= 0.5*0.12*8.75

= 0.525 k/ft

3.1.7 UPWARD SOIL PRESSURE :

Upward soil pressure at the bottom slab may calculated from the following-

- From top slab including fill

= 0.1125 + 0.672 + 0.02

= 0.8045 k/ft^{2 }

- From vertical wall

= ( 2*0.75*0.15*4 ) / length of culvert

= ( 2*0.75*0.15*4 ) / ( 2*0.75+4*1 )

= 0.164 k/ft^{2 }

3. From wheel load

= 1.1428/length of culvert

= 1.1428 / ( 1*4+2*0.75 )

= 0.21 k/ft^{2 }

4. From bottom slab

= 0.75*0.15

= 0.1125 k/ft^{2 }

5. Water pressure = 64*4/1000

= 0.26 k/ft^{2}

Total vertical pressure on foundation soil

= ( 0.8025+0.164+0.21+0.1125+0.26 ) k/ft^{2 }

= 1.55 k/ft^{2}

3.1.8 LOAD ON BOX CULVERT :

- Top slab load (uniformly distributed) = 0.81k/ft

- Top slab load (concentrated),

Rear wheel = 1.1428 k/ft

Front wheel = 0.2857 k/ft

- Bottom slab load = 1.55 k/ft

- Side wall load at top = 0.525 k/ft

- Side wall load at bottom = 0.81 k/ft

- Surcharge load = 0.156 k/ ft

3.1.9 CALCULATION OF DISTRIBUTION FACTOR :

Moment of inertia,

IAB = bh^{3}^{ }/12

= 12*9^{3}^{ }/12

= 729 in^{4 }[consider 1 ft strip]

Stiffness,

kAB =I/L [center line dimension]

= 729/57

= 12.8

IAB = 729 in^{4}

KAB = 12.8

IAC = 12*9 / 12

= 729 in^{4}

KAC = 729 / 57

= 12.8

Distribution factor,

DAB = 12.8 / (12.8+12.8)

= 0.50

DAC = 12.8 / (12.8+12.8)

= 0.50

DBA = 12.8 / (12.8+12.8)

= 0.50

3.1.10 CALCULATION OF FIXED END MOMENT :

MAB = -wl^{2 }/12-Pl/8

= -0.81*4.75^{2 }/12-1.143*4.75/8

= -2.202 k-ft

MBA = 2.202 k-ft

MAC = Pl^{2 }/12+wl^{2 }/30

= (0.156+0.525)*4.75^{2 }/12+(0.81-0.525)*4.75^{2 }/30

= 1.49 k-ft

MCA = -Pl^{2 }/12-wl^{2 }/20

= -(0.156+0.525)*4.75^{2 }/12-(0.81-0.525)*4.75^{2 }/20

= - 1.6 k-ft

MCD = wl^{2 }/12

= 1.55*4.75/12

= 2.91 k-ft

MDC = -2.91 k-ft

In case of concealed slab

Effective width, E = 1.75 * 8

= 14 ft.

Therefore, let us assume, the dispersion width is 14 ft considering following provisions of PCA manual, AASHTO-92, section 3.8.2.3,

Impact factor for wheel load, I = 0.0%

Weight of each vertical wall = 4 * 0.15 * 1 [consider 1 ft strip]

= 0.6 k/ft

The transmission and distribution of wheel loads through soil generally assumed to follow the principles of elasticity.

When the depth of fill is less than 2 ft, AASHTO specifies that, the wheel load be distributed as an exposed slab, when the depth of fill is more than 2 ft, concentrated loads are to be uniformly distributed over a square, the side of which are equal to 1.75 times the depth of fill.

Therefore, concentrated load ( conceal slab ) :

Live load from rear wheel, per ft of slab

= {16(1+Impact factor/100)}/14

= 1.1428 k/ft [Impact factor = 0%]

Live load from front wheel, per ft width of slab,

= {4(1+Impact factor/100)}/14

= 0.2857 k/ft

Concentrated load ( exposed slab ) with no impact

= 16 ( 1+0/100 ) / 4.57

= 3.5 k

3.1.6 SIDE WALL LOAD :

Coefficient of active earth pressure is calculated by using the Rankine’s formula,

ka = (1-sin 30^{0}) / (1+sin30^{0} )

= 0.33

But in our case, we consider co-efficient of active earth pressure at rest condition,

ka = (1-sin 30^{0} )

= 0.5

The effect of live load surcharge when acting along ( with approach slab), will be uniformly lateral load.

Uniformly lateral load due to surcharge equivalent to 2.6ft earth fill

h= 8+9/12+4+9/12

= 13.5

h1 = 8+9/12

= 8.75

Lateral pressure at the bottom of vertical wall

= 0.5*0.12*13.5

= 0.81 k/ft

Lateral pressure at centerline of top slab