from the

gable ends and - 0.5 for the remaining portion.

PART 6 STRUCTURAL DESIGN — SECTION 1 LOADS, FORCES AND EFFECTS

Table 22 External Pressure Coefficients ( $C_{pe}$ ) around Cylindrical Structures (Clause 4.5.3.3.7)

Position of Periphery, θDEGREE	Pressure Coefficients (Cpe)
Position of Periphery, θDEGREE	h / D = 25	h / D = 7	h / D = 1
0	1.0	1.0	1.0
15	0.8	0.8	0.8
30	0.1	0.1	0.1
45	-0.9	-0.8	-0.7
60	-1.9	-1.7	-1.2
75	-2.5	-2.2	-1.6
90	-2.6	-2.2	-1.7
105	-1.9	-1.7	-1.2
120	-0.9	-0.8	-0.7
135	-0.7	-0.6	-0.5
150	-0.6	-0.5	-0.4
165	-0.6	-0.5	-0.4
180	-0.6	-0.5	-0.4

Table 23 External Pressure Coefficients ( $C_{pe}$ ) for Roofs and Bottoms of Cylindrical Structures (Clause 4.5.3.3.8)

Coefficients of External Pressure (Cpe)
Structure According to Shape
a, b and c		d
H / D	Roof	(z / H) - 1	Roof	Bottom
0.5	- 0.65	1.00	- 0.75	- 0.8
1.00	- 1.00	1.25	- 0.75	- 0.7
2.00	- 1.00	1.50	- 0.75	- 0.6

Total force acting on the roof of the structure, $P = 0.785 \, \mathrm{D}^2 \, (\mathrm{C}_{\mathrm{pi}} - \mathrm{C}_{\mathrm{pe}}) \, p_{\mathrm{d}}$ . The resultant of $P$ lies eccentrically, $e = 0.1 \, \mathrm{D}$

PART 6 STRUCTURAL DESIGN — SECTION 1 LOADS, FORCES AND EFFECTS

FIG. 3 EXTERNAL PRESSURE COEFFICIENTS ON THE UPPER ROOF SURFACE OF CYLINDRICAL STRUCTURES STANDING ON THE GROUND

4.5.3.3.10 Roofs with skylight

The average external pressure coefficients for roofs with skylight are shown in Table 25.

4.5.3.3.11 Grandstands

The pressure coefficients on the roof (top and bottom) and rear wall of a typical grandstand roof which is open on three sides are given in Table 26. The pressure coefficients are valid for a particular ratio of dimensions as specified in Table 24 but may be used for deviations up to 20 percent. In general, the maximum wind load occurs when the wind is blowing into the open front of the stand, causing positive pressure under the roof and negative pressure on the roof.

4.5.3.3.12 Spheres

The external pressure coefficients for spheres shall be as given in Table 27.

4.5.3.3.13 Frames

When taking wind loads on frames of clad buildings it

is reasonable to assume that the pressures or suctions inside and outside the structure shall not be fully correlated. Therefore when taking the combined effect of wind loads on the frame, a reduction factor of $K_{c}=0.90$ may be used over the building envelope when roof is subjected to pressure and internal pressure is suction, or vice-versa.