CIVIL WORKS GUIDELINES FOR MICRO-HYDROPOWER IN NEPAL
117
Resolution of forces
α = 13° , β = 25°
Forces (kN)
X-component (kN) +
Y-component (kN) +
F1u = 3.90
- F1u sinα
= - 0.88
+ F1u cosα
= + 3.80
F1d = 3.63
- F1d sinβ
= -1.53
+ F1d cosβ
= +3.29
F2u = ±15.6
± F2u cosα
± 15.20
Positive during expansion 1
Negative during contraction 2
± F2usinα
± 3.51
Positive during expansion 1
Negative during contraction 2
F3 = 35.20
+ F3 sin[( β + α ) /2]
= + 11.46
- F3 cos[( β + α ) / 2]
= - 33.29
F4u = 2.97
+ F4u cosα
= +2.97cos13°
+2.89
+ F4u sinα
= - 2.97 sin13°
= 0.67
F6 = 45
± F6 ( cosα - cosβ )
± 45 ( cos13° - cos25° )
± 3.06
Positive during expansion 1
Negative during contraction 2
± F6 ( sinβ - sinα )
± 45 ( sin25° - sin13° )
± 8.90
Positive during expansion 1
Negative during contraction 2
F7u = 5.70
+ F7u cosα
= 5.70 cos13°
= + 5.55
+ F7u sinα
5.70 sin13°
= 1.28
F7d = 6.08
F8 = 0.26
= - F7d cosβ
= - 6.08 cos25°
= - 5.51
+ F8 sin [( β + α ) /2]
= 0.26 sin [(25° + 13°)/2]
= + 0.09
- F7d sinβ
= - 6.08 sin25°
= - 2.57
+ F8 cos [( β + α ) /2]
= 0.26 cos [(25° + 13°)/2]
= - 0.25
F10 = 23.45
+ F10 cos i
= 23.45 cos13°
= + 22.85
+ F10 sin i
23.45 sin13°
= + 5.28
WB = 354.64
SUM
0
ΣH = +53.18 1) Expansion
ΣH = + 16.66 2) Contraction
+354.64
ΣV = 345.26 1) Expansion
ΣV = 320.44 2) Contraction
Note that forces are positive in X-direction is towards the right and Y-direction downwards.
Calculate the centre of gravity of the block from the upstream face of the block taking the moment of mass.
The effect of the pipe passing through the block is negligible, so need not be calculated.
[{(3x2.5)3/2} + {(1/2)x3x1.05 (1/3)3}2] / [ {(3x2.25) + (1/2)3x1.05}2] = 1.41 m
... The weight of the block WB acts 1.41 m from point O .