Plan of Bridge Deck
The HB vehicle is placed on the bridge deck as shown above
Where L = span of bridge or beam
Where L = span of bridge or beam
X = varying distance of axle 1 from left support A
P = wheel load for number of units of HB vehicle under consideration
Taking moment about A
RB.L = 4P (9.6 +x) + 4P(7.8 + x) + 4P(1.8 + x) + 4Px
RB.L = 4P(9.6 + 7.8 + 1.8 +x +x +x + x)
= 4P(19.2 + 4x)
= 4P(19.2 + 4x)
RB = 4P x 4(4.8 + x)
L
RB = 16P(4.8 + x)
L
RB = 16P(4.8 + x)……………………………………………………………….(1)
L
Corresponding relation at A
RB =16P - 16P (4.8 + x)…………………………………………………………………………………..(2)
L
Maximum moment should exist under axle 2 at (x + 1.8)m distance from A
1-1(4.8 + 2x) = 1.8
L L
L – (4.8 + 2x) = 1.8
L – 4.8-2x = 1.8
L-2x = 6.6
L – 6.6 = 2x
X = L – 6.6 = L – 3.3
2 2
X = L – 3.3…………………………………………………………………………………………………………………(3)
2
This is the distance of axle 1 from A at maximum moment.
The distance of axle 2 from A is
X + 1.8 = L – 3.3 + 1.8 = L – 1.5
2 2
(x + 1.8) = L – 1.5…………………………………………………………………………………………………..(4)
2
i.e. the vehicle is placed such that the centire line of the bridge is equidistant from the axle
2 and the centre line of the HB vehicle.
Mmax = RA(x + 1.8) – 4P X 1.8
= (16P – 16P(4.8 +x))(x + 1.8) – 4.8 X 1.8
L
= (16P – 16P(4.8 +L – 3.3))(L -3.3 + 1.8) – 7.2P
L 2 2
= (16P – 16P(L + 1.5))(L -1.5) – 7.2P
L 2 2
= [(16P – 16P. L -16P . 3)( L – 1.5)] – 7.2P
L . 2 L . 2 2
= [(8P – 8P . 3) (L -1.5))] – 7.2P
L 2
= 8P(1 – 3) . (L -1.5) – 7.2P
L 2
= 8P[( L – 3) . (L -3)] -7.2P
L 2
Mmax = 8P( L – 3)2 – 7.2P ………………………………………………………………(5)
2L
Calculation for Max RA
From eqn 1
RA = 16P - 16P(4.8 + x)
L
RA is a maximum when X=0
Therefore;
RA = 16P (1 – 4.8)
L
RA = 16P (L – 4.8)………………………………………………..(6)
L
i need to know how do u form the equation 1-1/L(4.8+2x)=1.8/L ?
ReplyDelete1-1(4.8 + 2x) = 1.8
ReplyDeleteL L
where does this come from? pls help
It means maximum moment under the second axle.At a distance of x+1.8 or you could write the full moment equation and differentiate to obtain the maximum and solve for x.
ReplyDelete