**6. Numerical analysis of welded butt splices with cover plates in bridges**

The first welded bridge designers were aware that "a weld is the weakest place in the structure." Because of welding imperfections, their resistance is lower than that of the welded material. The simplest and the most economical way to eliminate these differences seemed to be enlargement of the welded joint section by adding cover plates which compensated for the weakened section. In the welded plate girders of railway bridges constructed up to 1939 and in the period from 1945 to 1953, the butt splices of webs and flanges were covered with one- or two-sided cover plates [3].

In the 154 railway bridges which were checked radiographically, internal cracking was discovered in 438 welded joints. In this group, there were 28 plate girder structures; the constructions of their lower flanges are shown in **Figure 11**. In 18 structures, their butt splices are covered with one-sided rhomboid cover plates from the side of the girder longitudinal axis. The rhomboid cover plates are from 90 to 200 mm in width and from 160 to 340 mm long.

To assess the endurance of such types of joints, fatigue strength tests were undertaken, which were discussed in Section 4. The results of the tests and the regression line are given in **Figure 8**. The determined infinitive fatigue strength value Zrj = 79 MPa at Ni = 2<sup>10</sup><sup>6</sup> load cycles constitutes only 26% of yield strength fy = 302 MPa for the steel of the specimens tested. It is worth mentioning that for three stress levels σ = 80, 100, and 140 MPa, on five specimens seven cracks appeared, as shown in **Figure 12**.

The results of the fatigue tests show a very low fatigue limit value for the welded butt splices covered with rhomboid plates. The problem was solved numerically using an FEM model as shown in **Figure 13**. More details of the numerical analysis are given in [38, 39].

*Quality and Fatigue Assessment of Welded Railway Bridge Components by Testing DOI: http://dx.doi.org/10.5772/intechopen.104439*

**Figure 11.** *Details of welded butt splices with cracks in 28 plate girder bridges.*

#### **Figure 12.**

*Cracks in flanges with rhomboid cover plates after fatigue tests: The top three specimens – Damaged and the bottom two specimens – Undamaged.*

For the numerical analysis, the welded splice was modeled using the FEM method (**Figure 14**) with Inventor Nastran software. Material parameters for structural steel are fy = 249 MPa and fu = 360 MPa. The stresses were calculated in four cross sections and on nine points for each section. Loading was modeled as 162, 173, 216, 260, and 303 kN tensile forces with 75, 80, 100, 120, and 140 MPa course tensile stresses in the flange. The same stress levels were formulated as for the laboratory fatigue tests.

Analysis of the tensile stresses in the welded joint allowed us to formulate some remarks:


#### **Figure 13.** *Numerical model for analysis of a welded butt splice with cover plates.*

#### **Figure 14.**

*Details of the numerical model with cracks and structural steel material data.*

• the stress concentration together with the smallest concentration factor for globular (spherical) nonmetallic inclusions of 2.04 are the reasons for the formation of one-sided stochastic cracking already at the 80-MPa stress level (**Figure 13**); thus σ = 80.1.69.2.04 = 275 MPa which is greater than the steel yield strength fy = 249 MPa [39].

Cracks appeared at three stress levels, σ = 80, 100, and 140 MPa, with a varied number of load cycles from 535,000 to 990,200.

These are fatigue cracks developing in stages, as opposed to the rapidly developing cracks in the fatigue tests of welded joints on specimens U, C, and P (**Figure 8**). All the cracks had a similar fracture as shown in **Figure 15**, with three developing trajectories: I – crack initiations, II – growth, and III – final fracture. The scheme of fatigue crack zones is shown in **Figure 16**.

The stress distribution on the circumference of the cracks is similar, with the smallest values in the upper zone. The values are equal to the upper values of yield *Quality and Fatigue Assessment of Welded Railway Bridge Components by Testing DOI: http://dx.doi.org/10.5772/intechopen.104439*

**Figure 15.**

*Fracture surface of a broken specimen after the fatigue testing (see Figure 13).*

**Figure 16.** *Scheme of a fatigue crack: Zone I – Origin, zone II – Fatigue zone and zone III – Final fracture.*

strength fy = 280 MPa, while the maximum stress σ 306 MPa appeared at the crack tip.

A study of the literature shows that no direct criterion has been established for precise cracking in zones I and II, e.g. the zones of settled crack growth, and zone III (unstable crack growth). This has not been achieved since 1913 (C. E. Inglis) despite the development of 64 growing hypotheses at the microstructure level and thousands of publications [27, 28, 40, 41]. For example, after the chapter, "Fatigue crack growth" in [27], there is a list of 469 supplementary readings. Crack growth is described there probabilistically in a way that is comprehensible only for specialists.

Considering the results of the numerical calculations of stresses in cracked joints in **Figure 17**, a new way for describing ductile fracture growth (zone II) may be suggested. The analysis takes into account two laws of physics:


There is a reduction in edge surface stresses on the top surface to the measured values 274–310 MPa, i.e. to the upper yield strength of the material fyH = 280 MPa. The

**Figure 17.** *Concentration of stresses at the ends of cover plates for stress levels: 100 and 140 MPa.*

growth of ductile fracture disappears at the edge points on the top surface. This phenomenon evolves in the nearby "deep" points of the fracture and according to the stress equalizing rule, it gradually restrains a two-sided fracture from proceeding to the tip of the fracture. The cracking growth in zone II disappears totally.

Generally, it should be stated that no comprehensive model for a general description of fatigue fractures has yet been devised. All models described in the literature relate only to growth zones I and II. The only known model for transition from fracture zone to final fracture, zone III, was devised by A.H. Cottrel and N.J. Petch [40, 42]. The Cottrel–Petch theory describes the ductile-brittle transition properties of steel. A basis for the transition is assumed yield strength σpl.

When the yield strength is larger than the fracture growth stress, then the material is brittle and vice versa. "Brittle fracture will occur when the work of applied stress σ during fracture growth reaches the effective energy of newly formed surfaces." This means that brittle fracture will occur under stress σ = σpl (**Figure 17**).

An explanation for this phenomenon in relation to the five cracks in the three damaged joints (**Figure 12**) is given in [38]. In the analysis, the results obtained during fatigue strength tests for three types of joints were used (**Figure 7**). Practically, this applies to the infinitive fatigue strength values Zrj given as a function of load cycles Ni.

*Quality and Fatigue Assessment of Welded Railway Bridge Components by Testing DOI: http://dx.doi.org/10.5772/intechopen.104439*
