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Proposal of concept for structural modelling of hybrid beams

Maciej Kożuch
Maciej Kożuch
 e 
Łukasz Skrętkowicz
Łukasz Skrętkowicz
   | 21 nov 2022
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Article Category: Original Study
Pubblicato online: 21 nov 2022
Pagine: 317 - 332
Ricevuto: 08 feb 2022
Accettato: 30 ago 2022
DOI: https://doi.org/10.2478/sgem-2022-0023
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© 2022 Maciej Kożuch et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

Different side views (upper row) and cross sections (middle and bottom rows) of girders with composite dowels. 1–5: With single dowel strip, 6–9: sections using two dowel strips [4].
Different side views (upper row) and cross sections (middle and bottom rows) of girders with composite dowels. 1–5: With single dowel strip, 6–9: sections using two dowel strips [4].

Figure 2

Bridge in Elbląg using both steel and concrete webs in the girder [4, 5].
Bridge in Elbląg using both steel and concrete webs in the girder [4, 5].

Figure 3

Steel T-sections of Elbląg bridge. High T-sections for mid-span regions, low T-sections for internal support regions [4].
Steel T-sections of Elbląg bridge. High T-sections for mid-span regions, low T-sections for internal support regions [4].

Figure 4

External span of the Elbląg bridge [4, 5].
External span of the Elbląg bridge [4, 5].

Figure 5

Hybrid beams of Sobieszewo bridge [4, 6].
Hybrid beams of Sobieszewo bridge [4, 6].

Figure 6

Hybrid girder of Sobieszewo bridge [7].
Hybrid girder of Sobieszewo bridge [7].

Figure 7

Cross section of one of the bridges along the S3 road being designed currently by Europrojekt Gdańsk.
Cross section of one of the bridges along the S3 road being designed currently by Europrojekt Gdańsk.

Figure 8

Cross section of the Dąbrowa Górnicza bridge and, on the right, longitudinal section showing the T-sections and rebar arrangement in the girder's web.
Cross section of the Dąbrowa Górnicza bridge and, on the right, longitudinal section showing the T-sections and rebar arrangement in the girder's web.

Figure 9

Bridge in Dąbrowa Górnicza after erection. Source: Nowak Mosty.
Bridge in Dąbrowa Górnicza after erection. Source: Nowak Mosty.

Figure 10

Concrete cracking ranges in (a) reinforced concrete beam, (b) composite beam, (c) hybrid beam.
Concrete cracking ranges in (a) reinforced concrete beam, (b) composite beam, (c) hybrid beam.

Figure 11

Different numerical models for composite bridges’ analysis (on basis of [9]).
Different numerical models for composite bridges’ analysis (on basis of [9]).

Figure 12

Hybrid beam assumed for FE analysis (rebars only in the tensile regions are displayed).
Hybrid beam assumed for FE analysis (rebars only in the tensile regions are displayed).

Figure 13

Side view, 3d view and cross section of a finite element model of the considered beam (steel web highlighted in blue).
Side view, 3d view and cross section of a finite element model of the considered beam (steel web highlighted in blue).

Figure 14

Tension stiffening model adopted in approach C according to annex L1 [27].
Tension stiffening model adopted in approach C according to annex L1 [27].

Figure 15

Tensile stress layout in in situ slab (top view), upper slab (top view) and concrete web of the prefab (side view) – uncracked analysis (step 1).
Tensile stress layout in in situ slab (top view), upper slab (top view) and concrete web of the prefab (side view) – uncracked analysis (step 1).

Figure 16

Tensile stress layout in in situ slab (top view), upper slab (top view) and concrete web of the prefab (side view) – cracked analysis (step 2).
Tensile stress layout in in situ slab (top view), upper slab (top view) and concrete web of the prefab (side view) – cracked analysis (step 2).

Figure 17

Tensile stress layout in in situ slab (top view), upper slab (top view) and concrete web of the prefab (side view) – cracked analysis (step 3).
Tensile stress layout in in situ slab (top view), upper slab (top view) and concrete web of the prefab (side view) – cracked analysis (step 3).

Figure 18

Comparison of cracked zones in the web in approaches A, B and C. Cracked zones in slabs are equal to the length of cracked zones in the top part of a web at the internal support.
Comparison of cracked zones in the web in approaches A, B and C. Cracked zones in slabs are equal to the length of cracked zones in the top part of a web at the internal support.

Figure 19

Bending moment envelope depending on the assumed approach (A, B, C).
Bending moment envelope depending on the assumed approach (A, B, C).

Figure 20

Influence of creep on the bending moment distribution in dependence of the assumed approach (A, B, C). Continuous lines – bending moments without creep, dotted lines – after creeping of concrete.
Influence of creep on the bending moment distribution in dependence of the assumed approach (A, B, C). Continuous lines – bending moments without creep, dotted lines – after creeping of concrete.

Figure 21

Bending moment distribution due to shrinkage in dependence of the assumed approach (A, B, C).
Bending moment distribution due to shrinkage in dependence of the assumed approach (A, B, C).

Bending moment values (kN m) along the girder's length (m), depending on the assumed approach (A, B, C). Numerical interpretation of Fig. 19.

No. 0 1 2 3 4 5 6 7 8 9 10 M+ / M0+ M− / M0−
Approach x [m] 0 2,03 4,06 6,09 8,12 10,15 12,18 14,21 16,24 18,27 20,3
Base state M+ uncracked (M0+) 0 1782 2940 3652 3749 3401 2626 1505 1 −1902 −4129 100,0%
M− uncracked (M0−) 0 529 787 789 520 −16 −820 −1892 −3252 −4922 −6865 100,0%
A M+ cracked A (Step 2) 0 1804 2984 3727 3853 3535 2786 1684 183 −1730 −3947 102,8%
M− cracked A (Step 2) 0 561 850 885 648 143 −628 −1668 −2996 −4634 −6547 95,4%
M+ cracked A (Step 3) 0 1816 3009 3768 3909 3607 2870 1779 279 −1637 −3845 104,3%
M− cracked A (Step 3) 0 579 884 936 716 229 −526 −1548 −2860 −4481 −6369 92,8%
M+ cracked A (Step 4) 0 1820 3017 3782 3928 3630 2898 1811 312 −1607 −3819 104,8%
M− cracked A (Step 4) 0 584 896 953 739 257 −492 −1508 −2814 −4432 −6321 92,1%
B M+ cracked B (15%) 0 1829 3035 3811 3968 3682 2954 1873 372 −1544 −3748 105,8%
M− cracked B (15%) 0 597 920 990 787 318 −419 −1423 −2717 −4321 −6194 90,2%
C M+ C (TS) 0 1781 3012 3760 3951 3590 2828 1616 125 −1902 −4068 105,4%
M− C (TS) 0 602 947 1019 824 343 −366 −1415 −2719 −4346 −6274 91,4%

Bending moment values (kN m) along the girder's length (m0 due to creep in dependence of the assumed approach (A, B, C). Numerical interpretation of Fig. 20.

No. 0 1 2 3 4 5 6 7 8 9 10 M+ / M0+ M− / M0−
Approach x [m] 0 2,03 4,06 6,09 8,12 10,15 12,18 14,21 16,24 18,27 20,3
Base state M uncracked t = 0 0 391 631 733 685 489 147 −345 −1006 −1853 −2868 100,0% 100,0%
M uncracked t = 100 y 0 442 730 885 887 741 449 8 −603 −1401 −2367 120,7% 82,5%
A M cracked A (Step 4) t = 100 y 0 442 731 886 888 844 452 12 −599 −1397 −2364 109,3% 92,2%
M cracked A (Step 4) t = 100 y 0 444 735 892 896 753 464 25 −584 −1379 −2342 121,7% 81,7%
B M cracked B (15%) t = 0 0 419 685 815 794 626 311 −154 −788 −1607 −2595 111,2% 90,5%
M cracked B (15%) t = 100 y 0 442 731 887 889 744 453 13 −598 −1393 −2360 121,0% 82,3%
C M cracked C (TS) t = 0 0 0 427 715 851 845 672 370 −105 −746 −1584 116,1% 89,9%
M cracked C (TS) t = 100 y 0 0 459 782 951 982 838 569 128 −480 −1286 129,7% 78,4%

Bending moment values (kN m) along the girder's length (m) due to shrinkage in dependence of the assumed approach (A, B, C). Numerical interpretation of Fig. 21.

No. 0 1 2 3 4 5 6 7 8 9 10 M− / M0−
Approach x [m] 0 2,03 4,06 6,09 8,12 10,15 12,18 14,21 16,24 18,27 20,3
Base state M uncracked Shrinkage 0 −35 −70 −106 −141 −177 −212 −247 −282 −319 −365 100,0%
A M cracked A (Step 4) Shrinkage 0 −34 −67 −101 −134 −168 −202 −235 −268 −304 −340 93,2%
B M cracked B (15%) Shrinkage 0 −26 −51 −77 −103 −129 −154 −180 −204 −233 −256 70,1%
C M cracked C (TS) Shrinkage 0 −29 −58 −88 −116 −147 −175 −204 −234 −263 −294 80,5%
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