BRIDGE DESIGN (SHEAR FORCE AND BENDING MOMENT CALCULATION) INPUT VARIABLES: CLEAR SPAN: BEARING WIDTH: FOOTPATH WIDTH: WEARING COAT: NO. OF LANES: CONCRETE GRADE: STEEL GRADE: CLEAR COVER: CURB HEIGHT:
5.5 400 1 100 2 25 415 30 225
m mm m mm N/mm2 N/mm2 mm mm
1) DESIGN DATA AND CONSTANTS: 8.3 200 10 0.29 0.903 1.09
m= k= j= Q=
2) DEPTH DETERMINATION: O/D FOR 5.5m SPAN = EFFECTIVE DEPTH = EFFECTIVE SPAN (Maximum of): I) ln+d = II) C/C dist. b/w supports = =
5.9
440 mm 397.5 mm
…(Assuming 80mm depth required for 1m span) …(Assuming 25mm dia bars to be used) 5.8975 m 5.9 m
m
3) dead load bending moment and dead load shear force: D.L OF SLAB = D.L OF WEARING COAT = TOTAL= BENDING MOMENT = SHEAR FORCE =
10.56 KN 2.2 KN 12.76 KN
…(Assuming unit wt. of concrete 24 KN/m3) …(Assuming unit wt. of wearing coat 22 KN/m3)
12.76 X 5.9^2/8 = 12.76 X 5.5 /2 =
55.52 KNm/m 35.09 KNm/m
IRC CLASS AA TRACKED VEHICLE: 4) LIVE load bending moment and shear force CALCULATION: EFFECTIVE LENGTH OF DISPERSION =
3.6+2 x (440+100)/1000 =
4.68 m
EFFECTIVE BREADTH OF DISPERSION FOR SINGLE WHEEL (MAX BENDING MOMENT CRITERIA):
TOTAL BREADTH OF CARRIAGEWAY = ASPECT RATIO = 1.61 VALUE OF α FOR ASPECT RATIO 1.61 FROM CHART IS = x= 2.95 m b1= 1.05 m 2.88x2.95x(1-2.95/5.9)+1.05=
7.5 m 2.88
5.3 m
TOTAL EFFECTIVE BREADTH OF DISPERSION : Bf = 2.625+2.05+2.65= 7.325 m 2.625
2.05
2.65
2.625
2.05
2.56
EFFECTIVE BREADTH OF DISPERSION FOR SINGLE WHEEL (MAX SHEAR FORCE CRITERIA):
ASPECT RATIO = 1.61 VALUE OF α FOR ASPECT RATIO 1.61 FROM CHART IS = x= 2.34 m b1= 1.05 m 2.88x2.34x(1-2.34/5.9)+1.05=
2.88
5.12 m
TOTAL EFFECTIVE BREADTH OF DISPERSION : Bf = 2.56+2.05+2.56= 7.17 m
5) impact factor: IMPACT FACTOR = TOTAL LIVE LOAD =
0.21625 851.375 KN 0.61
4.68
6) CALCULATION OF MAXIMUM BENDING MOMENT : 24.84
TOTAL DISPERSION AREA = 7.325 X 4.68 = UNIT LIVE LOAD = 851.375 / 34.281 =
34.281 m2 24.84 KN/m2 5.9
MAX BENDING MOMENT(L.L)= (24.84x4.68/2X5.9/2)-(24.84x4.68/2x4.68/4) = 103.46 KNm/m TOTAL BENDING MOMENT AT MID-SPAN (DL+LL)= 103.46 + 55.52 =
158.99 KNm/m
6) CALCULATION OF MAXIMUM SHEAR FORCE : TOTAL DISPERSION AREA = UNIT LIVE LOAD = 851.375 / 33.56 = MAX SHEAR FORCE (L.L) = TOTAL S.F AT SUPPORT (DL+LL)
33.56 m2 25.37 KN/m2
24.84x4.68x(5.9-4.68/2)/5.9 70.145 KN/m = 70.14 +35.09 =
4.68 105.24 KN/m
24.84
5.9
IRC CLASS AA TRACKED VEHICLE: WEIGHT PER WHEEL = 350 KN NO. OF WHEELS = 2 BREADTH OF WHEEL = 0.85 m LENGTH OF WHEEL = 3.6 m C= BREADTH OF CARRIAGEWA VALUE OF "C" = 1.2 m DIST. B/W C/L OF WHEELS = 2.05 m IMPACT FACTOR : FOR SPAN UPTO 9m: SPAN = 5.9 m If =
350 7.5
0.21625 ...(FOR ALL BRIDGE TYPES)
FOR SPAN OVER 9m: If =
If=
0.1 …(FOR SPAN UPTO 40M FOR RC BRIDGE) 0.1 …(FOR ALL SPANS FOR STEEL BRIDGE) 0.21625
C
350
350
0.85
3.6
IRC 70R TRACKED VEHICLE: WEIGHT PER WHEEL = NO. OF WHEELS = BREADTH OF WHEEL = LENGTH OF WHEEL = C= BREADTH OF CARRIAGEWAY= NO. OF LANES = VALUE OF "C" = DIST. B/W C/L OF WHEELS = IMPACT FACTOR : FOR SPAN UPTO 9m: SPAN = 5.9 m If =
350 KN 2 0.84 m 4.57 m 7.5 m 2 1.2 m 2.06 m
0.21625 ...(FOR ALL BRIDGE TYPES)
FOR SPAN OVER 9m: If =
If=
0.1 …(FOR SPAN UPTO 40M FOR RC BRIDGE) 0.1 …(FOR ALL SPANS FOR STEEL BRIDGE) 0.21625
350
C
350
0.84
4.57
IRC CLASS AA WHEELED VEHICLE: TOTAL WEIGHT = 400 KN NO. OF WHEELS = 8 BREADTH OF WHEEL = 0.3 m LENGTH OF WHEEL = 0.15 m C= BREADTH OF CARRIAGEWAY= VALUE OF "C" = 1.2 m
7.5 m
IMPACT FACTOR : SPAN= 5.9 m If= 0.25
37.5
1200
1050
300
300
2.2 1
62.5
62.5
37.5 150
300
700
300
300
300
IRC CLASS A WHEELED VEHICLE: TOTAL WEIGHT = NO. OF WHEELS =
554 KN 16
VALUE OF LENGTH & BREADTH: LOAD B W 27 0.15 0.2 68 0.2 0.38 114 0.25 0.5
1.1 27
B VALUE OF "C" =
0.15 m
WIDTH OF CARRIAGEWAY =
7.5 m
GAP BETWEEN TWO TRAINS OF VEHICLE =
1.2 m W
IMPACT FACTOR : SPAN = 5.9 m FOR R.C BRIDGE, If= 0.378
3.2 27
1.2 114
4.3 114
3 68
3 68
3 68
68
1.8
IRC 70R WHEELED VEHICLE:
0.91
3.96 80
1.52 120
2.13 120
170
COLUMN "l": TOTAL WEIGHT = NO. OF WHEELS = C=
1000 KN 28
BREADTH OF CARRIAGEWAY= NO. OF LANES = VALUE OF "C" = 1.2 m
7.5 m 2 0.41
IMPACT FACTOR : SPAN= 5.9 m If= 0.25
COLUMN "m": TOTAL WEIGHT = NO. OF WHEELS = C=
1000 KN 28
BREADTH OF CARRIAGEWAY= NO. OF LANES = VALUE OF "C" = 1.2 m
7.5 m 2 0.41
IMPACT FACTOR : SPAN= 5.9 m If= 0.25
COLUMN "n": TOTAL WEIGHT =
1000 KN
NO. OF WHEELS = C=
56
BREADTH OF CARRIAGEWAY= NO. OF LANES = VALUE OF "C" = 1.2 m
7.5 m 2
0.23
IMPACT FACTOR : SPAN= 5.9 m If= 0.25
1.37 170
3.05 170
1.37
0.91
170
2.79
0.61
0.04
2.79
0.61
0.385
0.38
2.79
0.51
0.05 0.25
0.76
DETAILING: 1
100mm thick wearing coat 12mm dia @200mmC/C
20mm dia @140mm C/C 12mm dia @185mm C/C 9.5 CROSS SECTION ALONG BREADTH
20mm dia @280mm C/C
12mm dia @185mm C/C 0.85l
20mm dia @140mm C/C
5.9 CROSS SECTION ALONG LENGTH
2 - 12mm dia bars
a @200mmC/C
a @140mm C/C
16mm dia @170mm C/C
12mm dia @200mmC/C 0.1 0.44
a @185mm C/C
a @140mm C/C
NOTE: ALL DIMENSIONS ARE IN metres