# Investigations on Interface Shear Fatigue of Semi-Precast Slabs with Lattice Girders

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## Abstract

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## Featured Application

**The presented research supports the application of semi-precast slabs with lattice girders in industrial buildings and bridge structures exposed to cyclic loading.**

## Abstract

## 1. Introduction

## 2. Lattice Girders for Use in Cyclically Loaded Structures

#### 2.1. General

#### 2.2. Fatigue Tests from Literature

_{Dia}= 180–230 N/mm

^{2}. After reaching the N = 2.0 million load cycles, the specimens were loaded monotonically until failure. Comprehensively for all test series, the shear span to effective depth ratio was kept between a/d = 3.4–3.8, and the concrete compressive strength varied between f

_{cm,cyl}= 16.1–39.3 N/mm

^{2}for the precast slab and f

_{cm,cyl}= 13.9–32.5 N/mm

^{2}for the in situ concrete. The lattice girders in the slab’s cross section were placed in one, two, or three rows to determine the effect of the amount of interface reinforcement. The interface quality was left as cast, with an additional bond breaker or intentionally roughened by raking (according to [29]). Figure 3 shows an exemplary test specimen from the test series conducted for lattice girder KTS [50].

_{cm,cyl}= 20 N/mm

^{2}and with an interruption of bond by a cladding tube installed above the welded node (Figure 4a). The cyclic loading was applied to the diagonal with a constant stress range and a frequency of f = 100 Hz.

_{Rsk}= 92 N/mm

^{2}could be determined for N = 2.0 million load cycles, which was adopted to the fatigue verification of lattice girders (see Section 2.3).

#### 2.3. Fatigue Design of Semi-Precast Slabs with Lattice Girders in Germany

_{Rsk}= 92 N/mm

^{2}for N = 2.0 million load cycles. Based on the research in Section 3, more detailed verifications using an S–N curve have recently been proposed. The S–N curve and its derivation can be found in Section 3.5.

_{Rdi}= c·f

_{ctd}+ μ·σ

_{n}+ ρ·f

_{yd}·(1.2·μ·sinα + cosα) ≤ 0.5·ν·f

_{cd}

- v
_{Rdi}design (d) shear resistance (R) of interface (i) - c coefficient of adhesion
- f
_{ctd}design value of concrete (c) tensile (t) strength of the weaker concrete layer - μ coefficient of friction
- σ
_{n}external normal (n) stress perpendicular to the interface acting simultaneously with the shear stress- compressive stress: 0 ≤ σ
_{n}≤ 0.6·f_{cd} - tensile stress: σ
_{n}< 0 with c·f_{ctd}= 0

- ρ interface reinforcement ratio ρ = A
_{si}/A_{i}- with
- A
_{si}the area (A) of steel (s) reinforcement crossing the interface including shear reinforcement from shear design with sufficient anchorage at both sides of the interface - A
_{i}the area of the interface

- f
_{yd}design yield (y) strength of the interface reinforcement - α inclination of interface reinforcement 45° ≤ α ≤ 90°
- ν strength reduction factor for concrete cracked in shear
- f
_{cd}design concrete cylinder compressive strength.

_{n}= 0). Furthermore, the stress range is increased by the term 1/0.6. The factor 0.6 is based on regulations in DIN 1045 [54], which includes the conservative estimation of a flat angle of compression strut by a reduction factor of 0.85 and a correction factor 0.7 for the increased fatigue failure potential of the bent bars [55]. Substituting the yield strength of the reinforcement by the approved stress range and the partial fatigue safety factor for steel, as well as considering the inclination of every second angle of the diagonals with α

_{1}= 90°, the verification of the stress range at an interface with lattice girders KTS or EQ follows Equation (2) [41,42].

- Δv
_{Rdi,fat,LG}range of fatigue (fat) design (d) shear resistance (R) of interface (i) using lattice girders (LG) - Δσ
_{Rsk}approved characteristic stress range with Δσ_{Rsk}= 92 N/mm^{2}for N = 2.0 million load cycles - γ
_{s,fat}partial safety factor of reinforcement under fatigue γ_{s,fat}= 1.15 - α
_{2}inclination of inclined diagonal in accordance to Figure 2.

_{Rdi,max,fat}= 0.5·v

_{Rdi,max}

- v
_{Rdi,max,fat}maximum fatigue shear resistance

_{pre}≥ 6 cm. The lattice girders (LG) shall have a minimum height of h

_{LG}≥ 10 cm with an inclination of the diagonals of α

_{2}≥ 45° and the horizontal bars at the bottom side of the lattice girder may not be considered as longitudinal reinforcement. The diameter of the longitudinal reinforcement (sl) in the precast slab is limited to a maximum (max) value of Ø

_{sl,max}= 16 mm and shall be sufficiently anchored at the supports. Furthermore, a staggering of the longitudinal reinforcement is not permitted.

C20/25 | C25/30 | C30/37 | C35/45 | C40/50 | C45/55 | C50/60 | |
---|---|---|---|---|---|---|---|

v_{Rdi,max} [N/mm^{2}] | 2.4 | 2.8 | 3.3 | 3.6 | 3.8 | 4.0 | 4.1 |

## 3. Small Size Fatigue Tests to Determine S–N Curves for Lattice Girders

#### 3.1. Introduction

_{Rsk}= 92 N/mm

^{2}for N = 2.0 million load cycles. In order to extend the range of application by deriving S–N curves for lattice girders, small-size fatigue tests with lattice girder diagonals cast in concrete cubes have been conducted at the Institute of Structural Concrete (IMB), RWTH Aachen [43,56], using the procedure of the interactive method [57,58] (Figure 5b). This procedure had also been adapted to derive S–N curves for other lattice girder systems, e.g., in [36].

#### 3.2. Description of Test Specimens and Test Setup

_{chord}= 5 mm and were cast up to the edges of the cube to prevent restraints at the ends of the chords. The diagonal (dia) bar had a length of 300 mm and a diameter of Ø

_{dia}= 7 mm, which satisfies the required test length of 140 mm or 14·Ø = 98 mm according to [59].

#### 3.3. Test Procedure

_{min}= 125 N/mm

^{2}, and the stress ranges were applied by adjusting the maximum load σ

_{max}. Even though constant minimum stress contradicts the general determination of a constant maximum stress for establishing the fatigue resistance of reinforcement with of σ

_{max}= 300 N/mm

^{2}[59,60], the interactive method recommends a constant minimum stress to cover stress ranges Δσ ≥ 300 N/mm

^{2}and to ensure a more realistic evaluation that considers the constant permanent loads of the structure. The fatigue tests started with a maximum stress in the range of the yield strength. For the following four tests, the stress range was decreased stepwise until reaching the estimated fatigue limit. Due to the parallel statistic evaluation of the test results, the path of applied stress ranges could be subsequently adjusted (Figure 5b). Tests exceeding the limit of load cycles (5.0 million load cycles) without fatigue failure were stopped and subsequently cyclically tested with a higher stress range. To achieve a reasonable path of the S–N curve after statistic evaluation, 33 tests with lower chords and 25 tests with upper chords were conducted.

#### 3.4. Results of Small-Size Fatigue Tests

_{dia}did not occur. The yield strength of the static test was determined as f

_{y}= 564–573 N/mm

^{2}for the specimens with diagonals and lower chords and between f

_{y}= 558–567 N/mm

^{2}for diagonals and upper chords.

^{2}and resisted N = 162,177 load cycles. Figure 7c gives a detailed view of the fatigue fracture.

_{Rsk}= 92 N/mm

^{2}for N = 2.0 million load cycles was satisfied for all tests.

#### 3.5. Evaluation of S–N curves for Lattice Girders

_{n}result in 1.69 for the lower chord, 1.71 for the upper chord, and 1.64 for the overall evaluation.

- Δσ
_{Rsk}expected stress range - Δσ
_{Rsk}(N*) stress range at N* load cycles - N* number of load cycles at break of slope
- N expected number of load cycles
- k stress exponents
- with
- k = k
_{1}stress exponent for N < N* - k = k
_{2}stress exponent for N > N* with k_{2}= 2·k_{1}—1

- f
_{yk}characteristic yield strength.

_{Rsk}= 92 N/mm

^{2}, which was already used for the simplified verification (see Section 2.3). The shape of the design curve was fitted to test data. It adopts the coefficients k

_{1}= 5 and k

_{2}= 9 from the design curve in [29] for stirrups as shear reinforcement (Figure 10).

## 4. Fatigue Tests on Semi-Precast Slabs with Lattice Girders

#### 4.1. Introduction

_{t}= 0.4 mm. Achieving the minimum roughness depth of a rough interface according to the regulations in [29] with R

_{t}≥ 1.5 mm without mechanical post-treatment is difficult to implement. Therefore, a smaller limit of a rough surface in accordance with [63] with R

_{t}= 0.9 mm (‘rough’) without mechanical post-treatment has been investigated. For comparison, also a rough interface with slightly roughening after concrete casting was provided.

#### 4.2. Description of Test Specimens

_{pre}= 7 cm and a width of b = 85 cm. To extend the application of the limited diameter of the longitudinal (l) reinforcement in the technical approvals of Ø

_{l}≤ 16 mm and to exclude flexural failure, longitudinal reinforcement bars with Ø

_{l}= 20 mm and a yield strength of f

_{y}= 900 N/mm

^{2}with a longitudinal reinforcement ratio of ρ

_{l}= 2.0% were applied. The lower chords of the lattice girders have not been considered for determination of longitudinal reinforcement ratio.

#### 4.3. Fabrication of Test Specimens

_{t}= 0.9 mm for Specimens EG03–EG08 without mechanical post-treatment. Specimen EG09 had a rough surface by slightly roughening after concrete casting. In Test Series 1, two, three, and four rows of lattice girders were applied, and the concrete strength for both precast slab and in situ concrete varied between C25/30 and C50/60. For the specimens of Test Series 2 with a precast slab of 7 cm, the interface roughness was about R

_{t}= 0.9 mm, in accordance with Series 1. The in situ concrete layer for EG10–EG13 was 29 cm. To determine the effect of the height of the concrete cover in the compression zone, the in situ concrete layer of Specimen EG14 was reduced to 26 cm. The interface reinforcement varied between two and four rows of lattice girders and the concrete strength was C25/30 and C50/60.

_{t}= 10 mm bars and yield strength of f

_{y}= 500 N/mm

^{2}. To ensure a crack formation of flexural cracks in the area of the welded sections of the lattice girders, triangular crack inducers were placed at the bottom side of the concrete slab at the position of the welds to produce comparable conditions of flexural crack initiation and shear crack propagation. To prevent shear failure of the slab at the midspan between the load application point and support in the second sub-tests (Figure 11), additional stirrups were applied, since the diagonals of the lattice girders declining towards the support cannot fully participate in the shear resistance (Figure 13).

#### 4.4. Test Setup and Test Execution

_{t}≈ 0.9 mm, the interface resistance of a rough interface was considered. The reference value for specimens with high interface reinforcement ratios was the calculated static shear resistance.

_{s}= 200 N/mm

^{2}. The fatigue load was applied in a force-controlled manner, starting with a frequency of f = 0.1 Hz with continuous measurements of strain gauges and displacement transducers. After 100 load cycles, the frequency was increased to f = 2.8–5.8 Hz, depending on the deflection of the specimens. The displacement and strain measurements were monitored in periods after 1000 or 2000 load cycles. Depending on the reached number of load cycles, crack distribution, and displacement and strain measurements, the load range was increased in the first instance followed by increasing the maximum load.

#### 4.5. Test Results

#### 4.5.1. General

#### 4.5.2. Influence of Interface Roughness

- left as cast with bond breaker (very smooth, EG02)
- left as cast with a roughness depth of R
_{t}= 0.24 mm determined by the sand-patch method (smooth, EG01) - left as cast with an aspired roughness depth of R
_{t}≈ 0.9 mm (‘rough’, EG03) - left as cast with slightly roughening to R
_{t}≈ 2.0 mm after casting (rough, EG09)

^{2}could be determined at the welded nodes. Since the strain gauges were not placed in the immediate area of the failure crack, the stress ranges in the fractured girder nodes might have been considerably higher.

^{2}and fracture after exposure of the specimen could be determined. The horizontal slip of the unimpaired side only showed small displacements with a slight increase during the first fatigue sub-test. A failure, however, did not occur for another N > 1.5 million load cycles.

#### 4.5.3. Influence of Interface Reinforcement Ratio

_{t}= 0.9 mm.

#### 4.5.4. Influence of Steel Strains

_{dia}and the welded node ε

_{wel}of the lattice girders for Specimen EG12 to evaluate the influence of the stress ranges in the lattice girders. The stress range in the diagonals of the lattice girders calculated from the measured steel strain range was about Δσ

_{dia}= 167 N/mm

^{2}for a period of N > 2.0 million load cycles. This exceeds the approved stress range by 76% according to the technical approvals of the lattice girders of Δσ

_{Rsk}= 92 N/mm

^{2}. The measured stress ranges of the welded nodes were determined to be only Δσ

_{wel}= 42 N/mm

^{2}. After the exposure of the lattice girders, fractures could only be determined in the diagonal and vertical bars of the lattice girders (Figure 19) but not in the welded nodes.

_{max,test}to the calculated stress ranges Δσ

_{calc,1}, determined by the initially applied shear range ΔV

_{1}according to the interface fatigue regulations of the technical approvals [38,39]. The measured stress ranges in the diagonals of the lattice girders, as well as the calculated stress ranges were generally larger than the stress range limit of the technical approvals with Δσ

_{Rsk}= 92 N/mm

^{2}. Despite these high stress ranges, the slabs usually resist more load cycles than expected. Structural failure of the slabs induced by fatigue failure of the lattice girders (in Table 5, tests with fractured lattice girders are labeled by * in the column of Δσ

_{max,test}) could generally not be determined after the initially applied load level ΔV

_{1}but only after increasing the top load or the amplitude. Despite Specimen EG09, which can be assessed as aberration, structural failure with fractured lattice girders could only be determined for specimens with large numbers of load cycles and high stress ranges. The failure of individual bars does not generally lead to structural failure, which has already been shown in other fatigue tests on shear reinforcement [9,10].

#### 4.6. Test Evaluation and Comparison to Design Regulations

_{test,Rki}were related to the approved stress range according to the technical approvals Δσ

_{Rsk}= 92 N/mm

^{2}and plotted over the achieved number of load cycles (Figure 20a–c). Even though the design is limited to N = 2.0 million load cycles, all tests were related to the approved stress range of Δσ

_{Rsk}= 92 N/mm

^{2}. Specimens with divergent failure modes, e.g., anchorage failure of lattice girders or longitudinal reinforcement, were excluded. To determine the calculated stress range, the applied shear stress ranges Δv = β ∙ ΔV/(b

_{i}∙ z) were calculated in accordance with [28] (Equation (6.24), Chapter 6.2.5) with β = 1.0 and the applied shear ranges ΔV. The applied shear stress range was then implemented in the interface shear design expression according to [28] (Equation (6.25), Chapter 6.2.5), Equation (1) taken from [29] (Equation (6.25), Chapter 6.2.5) and Equation (2) taken from the technical approvals (TA) of the lattice girders ([41,42], Equation (1), Chapter 3.2.3.5), without partial safety factors.

_{Rsk}= 92 N/mm

^{2}, the expression of the TA (Figure 20c) gives the best accordance to the test data. The expression according to [28] (Figure 20a), which allows a 50% consideration of the adhesive term for fatigue, and the expression according to [29] (Figure 20b), which neglects the term of adhesion for fatigue and increases the resistance of the interface reinforcement by the factor 1.2, show a similar trend level. The [28] approach, however, gives a larger range of scatter, especially for large numbers of load cycles, whereas [29] shows a small decrease of scatter for large numbers of load cycles.

_{Rsk}= 92 N/mm

^{2}(Figure 20c), the evaluation with the S–N curve gives a better agreement, especially for N ≤ 2.0 million load cycles. For N > 2.0 million load cycles, the S–N curve gives smaller allowable stress ranges, which lead to slightly higher related stress ranges in the lattice girders. However, with the S–N curve, the range of application for fatigue design of lattice girders can be extended to a reliable verification allowing N > 2.0 million load cycles.

## 5. Tests on Continuous Semi-Precast Slabs with Lattice Girders

## 6. Summary and Conclusions

- For the fatigue tests, higher scatter occurred compared to static tests. The scatter concerns the failure mode, interface delamination, strain of lattice girders, and achieved number of load cycles.
- The failure of specimens with low degrees of interface reinforcement was generally induced by interface failure after high numbers of load cycles with N > 2.0 million. Therefore, the bearable fatigue load level generally increases with increasing roughness. Only one specimen with a rough interface had an unexpected premature failure, which needs further investigation.
- Specimens with medium interface reinforcement ratios failed predominantly by vertical shear with only small interface delamination.
- The failure of specimens with high interface reinforcement ratios was generally introduced by anchorage failure of the lattice girder in the compression zone or by anchorage failure of the longitudinal reinforcement.
- The stress ranges in the lattice girders determined by test results were considerably higher compared to the approved stress range according to the technical approvals.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Lattice girder types approved for fatigue in semi-precast slabs (

**a**–

**c**) and element walls (

**a**,

**d**).

**Figure 3.**Test specimen and test setup for fatigue tests with lattice girders KTS according to [50].

**Figure 5.**S–N curve (

**a**) and process description of test procedure (

**b**) according to the interactive method [57].

**Figure 6.**Schematic depiction of fatigue test setup (

**a**), node of lattice girder in formwork (

**b**), and test setup for fatigue tests (

**c**) [43].

**Figure 7.**Fracture pattern of small size specimen under monotonic loading (

**a**), cyclic loading (

**b**), and fatigue fracture of welded node (red marking) (

**c**) with definition of fatigue zone (orange) and final rupture zone (blue) (

**d**).

**Figure 8.**Test results of small size fatigue tests for lower and upper chords with reference tests from literature.

**Figure 9.**Fatigue test results of lower and upper chords with mean functions (

**a**) and 5% quantile functions (

**b**) [43].

**Figure 12.**Overview of test specimens and test parameters [43].

**Figure 14.**Measurement instrumentation for Specimen EG10: strain gauges (SG) at reinforcement and displacement transducers (W).

**Figure 15.**Test setup for fatigue tests: Sub-Test I for Test Series 0/1 (

**a**), Sub-Test I for Test Series 2 (

**b**), Sub-Test II for Test Series 0/1 (

**c**), and Sub-Test II for Test Series 2 (

**d**).

**Figure 16.**Influence of interface roughness: crack patterns of Specimens EG01, EG02, EG03, and EG09.

**Figure 17.**Influence of interface roughness: load–deflection curve of Specimens EG01—EG03 (

**a**), development of horizontal slip for Specimens EG02 and EG03 (

**b**).

**Figure 18.**Comparison of interface reinforcement ratio: Crack patterns of Specimens EG03, EG04, and EG08.

**Figure 19.**Influence of steel strains: load history, strain measurements of lattice girder, and fractured lattice girder for Specimen EG12.

**Figure 20.**Evaluation of calculated stress ranges for the design of lattice girders as interface reinforcement [53]: simplified verification according to EC2:2011 (

**a**), EC2+NA(D) (

**b**) and technical approvals (

**c**) and verification using the S-N curve (

**d**).

Geometry | Lattice Girder | Test Setup | ||
---|---|---|---|---|

Baustahlgewebe | Filigran | |||

slabs | KTS n = 10 | EQ n = 2 | ||

KT100 n = 14 | ||||

walls | KTW n = 3 |

Series 0 | Series 1 | Series 2 | |
---|---|---|---|

dimensions (l/b/h) (cm) | 190/85/16 | 180/85/16 | 420/85/36 (EG10–13)390/85/33 (EG14) |

height precast slab/ in situ concrete (cm) | 7/9 | 7/9 | 7/29 (EG10–13) 7/26 (EG14) |

effective depth d (cm) | 13 | 13 | 33 (EG10–13) 30 (EG14) |

distance load-support a (cm) | 50 | 50 | 130 |

lattice girder type | KTS 100 | KTS 100 | EQ 30 |

shear slenderness a/d | 4.0 | 4.0 | 4.0 |

long. reinforcement ρ_{l} (%) | 2.0 | 2.0 | 2.0 |

Test | h_{ges} | a | n_{LG} | f_{ym,LG} | n_{l} | f_{ym,l} | f_{cm,pre} | f_{cm,in situ} | Roughness | R_{t,sand} | R_{t,laser} |
---|---|---|---|---|---|---|---|---|---|---|---|

(cm) | (cm) | (-) | (N/mm^{2}) | (-) | (N/mm^{2}) | (N/mm^{2}) | (N/mm^{2}) | (-) | (mm) | (mm) | |

EG01 | 16 | 50 | 2 | 546 | 7 | 954 | 25.3 | 35.6 | smooth | 0.24 | 0.42 |

EG02 | 16 | 50 | 2 | 546 | 7 | 954 | 25.6 | 33.9 | very smooth ^{1} | 0.26 | 0.43 |

EG03 | 16 | 50 | 2 | 546 | 7 | 939 | 27.7 | 33.2 | ‘rough’ (R _{t} ≈ 0.9mm) | 0.64 | - |

EG04 | 16 | 50 | 3 | 546 | 7 | 939 | 27.9 | 34.0 | ‘rough’ (R _{t} ≈ 0.9 mm) | 0.93 | - |

EG05 | 16 | 50 | 4 | 546 | 7 | 939 | 28.2 | 35.2 | ‘rough’ (R _{t} ≈ 0.9 mm) | 0.78 | - |

EG06 | 16 | 50 | 2 | 546 | 7 | 939 | 51.1 | 61.3 | ‘rough’ (R _{t} ≈ 0.9 mm) | 0.97 | 1.33 |

EG07 | 16 | 50 | 3 | 546 | 7 | 939 | 51.1 | 61.3 | ‘rough’ (R _{t} ≈ 0.9 mm) | 1.01 | 1.19 |

EG08 | 16 | 50 | 4 | 546 | 7 | 939 | 51.4 | 61.3 | ‘rough’ (R _{t} ≈ 0.9 mm) | 1.07 | 1.04 |

EG09 | 16 | 50 | 2 | 546 | 7 | 939 | 32.9 | 34.4 | rough (R _{t} > 1.5 mm) | 2.02 | - |

EG10 | 36 | 130 | 2 | 554 | 18 | 939 | 36.0 | 32.0 | ‘rough’ (R _{t} ≈ 0,9 mm) | 0.82 | 1.01 |

EG11 | 36 | 130 | 4 | 554 | 18 | 939 | 37.2 | 36.0 | ‘rough’ (R _{t} ≈ 0,9 mm) | 0.78 | 0.85 |

EG12 | 36 | 130 | 2 | 554 | 18 | 939 | 48.6 | 55.6 | ‘rough’ (R _{t} ≈ 0.9 mm) | 1.02 | 0.63 |

EG13 | 36 | 130 | 4 | 554 | 18 | 939 | 49.0 | 56.8 | ‘rough’ (R _{t} ≈ 0.9 mm) | 1.19 | 1.67 |

EG14 | 33 | 120 | 4 | 554 | 17 | 939 | 31.5 | 34.8 | ‘rough’ (R _{t} ≈ 0.9 mm) | 0.96 | - |

_{ges}: overall slab height; a: distance between load application and support; n

_{LG}: number of lattice girder rows; f

_{ym,LG}: mean yield strength of the diagonals of the lattice girders; n

_{l}: number of longitudinal reinforcement bars; f

_{ym,l}: mean yield strength of longitudinal reinforcement; f

_{cm,pre}: mean concrete compressive strength of precast slab; f

_{cm,in situ}: mean concrete compressive strength of in situ concrete; R

_{t,sand}: mean roughness depth by sand patch method; R

_{t,laser}: mean roughness depth by laser triangulation;

^{1}: additionally weakened by formwork oil.

Series | Test | V_{max,1} | ∆V_{1} | N_{1} | V_{max,f} | ∆V_{f} | N_{f} | N_{ov} | ∆σ_{calc,1} | ∆σ_{max,test} | Failure |
---|---|---|---|---|---|---|---|---|---|---|---|

(kN) | (kN) | (-) | (kN) | (kN) | (-) | (-) | (N/mm^{2}) | (N/mm^{2}) | |||

Series 0 | EG01a | 116 | 35 | 1.50 × 10^{6} | 162 | 58 | 0.18 × 10^{6} | 4.18 × 10^{6} | 109 | 270 | I/V |

EG01b | 162 | 58 | 350 | 4.18 × 10^{6} | V | ||||||

EG02a | 116 | 35 | 1.50 × 10^{6} | 116 | 58 | 1.16 × 10^{6} | 2.66 × 10^{6} | 109 | 215 * | I | |

EG02b | 116 | 58 | 0.93 × 10^{6} | 3.59 × 10^{6} | I/V | ||||||

Series 1 | EG03a | 152 | 90 | 2.07 × 10^{6} | 2.07 × 10^{6} | 279 | 230 * | I/V | |||

EG03b | 152 | 90 | 1.17 × 10^{6} | 3.24 × 10^{6} | V | ||||||

EG04a | 165 | 83 | 3.00 × 10^{6} | 165 | 112.5 | 1.36 × 10^{6} | 4.36 × 10^{6} | 171 | 215 * | V | |

EG04b | 260 ^{1} | V | |||||||||

EG05a | 226 | 133 | 2.70 × 10^{4} | 2.70 × 10^{4} | 176 | 125 | V_{DZ} | ||||

EG05b | 271 ^{1} | V | |||||||||

EG06a | 172 | 105 | 2.25 × 10^{6} | 197 | 120 | 0.35 × 10^{6} | 2.60 × 10^{6} | 326 | 195 | I/V | |

EG06b | 197 | 120 | 1.12 × 10^{4} | 2.62 × 10^{6} | I/V | ||||||

EG07a | 172 | 88 | 2.00 × 10^{6} | 197 | 120 | 3.32 × 10^{4} | 4.03 × 10^{6} | 121 | 55 | V | |

EG07b | 197 | 120 | 2.25 × 10^{6} | 6.28 × 10^{6} | V | ||||||

EG08a | 215 | 110 | 2.0 × 10^{6} | 215 | 152.5 | 1.95 × 10^{6} | 3.95 × 10^{6} | 171 | 115 * | V | |

EG08b | − ^{2} | ||||||||||

EG09a | 155 | 93 | 8677 | 8677 | 187 | 175 * | I/V | ||||

EG09b | 155 | 61 | 1.09 × 10^{6} | 1.09 × 10^{6} | I/V | ||||||

Series 2 | EG10a | 282 | 150 | 2.00 × 10^{6} | 372 | 225 | 1000 | 2.00 × 10^{6} | 193 | 100* | I/V |

EG10b | −^{2} | ||||||||||

EG11a | 537 | 195 | 0.31 × 10^{6} | 0.31 × 10^{6} | 125 | 115 | V_{DZ}/V_{L} | ||||

EG11b | 537 | 195 | 0.90 × 10^{6} | 1.21 × 10^{6} | V_{L} | ||||||

EG12a | 359 | 135 | 2.00 × 10^{6} | 420 | 233 | 0.74 × 10^{6} | 4.12 × 10^{6} | 173 | 255 * | I/V | |

EG12b | 420 | 233 | 0.35 × 10^{6} | 4.47 × 10^{6} | V/V_{L} | ||||||

EG13a | 519 | 165 | 435 | 435 | 105 | 115 | V_{DZ}/V_{L} | ||||

EG13b | 519 | 165 | 9129 | 9564 | V_{L} | ||||||

EG14a | 487 | 178 | 1.63 × 10^{6} | 1.63 × 10^{6} | 125 | 175 | V_{DZ}/V_{L} | ||||

EG14b | 487 | 178 | 2.87 × 10^{4} | 1.66 × 10^{6} | V/V_{L} |

_{max,1}: maximum shear at start of test; ∆V

_{1}: shear range at start of test; N

_{1}: number of load cycles after first loading sequence; V

_{max,f}: maximum shear at failure; ∆V

_{f}: shear range at failure; N

_{f}: number of load cycles in last loading sequence before failure; N

_{ov}overall number of load cycles; ∆σ

_{calc,1}: calculated stress range in lattice girders according to technical approval with ∆V

_{1}; ∆σ

_{max,test}: measured maximum stress range in lattice girders by strain gauges; I: interface failure; V: shear failure; V

_{DZ}: anchorage failure of lattice girder in the compression zone; V

_{L}: anchorage failure of longitudinal reinforcement; *: fracture of lattice girders;

^{1}: residual load capacity;

^{2}: no Sub-Test II.

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**MDPI and ACS Style**

Hillebrand, M.; Schmidt, M.; Wieneke, K.; Classen, M.; Hegger, J. Investigations on Interface Shear Fatigue of Semi-Precast Slabs with Lattice Girders. *Appl. Sci.* **2021**, *11*, 11196.
https://doi.org/10.3390/app112311196

**AMA Style**

Hillebrand M, Schmidt M, Wieneke K, Classen M, Hegger J. Investigations on Interface Shear Fatigue of Semi-Precast Slabs with Lattice Girders. *Applied Sciences*. 2021; 11(23):11196.
https://doi.org/10.3390/app112311196

**Chicago/Turabian Style**

Hillebrand, Matthias, Maximilian Schmidt, Katrin Wieneke, Martin Classen, and Josef Hegger. 2021. "Investigations on Interface Shear Fatigue of Semi-Precast Slabs with Lattice Girders" *Applied Sciences* 11, no. 23: 11196.
https://doi.org/10.3390/app112311196