Excel tool based on rigorous calculation of K-alfa(m) (m=1,2,..up to 10 and more harmonics order) K-alfa synthetizes the effect on longitudinal bending moments when loads move on decks. Based onworks developed by Guyon-Massonet- Bares

1. THE POWER OF INFLUENCE LINES
(Grid of beams modeled as hortotropic concrete plate)
What method ? Guyon-Massonet- Bares
Mechanical Data ? Dimensionless: Alfa, Teta
Torsional rigidity of deck Alfa = 0.0949
Transverse flexibility of deck Teta = 0.5047
Bridge deck width? 2B = 10 [meters]
Excel tool based on rigorous calculation of Kalfa(m) (m=1,2,..10 harmonics #), deck has
four girders spaced at 2.50 [m] each other.
Calculate influence line of K(alfa) for intermediate girders (Y= +/- 1.25).
Calculate influence line of K(alfa) for edge girders (Y= +/- 3.75).
Results: (at 1° harmonic)
Intermediate girders (Y=+/- 1.25) => Each load positions of an hypothetical moveable
load contribute to increase girder bending moments (All values of K(alfa) are positive).
Edge girders (Y=+/- 3,75) => Positions Ecc= -5.00 / -3.75 of a moveable load decreases
bending moments (these two value are negative).
10 [m]
8 [-] NOTE: divide in even part (to "pass" at Y=0) Input data in green cells
1,250 [m]
1
harmonic # (Fourier series):
Transverse load position:
No. Section Pos. (-B <= Y <= +B)
1,250 1,25 -5,00 1,25 -3,75 1,25 -2,50 1,25 -1,25 1,25 0,00 1,25 1,25 1,25 2,50 1,25 3,75 1,25 5,00
1 K(α)
2 K(α)
3 K(α)
4 K(α)
5 K(α)
6 K(α)
7 K(α)
8 K(α)
9 K(α)
10 K(α)
Total
Tool by: Lorenzo Sperduto
-0,2701909 0,2183722 0,8189040 2,0432463 10,4962637 59,3016806 10,7494147 2,2372451 0,2520058
0,0000133 -0,0001175 0,0015280 -0,0096335 -0,2184773 10,7098337 -0,2184844 -0,0095042 -0,0002696
-0,0497401 0,0088411
-0,1130356 0,0276745-0,0001058 0,0001653 0,0083738 -0,1116743 0,3275039 8,5678830 0,3274673
0,0000515 -0,0002954 0,0051811 -0,0496088 0,0057368 9,6388513 0,0057321
-0,0009425 0,0028894 0,0012047 -0,1779126 0,7334192 7,4969751 0,7330484 -0,1817991 0,0414183
-0,0001618 0,0064729 -0,0330432 -0,2015303 1,1848218 6,4260949 1,1839220 -0,2078142 -0,0013550
0,0123846 -0,0046367 -0,0980193 -0,1093426 1,6124055 5,3557271 1,6157027 -0,1177875 -0,1758464
0,0223788 -0,0561145 -0,1372118 0,1622583 1,9178111 4,2937070 1,9412150 0,1374559 -0,4676932
Bridge deck width (2B):
Number of subdivision:
Sections spaced at:
-0,1058538 -0,1191158 -0,0015882 0,5961973 1,9981381 3,2570487
1 2 3 4 5
0,1662967 0,4216995
-3,75-5,000
Ecc.
-2,50
0,6808413
-1,25
0,9374635
-0,3642520 -0,0325749 0,3916376 1,0070293 1,7665145 2,2289887 1,7612483 0,9248111 0,0872166
7 8 9
2,0324572 0,5133843 -0,5657338
Transverse load posion of load (-B <=Ecc. <= +B)
Influence line of K(α) load distribution coefficients finalised to calculate longitudinal bending moments on the girders
Center lineNegative Y posItions of girders Positive Y positions of girders
Ecc. Ecc. Ecc.
1,3412745
5,00
1,2977533
3,750,00
1,1683901
1,25
1,3265712
2,50
1,3671061
Ecc. Ecc. Ecc. Ecc. Ecc.
6
10 [m]
8 [-] NOTE: divide in even part (to "pass" at Y=0) Input data in green cells
1,250 [m]
1
harmonic # (Fourier series):
Transverse load position:
No. Section Pos. (-B <= Y <= +B)
3,750 3,75 -5,00 3,75 -3,75 3,75 -2,50 3,75 -1,25 3,75 0,00 3,75 1,25 3,75 2,50 3,75 3,75 3,75 5,00
1 K(α)
2 K(α)
3 K(α)
4 K(α)
5 K(α)
6 K(α)
7 K(α)
8 K(α)
9 K(α)
10 K(α)
Total
Tool by: Lorenzo Sperduto
-0,6566411 -0,3962926 -0,1228324 0,2183722 0,8006832 2,2372451 11,5540800 63,3189382 9,8096564
0,0000000 -0,0000003 0,0000068 -0,0001175 0,0015272 -0,0095042 -0,2225093 10,7988814 -1,7687035
9,7696823 -1,6969423
8,7380755 -1,3581763-0,0000015 0,0000083 -0,0000948 0,0001653 0,0085294 -0,1130356 0,3255913
-0,0000002 0,0000010 0,0000045 -0,0002954 0,0052206 -0,0497401 0,0006532
0,0000148 -0,0000302 -0,0002374 0,0028894 0,0013386 -0,1817991 0,7424250 7,6926297 -0,7013119
0,0000116 -0,0002065 0,0009338 0,0064729 -0,0337465 -0,2078142 1,2096641 6,6306532 0,2765045
-0,0006928 0,0007786 0,0048500 -0,0046367 -0,1001757 -0,1177875 1,6428858 5,5779366 1,4970124
0,0018547 0,0047206 -0,0029865 -0,0561145 -0,1436605 0,1374559 1,9322726 4,6061247 2,7671206
Bridge deck width (2B):
Number of subdivision:
Sections spaced at:
0,0207731 -0,0110555 -0,0607947 -0,1191158 -0,0514839 0,5133843
1 2 3 4 5
-0,5819041 -0,2705224
-3,75-5,000
Ecc.
-2,50
0,0567460
-1,25
0,4216995
-0,0966968 -0,1199861 -0,1212600 -0,0325749 0,2674186 0,9248111 1,9987869 3,2024693 3,9878575
7 8 9
2,0225188 3,8133078 3,7543549
Transverse load posion of load (-B <=Ecc. <= +B)
Influence line of K(α) load distribution coefficients finalised to calculate longitudinal bending moments on the girders
Center lineNegative Y posItions of girders Positive Y positions of girders
Ecc. Ecc. Ecc.
2,4891778
5,00
3,0519404
3,750,00
0,8457154
1,25
1,3412745
2,50
1,9017915
Ecc. Ecc. Ecc. Ecc. Ecc.
6