Download Analysis of Spacing and Moment Capacity for Longitudinal Girders in a Bridge and more Assignments Highway Engineering in PDF only on Docsity!
1. T Girder Bridge Design AASHTO
Material Properties Concete A (C35) = 28 MPa Art 5.4.2. Yield strength of Reinforcing bars = 420 MPa Art 5.4.3. Modulus of Elasticity of Reinforcing bars Es = 200 Gpa Density of Concrete = 24 Denisity of Wearing Surface = 22 Design Method Load and resistance Factor Design ( LRFD ) method according to American Association of state Highway and Transportation Officials (AASHTO) code , SI Units, Third Edition, 2005
1.1 Preliminary Design Dimensions
Fig 1.1 Longitudinal section Fig 1.2 Cross-section Total cross - sectional length = 9.37 m Clear span = 22 m AASHTO f'c fy gc KN/m^3 gs KN/m 3
Depth of girder For simple span T-girder, D = 0.07*L , where L is span length Table 2.5.2.6.3.
From this the minimum depth of T-girder will be 1.575 m Take D = 1.8 m Spacing between longitudinal girders S varies from 1.8 to 3.6 m C is a function of S and it varies from 0.25S up to 0.75S from the geometry of the T –girder above take c = 0.5 S S = 2.3425 m Take S = 2.5 m C = 1. Take C = 1.2 m Web width Minimum thickness = 200 mm without pre-stressing Art 5.1.4.1.3.1c But this width of the web has to satisfy the clear spacing between bars. The clear spacing between bars in a raw should not be less than 1.5 Φ or the maximum aggregate size. Minimum concrete cover of 50mm is provided. Consider splice spacing of bars=1.5Φ Taking 32mm bars, 4 32 bars in a row require a beam width of 436 mm 450 mm 183.333 mm 180 mm for structural thickness of the slab. bw > Take bw = Slab thickness Take ts =
L = 25. 0 +
D min = 0. 07 ∗ L = 2 c + 3 S = 9. 97 m S + 3 S = 9. 97 m bw ≥ 3 ∗ 1. 5 φ + 6 ∗ φ + cov er bw ≥ 3 ∗ 1. 5 ∗ 32 + 6 ∗ 32 + 2 ∗ 50 ts min = S + 3000 30 ts min = 2500 + 3000 30 =
**1.2 Deck Slab AASHTO
- Dead loads A. Self Weight** Wearing surface: 75mm thick asphalt pavement 0.075 * 1. RC slab
Overhang slab = 5.820 0.180 0. Curb (200mm above slab) 0.2 * 24 KN/m2 = 4.320 Over hang slab Concrete barrier wall
W1 = 2.640 KN/m at X = 0.100 m from A W2 = 0.420 KN/m at X = 0.312 m from A 0. W3 = 3.852 KN/m at X = 0.268 m from A 6.912 KN/m 1.425 0. x = 0.206 m from A
A
B. Dead Load Moments An approximate analysis of strips perpendicular to girders will be consider Art 9.6. The extreme positive moment in any deck panel between girders shall be taken to apply to all positive Art.4.6.2.1. moment regions similarly, the extreme –ve moment over any girder shall be taken as continuous beams with span length equal to c/c distance between the girders. gs = (^) KN/m^2 ts * gc = (^) KN/m^2 KN/m^2 KN/m^2
å w =
åMA = å w * x=
KN
m^3
RC Slab + 75mm Asphalt = 5. AASHTO Over hang Slab + Curb = 10. 1m widths will be taken 6.912 10. = 15.461 KNm/m 1.240 1. Moment at support B and C Using influence line segment coefficient table II Influence line segment coefficient = -0. S = 2.400 m Mb = Mc = -4.985 5.220 10. = 18.612 KN 10.800 6. Rb1 = = 0.085 2. KN/m^2 KN/m^2 åFy = 0 Ra1 = 10.8 * 1.24 + 5. åMA = 0 2.5Rb1 = 5.312 + (6.212.5^2 )/2 + (10.8 - 6.21 ) 0.5 * 0.085^2 - 14. åFy = 0 Ra2 = (10.8 - 6.21 )0.085+ 6.212.5 -10. åMA = 0 2.5Rc1 + 5.32 - (6.21 * 2.52^2 )0.5 - 5.312 = 0 Rb2=Rc1= M (^) end =
- 8 ∗ 1. 24
2
- 22 ∗ 1. 109 M (^) b = M (^) c = 6. 21 KN / m ∗(− 0. 1 )∗ 2. 5 2
- 092 ∗(− 0. 1 )=(− 5. 31 ) KNm / m
first interior span. P1= 72.500 KN P2 = 72.500 KN a1 = 1.000 m a2 = 0.300 m b1 = 1.500 m b2 = 2.200 m S = 2.500 m P1 P a1 b1 a2 b2 AASHTO 1.24m 2.500 m 2.500 m 2.500 m 1.24m 2.500 2.500 2. K 0.750 1.000 0. DF 0.000 0.429 0.571 0.571 0. FEM 0.000 -30.450 16.843 -2.297 0. 5.831 7.775 3. -0.455 -0.909 -0. 0.195 0.260 0. -0.037 -0.074 -0. 0.016 0.021 0. -0.006 -0. -24.408 24.408 0.742 -0. M at B = 24. M at C = 0. 1m 1.5m 0.3m 2.22m ∑Ma = 0 ∑Mb = 0 38.763 KN -1.360 KN ∑Fy = 0 ∑Fy = 0 33.737 KN 73.860 KN ∑Md = 0 Mc Rc2 *2.5 - 0.742 = 0 Rc2 Rd1 Rc2 = 0.297 KN ∑Fy = 0 33.737 KNm 0.297 + Rd1 = 0 Rd1 = -0. E = 660+0.55S E = 2035.000 mm Ra = 33.737 KN Rb = 112.623 KN Rc = -1.063 KN Rd = -0.297 KN Ra1 Ra2 Rb1 Rb2 Rc1 Rc2 Rd1 Rd Mb Mc Mb Ra2 Rb1 Rb2 Rc Rb1 = Rc1= Ra2 = Rb2 = Mmax = 0.4 * S * Ra Mmax =
2. 5 × Rb 1 = 24. 408 + 1 × 72. 5
Ra 2 + 38. 763 − 72. 5 = 0
- 5 × RC 1 =− 0. 742 + 0. 3 × 72. 5 − 24. 408 Rb 2 + Rc 1 − 72. 5 = 0
Multiple Presence factor = 1. = 19.894 KNm/m = 66.412 KN/m AASHTO C. Maximum interior –ve live load moment The critical placement of live load for maximum –ve moment is at the first interior deck support with one lane loaded (m=1.2) The width of the equivalent transverse strip is E = 1220 + 0.25S E = 1845. P1= 72.500 KN P2 = 72.500 KN a1 = 1.600 m a2 = 0.900 m b1 = 0.900 m b2 = 1.600 m S = 2.500 m P1 P a1 b1 a2 b 1.24m 2.500 m 2.500 m 2.500 m 1.24m 2.500 2.500 2. K 0.750 1.000 0. DF 0.000 0.429 0.571 0.571 0. FEM 0.000 -34.243 26.726 -15. 3.221 4.295 2. 3.682 7.363 5. -1.578 -2.104 -1. 0.301 0.601 0. -0.129 -0.172 -0. 0.049 0. -32.728 32.728 -6.010 6. M at B = 32. M at C = 6.
a1 72. b1 a2 b ∑Ma = 0 ∑Mb = 0 Rc12.5 - 6.010 - 72.50.9 + 32.728 = 0 Mmax p = Rb = Ra1 Ra2 Rb1 Rb2 Rc1 Rc2 Rd1 Rd Mb Mc Mb Ra2 Rb1 Rb2 Rc
M max p =
1. 2 × M max
E
- 2 × 33. 737
- 035
Rb =
1. 2 × Rb
E
- 2 × 112. 623
- 035 Rb 1 × 2. 5 − 32. 728 − 72. 5 × 1. 6 = 0
M at B = 14.842 KN/m M at C = 3.707 KN/m AASHTO Ra1 Ra2 Rb1 Rb2 Rc1 Rc2 Rd1 Rd 72.500 72. Mb Ra2 Rb ∑Ma = 0 Rb12.5 -14.842 - 72.50.585 -72.5*2.385 = 0 Rb1 = 92.067 KN ∑Fy = 0 Ra2 + 92.067 -72.5 - 72.5 = Ra2 = 52.933 KN Ra = 52. Multiple Presence factor = 1. Ra = 31.214 KN/m Action DC LL 0.000 31. -15.461 0. 0.000 75. -4.985 -21. -18.785 19. Gravity Load Combination 0.950 ductility factor Art 1.3. 0.950 continuous factor Art 1.3. 1.000 operationally important η = 0. Ra Ma Rb Mb Mmax span ηD = ηR = ηI =
RA =
1. 2 × Ra
E
η ∑ γ i Qi = η [ γ P − DC + γ P − DW + 1. 75 (^ LL + IM )^ ]
η = ηD × ηR × ηI ≥ 0. 95
Reactions and maximum moments for Strength I Limit State 0.95 [1.25 (24.103) + 1.5 (0) + 1.75 (1.33 * 31.214)] 69.017 KN/m AASHTO 0.95 [1.25 (18.186) + 1.5 (0) + 1.75 (1.33 * 75.824)] 167.655 KN/m 0.95 [1.25 (-14.092) + 1.5 (0) + 1.75 (1.33 * 0)] -18.360 KNm/m 0.95 [1.25 (-5.290) + 1.5 (0) + 1.75 (1.33 * -21.287)] -52.987 KNm/m 0.95 [1.25 (-12.079) + 1.5 (0) + 1.75 (1.33 * 19.894)] 21.680 KNm/m .
RA = 0.95 [1.25 (RA-DC) + 1.5 (RA-DW) + 1.75 (1.33 RA-LL)]
RA =
RA =
RB = 0.95 [1.25 (RB-DC) + 1.5 (RB-DW) + 1.75 (1.33 RB-LL)]
RB =
RB =
MA = 0.95 [1.25 (MA-DC) + 1.5 (MA-DW) + 1.75 (1.33 MA-LL)]
MA =
MA =
MB = 0.95 [1.25 (MB-DC) + 1.5 (MB-DW) + 1.75 (1.33 MB-LL)]
MB =
MB =
MMAX SPAN = 0.95 [1.25 (Mmaxspan DC) + 1.5 (Mmax span-DW) + 1.75 (1.33 Mmax span-LL)] MMAX SPAN = MMAX SPAN =
