Design Specifications of Tower: 1. 2. 3. 4. 5.
Length of the pole = 9m Top Inner Diameter of the Pole = 120mm Bottom Inner Diameter of the pole = 255mm Angle of Winding = 6.5 degrees Materials Used = Epoxy YD128 & Hardener HY951
For three cases of wind speeds 100 km/hr, 150 km/hr, 200 km/hr. 1. Layup sequence for a 9 meter pole with a deflection value of 1350 mm. 2. Values of bending bending strength, Torsional Torsional strength etc. etc. Layup sequence for a 9 m pole is as follows 1. 2. 3. 4. 5.
Helical @ 6.5 deg Helical @ 6.5 deg Helical @ 6.5 deg Helical @ 6.5 deg Hoop
The Deflection of the tower should not exceed 5% 5 % of the total height of the tower. 9
Ex Ex Ex PRXY PRYZ PRZX GXY GYZ GZX
Units ( in N/m2) 110e9 8.7e9 8.7e9 0.27 0.27 0.27 2.7e9 2.7e9 2.7e9
Lower angles are considered for practical limitation
Towers are generally considered as rigid structures and hence static wind pressures are computed as per the Indian standard standard code. In computing the wind pressures variation along the height, exposed areas of the columns and braces are considered.
: Tanks supported on staging are treated as point like structures. As the height of the staging is increased the tower becomes slender. The fundamental frequency of this point like structure mainly depends on the mass concentrated at the top. The value of the frequency gets reduced with the increase in the height of the tower.
Wind pressures acting at any height on a structure are computed by the methods recommended by the IS code (IS 875-(Part 3)-1987). The code has recommended two methods for computing the wind pressures based on the requirement. Design wind speed (Vz) at any height height can be calculated calculated as follows: Vz=Vb*K1*K2*K3, Where Vz = Design wind speed at any height z in m/sec, Vb=Basic wind speed speed for any site, K1 = probability factor (risk coefficient), K2 = Terrain, height and structure size factor and K3 = Topography factor K1, K2 and K3 are given by means of tables in the code. The design wind pressure at any height above mean ground level shall be obtained by the following relationship between wind pressure and wind velocity. Pz=0.6VZ2, Where Pz = Design wind pressure in N/m2 at height z, Vz = Design wind wind velocity in m/s m/s height z.
The variation of hourly mean wind speed with height shall be calculated as follows. VZ=Vb*K1*K2*K3. Where Vz =hourly =hourly mean wind wind speed in m/s at height height z. Vb = regional regional basic wind speed in m/s; K1 = probability factor. K2 = terrain and height factor. K3= topography factor.
These factors are given in the code.
Along wind load on structure on strip area (Ae) at any height (Z) is given by: Fz= Cf*Ae*Pz*G Where, Fz = along wind load on the structure at any height z corresponding to strip area Ae, Cf = force coefficient for the building, Ae = effective frontal area considered for the structure at height z, Pz = design pressure at height z due to hourly mean wind obtained as 0.6*vz2 (N/m2), G= gust factor (peak load /mean load) and is given by: G=1+gf r* sqrt (B (1+ ( Φ)) 2+SE/ β) gfr = peak factor defined as the ratio of the expected peak value to the root mean value of a fluctuating load, and r= roughness factor which is dependent on the size of the structure in relation to the ground roughness. The value of 'gfr' is obtained from (Fig. 8 of the code). B = background factor indicating a measure of slowly varying component of fluctuating wind load and is obtained from Fig. 9 of the code . S= size reduction factor is obtained from Fig.10 of the code. E = measure of available energy in the wind stream at the natural frequency of the structure is obtained from Fig.11 of the code. β= Damping coefficient (as fraction of critical damping) of the structure (Table 34 of
the code). Φ= gfr*sqrt((B)/4) and is to be accounted only for buildings less than 75 m height in
terrain category 4 and for buildings less than 25 m high in terrain category 3, and is to be taken as zero in all other cases. λ= Cy b/Cz h and Fo = Cz *fo*h/Vh
Where Cy = lateral correlation constant which may be taken as 10 in i n the absence of more precise load data, Cz = longitudinal correlation constant which may be taken as 12 in the absence of more precise load data, B = breadth of a structure normal to the wind stream, H = height of a structure,
Vh = Vz = hourly mean wind speed speed at height z, fo - natural frequency of the structure, and L (h) = a measure of turbulence length scale.
The present study deals with the computation of deflection, torsional strength, bending strength on towers of 9m height. The wind pressures pressures are computed by using both the methods as already described. Towers with height 9m and varying speeds 100 km/hr, 150 km/hr, 200 km/hr are considered for wind pressure analysis SUBJECTED TOgust loads. The details details are are as follows:
100*(5/18) = 27.77 m/sec As per clause 5.3 of code, the design wind speed is given by Vz = Vb * K1* K2* K3. Where, Risk coefficient coefficient (K1) = 1.0 (Table 5.3.1 of the the code). Topography factor (K3) =1.0 (as per clause 5.3.3of the code) . Terrain factor (K2) = 0.978 (at 9m high tower, as per Table 2.3 of the code) . Design Wind Speed Vz = 27.7* 1.0* 0.978*1.0 = 27.09m/sec. Design Wind Pressure at 9m high water tower = Pz = 0.6* Vz 2 = 0.6* (27.09) 2 = 440.32 N/Sq.m.
: The basic wind speed (Vb) at 9m height is 27.7 m/sec. Risk coefficient (K1) = 1.0 (Table 2.2 of the code). Topography factor (K3) = 1.0 (as per clause 5.3.3 of the code). Terrain factor (K2) = 1.0 (for category 3 at 9 m high tower, as per the code) and as per clause 8.2.1 of the code. Hourly Mean Wind Speed in m/sec at height ‘z’ is Vz = Vb * K1* K2* K3. = 27.7* 1.0* 1.0* 1.0* 1.0 = 27.7 m/sec. m/sec. Mean wind pressure at 9m height = Pz = 0.6* Vz2 = 0.6 * (27.7)2 = 460.374 N/Sq.m. G = gust factor) (Peak Load/Mean Load/Mean Load), Load), and is given by: by: G = 1+ gf r Sqrt Sqrt (B (1+ø) 2 + SE/ β) From Fig. 5 of the code, peak and roughness factor gf r = 1.125 at 9 m height. From Fig. 5 of the code Turbulence length scale L (h) = 1125 at 9 m height. Where, Cy = lateral correlation correlation constant = 10, 10, Cz = longitudinal correlation constant constant = 12, h = height of a structure = 9 m,
= (10*0.1935)/ (12*9) = 0.01791 and Cz *h/L (h) = (12*9)/1125 = 0.096 From fig. 9 of the code, background bac kground factor ‘B’ = 0.82 at 9m 9m height. Reduced frequency Fo = Cz *fo*h/Vh Where, natural natural frequency of 9 m high water tower = fo = 0.9 cycles/sec cycles/sec Vz = Hourly mean mean wind speed at 9 m height = 27.7 m/sec. Fo = (12*0.9*9)/27.7 = 3.50 From fig.10 of the code, Size reduction factor ‘S’ = 0.4 at 9 m height. fo*L(h)/Vh = (0.9*1125)/27.7 = 36.55 ø = gf r. Sqrt(B)/4 = 1.125*Sqrt(0.82)/4 = 0.25 From fig. 11 of the code, the th e gust energy factor ‘E’ = 0.05. Damping coefficient of the structure β = 0.020 As per code, gust factor G=1+ gf r Sqrt (B (1+ ø)² + SE/ β) = 1+1.125 Sqrt (0.82 (1+0.25) ² + (0.4*0.05)/0.020) = 2.69 F= Cf*Ae*Pz*G = 1.2*1*460.374*2.69 =
150*(5/18) = 41.66 m/sec As per clause 5.3 of code, the design wind speed is given by Vz = Vb * K1* K2* K3. Where, Risk coefficient coefficient (K1) = 1.0 1.0 (Table 2.2 of the code) code) (4). Topography Topography factor (K3) =1.0 (as per clause 5.3.3of the code). Terrain factor (K2) = 0.978 (at 9m high tower, as per Table 2.3 of the code). Design Wind Speed Vz = 41.66* 1.0* 0.978*1.0 = 40.74m/sec. Design Wind Pressure at 9m high water tower = Pz = 0.6* Vz2 = 0.6* (40.74) 2 = 995.8 N/Sq.m.
: The basic wind speed (Vb) at 9m height is 41.66 m/sec. Risk coefficient (K1) = 1.0 (Table 2.2 of the code). Topography factor (K3) = 1.0 (as per clause 5.3.3 of the code).
Terrain factor (K2) = 1.0 (for category 3 at 9 m high tower, as per the code) and as per clause 8.2.1 of the code. Hourly Mean Wind Speed in m/sec at height ‘z’ is Vz = Vb * K1* K2* K3. = 41.66* 1.0* 1.0* 1.0 = 41.66 m/sec. Mean wind pressure at 9m height = Pz = 0.6* Vz2 = 0.6 * (41.66)2 = 1041.3 N/Sq.m. G = gust factor) (Peak Load/Mean Load/Mean Load), Load), and is given by: by: G = 1+ gf r Sqrt Sqrt (B (1+ø) 2 + SE/ β) From Fig. 5 of the code peak and roughness factor gf r = 1.125 at 9 m height. From Fig. 5 of the code Turbulence length scale L (h) = 1125 at 9 m height. Where, Cy = lateral correlation correlation constant = 10, Cz = longitudinal correlation constant constant = 12, h = height of a structure = 9 m, = (10*0.1935)/ (12*9) = 0.01791 and Cz *h/L (h) = (12*9)/1125 = 0.096 From fig. 9 of the code, background bac kground factor ‘B’ = 0.82 at 9m 9m height. Reduced frequency Fo = Cz *fo*h/Vh Where, natural natural frequency of 9 m high water tower = fo = 0.9 cycles/sec cycles/sec Vz = Hourly mean mean wind speed at 9 m height = 41.66 m/sec. Fo = (12*0.9*9)/41.66 = 2.33 From fig.10 of the code
Size reduction factor ‘S’ = 0.5 at 0.5 at 9 m height.
fo*L(h)/Vh = (0.9*1125)/41.66 = 24.30 ø = gf r. Sqrt(B)/4 = 1.125*Sqrt(0.82)/4 = 0.25 From fig. 11 of the code, the th e gust energy factor ‘E’ = 0.053. 0.05 3. Damping coefficient of the structure β = 0.020 As per code, gust factor G=1+ gf r Sqrt (B (1+ ø)² + SE/ β) = 1+1.125 Sqrt (0.82 (1+0.25) ² + (0.5*0.053)/0.020) = 2.816 F= Cf*Ae*Pz*G = 1.2*1*1041.3*2.816 1.2*1*1041.3*2.816 =
200*(5/18) = 55.55 m/sec As per clause 5.3 of code, the design wind speed is given by Vz = Vb * K1* K2* K3.
Where, Risk coefficient (K1) = 1.0 (Table 2.2 of the the code). Topography factor (K3) =1.0 (as per clause 5.3.3of the code). Terrain factor (K2) = 0.978 (at 9m high tower, as per Table 2.3 of the code). Design Wind Speed Vz = 55.55* 1.0* 0.978*1.0 = 54.32 m/sec. Design Wind Pressure at 9m high water tower Pz = 0.6* Vz2 = 0.6* (54.32) 2 = 1770.39 N/Sq.m.
: The basic wind speed (Vb) at 9m height is 55.55 m/sec. Risk coefficient (K1) = 1.0 (Table 2.2 of the code). Topography factor (K3) = 1.0 (as per clause 5.3.3 of the code). Terrain factor (K2) = 1.0 (for category 3 at 9 m high tower, as per the code) and as per clause 8.2.1 of the code (4). Hourly Mean Wind Speed in m/sec at height ‘z’ ‘ z’ is Vz = Vb * K1* K2* K2* K3. = 55.55* 1.0* 1.0* 1.0 = 55.55 m/sec. Mean wind pressure at 9m height = Pz = 0.6* Vz 2 = 0.6 * (55.55)2 = 1851.4 N/Sq.m. G = gust factor) (Peak Load/Mean Load/Mean Load), Load), and is given by: by: G = 1+ gf r Sqrt Sqrt (B (1+ø) 2 + SE/ β) From Fig. 5 of the code peak and roughness factor gf r = 1.125 at 9 m height. From Fig. 5 of the code Turbulence length scale L (h) = 1125 at 9 m height. Where, Cy = lateral correlation correlation constant = 10, Cz = longitudinal correlation constant constant = 12, h = height of a structure = 9 m, = (10*0.1935)/ (12*9) = 0.01791 and Cz *h/L (h) = (12*9)/1125 = 0.096 From fig. 9 of the code, background background factor ‘B’ = 0.82 at 9m 9 m height. Reduced frequency Fo = Cz *fo*h/Vh Where, natural natural frequency of 9 m high water tower = fo = 0.9 cycles/sec cycles/sec Vz = Hourly mean mean wind speed at 9 m height = 55.55 m/sec. Fo = (12*0.9*9)/55.55 = 1.74 From fig.10 of the code
Size reduction factor ‘S’ = 0.6 at 0.6 at 9 m height.
fo*L(h)/Vh = (0.9*1125)/55.55 = 18.22
ø = gf r. Sqrt(B)/4 = 1.125*Sqrt(0.82)/4 = 0.25 From fig. 11 of the code, the th e gust energy factor ‘E’ = 0.055. 0.05 5. Damping coefficient of the structure β = 0.020 As per code, gust factor G=1+ gf r Sqrt (B (1+ ø) ² + SE/ β) = 1+1.125 Sqrt (0.82 (1+0.25) ² + (0.6*0.053)/0.020) = 2.92 F= Cf*Ae*Pz*G = 1.2*1*1851.4*2.816 1.2*1*1851.4*2.816 =
All Dimensions are in mm Along vertical the given line is divided into 50 parts Each part along vertical = 9000/50 =180 mm Along the circumference the given line is divided to 50 parts = π D/50
= (3.1417*120)/50 = 7.54008 mm Pressure = Force / Area = (1486.08/50) / (180*7.54008) = 0.021 N/mm2 = 0.021*106 N/m2 S.No
Speed(m/sec)
Force (N)
Pressure( N/m2)
1. 2. 3.
27.7 41.66 55.55
1486.08 3518.76 6256.25
0.021*106 0.051*106 0.092*106
= wl4 / (8Es ( π π /64(Ds -1204)) = wl4 / (8Ec ( π /64(Dc -1204))
wl4 / (8Es ( π π /64(Ds -1204)) = wl4 / (8Ec ( π π /64(Dc -1204)) Ec (Dc4 -1204) = Es (Ds4 – 120 1204) Dc4 – 120 1204 = Es / Ec (Ds4 – 120 1204) Dc4 = 200/110 (Ds4 – 120 1204) +1204 Dc4 = 1.8 Ds4 – 1.8*120 1.8*1204 +1204 Dc4 = 1.8 Ds4 + (1204) (1-1.8) Dc4 = 1.8 Ds4- 0.8*(1204) Dc4 = 1.8 (132)4- 0.8*(1204)
(Total thickness = 12mm)
Dc4 = 546.4*106- 165.8*106 Dc4 = 380.6*106 Dc= 139.67 mm
(140-120 = 20 mm)
Thickness of composite = 10 mm
= wl4 / 8EI w= 1486.08/9
= 165.12 N/m = 165.12*94 / (8*200*109((π/64) (0.132 (0.1324 – 0.120 0.1204) = 0.143 m (or) 143 mm wl4 / 8EI =165.12*94 / (8*110*10 9((π/64) (0.139.67 (0.139.674 – 0.120 0.1204) = 0.143 m (or) 143 mm
15.244 15.491
37.021 37.62
Speed Vs. Deflection
68.961 67.866
68.961mm
69 66 63 67.866mm
60 57 54 51 48 n 45 o i t c 42 e l f e 39 D
37.021mm
36
37.62mm
33 30 27 24 21
15.224mm
18 15
15.491mm
12 9 6 3 0
100
150
200
Composite
15.491
37.62
67.866
Steel
15.224
37.021
68.961
Speed Composite
Steel
ELEM
7499
VALUE
-0.21509E+07
ELEM
2449
VALUE 0.19913E+07
7546 -0.71588E+06
2549 0.41323E+06
7250 -0.24936E+06
2450 0.23387E+06
ELEM VALUE
7499 -0.52235E+07
ELEM
2449
VALUE
0.48361E+07
7546
7250
-0.17386E+07
-0.60559E+06
2549 0.10036E+07
2450 0.56796E+06
ELEM
7546
VALUE
-0.31362E+07
ELEM
2549
VALUE 0.18104E+07
7499 -0.94228E+07
2449 0.87240E+07
7250 -0.10924E+07
2450 0.10246E+07
Four load cases are applied to the two corners of the free end a. 1468.08 N at each corner. The time at the end of the load step is 10 seconds b. -1468.08 N at each corner. The time at the end of the load step st ep is 20 seconds c. 1468.08 N at each corner. The time at the end of the load step is 30 seconds d. -1468.08 N at each corner. The time at the end of the load step st ep is 40 seconds The material fatigue properties are described by Number of cycles , N
Fatigue strength, Sf
<103
0.9Su (0.9) 2
103 to 106
>106
N-(1/3)log(0.9Su/Se) Se
Where Su is the ultimate strength and Se is the endurance limt (Fatigue limit). Assume the ratio of Su /Se is equal to 0.6. Location: Anode in the model for which fatigue stresses are stored. Event: A set of stress conditions that occur at different times during stress cycle Loading: one of the stress conditions that is a part of event The events to be used in the analysis are Event No.
Load No.
Loading
Number of Repetitions
Scale factor
1 1
1 2
1468.0 N -1468.0 N
500,000 500,000
1 1
2 2
1 2
1468.0 N -1468.0 N
5000 5000
1 1
Location 3 Node 35 Fixed end The combination of event 2 , load 1 and event 2, load 2 produces an alternating stress intensity of 0.45992*107 N/m2, It was subjected to 5000 cycles while from the S-N table , the maximum number of cycles that are allowed at that stress intensity is 0.1*107 . The partial usage value, 0.00500 is the ratio of cycles used/cycles allowed.
The combination of event 1 , load 1 and event 1, load 2 produces an alternating stress intensity of 0.45992*107 N/m2, It was subjected to 50,000 cycles while from the S-N table , the maximum number of cycles that are allowed at that stress intensity is 0.1*107 . The partial usage value, 0.50000 is the ratio of cycles used/cycles allowed.
The cumulative fatigue usage is the sum of the partial usage factors fact ors (Miner’s Rule)
Location 3 Node 35 Fixed end The combination of event 2 , load 1 and event 2, load 2 produces an alternating stress intensity of 0.11024*108 N/m2, It was subjected to 5000 cycles while from the S-N table , the maximum number of cycles that are allowed at that stress intensity is 0.1*107 . The partial usage value, 0.00500 is the ratio of cycles used/cycles allowed.
The combination of event 1 , load 1 and event 1, load 2 produces an alternating stress intensity of 0.11024*108 N/m2, It was subjected to 50,000 cycles while from the S-N table , the maximum number of cycles that are allowed at that stress intensity is 0.1*107 . The partial usage value, 0.50000 is the ratio of cycles used/cycles allowed.
The cumulative fatigue usage is the sum of the partial usage factor fact orss (Miner’s Rule)
Location 3 Node 35 Fixed end The combination of event 2 , load 1 and event 2, load 2 produces an alternating stress intensity of 0.1000*10-29 N/m2, It was was subjected to 5000 5000 cycles while from the S-N table , the maximum number of cycles that are allowed at that stress intensity is 0.1*107 . The partial usage value, 0.00500 is the ratio of cycles used/cycles allowed.
The combination of event 1 , load 1 and event 1, load 2 produces an alternating stress intensity of 0.19600*108 N/m2, It was subjected to 50,000 cycles while from the S-N table , the maximum number of cycles that are allowed at that stress intensity is 0.1*107 . The partial usage value, 0.50000 is the ratio of cycles c ycles used/cycles allowed.
The cumulative fatigue usage is the sum of the partial usage factors fact ors (Miner’s Rule)
