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EM 1110-2-6054 1 Dec 01 K I = 1.12 σ π σ σ ys = a MK Q 207 = 0.6 and Q = 1.39 (Figure 6-14). 345 Assume Mk = 1.0. With FS = 2.0, 2 a cr = 0.5 Q  K Ic    = 1.8 cm (0.71 in.) π  1.12 σ  (for crack sizes up to a = 1.8 cm (0.71 in.), Mk = 1.0) and for ferrite-pearlite steel, da/dN = 6.9×10-9 (∆KI)3 (Equation 6-8): ∆ K I = 1.12∆σ b. a = 348.5 a MPa m Q ( 50.5 a ksi in. ) Fatigue life can be determined as: N = ∫ aa cri N= π da (6.9 × 10 −9 )(∆ K I ) 3 1 (6.9 × 10 −9 a cr )(348.5) 3  1 1 N = (6.9)   a a cr  i ∫ ai a -3/2 da    c. The curve for fatigue life N as a function of initial crack length ai for this example is shown in Figure 7-5. Figure 7-5. Fatigue life N versus initial crack-length ai curve (1 in. = 2.4 cm) 7-13 EM 1110-2-6054 1 Dec 01 7-4. Example of Fracture and Fatigue Evaluation a. Single-edge crack. (1) Figure 7-6 shows a horizontal girder with a single-edge crack. The initial crack length is assumed to be 3 mm (1/8 in.). The flange plate containing the edge crack is assumed to be under a cyclic load from zero to maximum tension (i.e., fatigue ratio R = 0). The stress ranges vary from 124 MPa (18 ksi) to 186 MPa (27 ksi). The fatigue life can be calculated using the following crack growth equation (Equation 6-8): da 3 = 6.9 × 10 -9 (∆ K I ) dN where K I = 1.12 σ π a k ( a / b) By integrating the crack growth equation, the life of the propagating crack can be determined for any crack length: N = ∫ aa icr da 3 (6.9 x 10-9 ) (∆ K I ) where KI is a function of crack length and from Equation 6-2:     1  K Ic  acr = π  a    1.12 σ k    b    2 With KIc assumed to be 38.4 MPa- m (35 ksi- in . ) and a maximum stress of 124 MPa (18 ksi), acr = 2.3 cm (0.89 in.) using the procedure described in paragraph 7-2d(1)(a). (2) Figure 7-7a shows the calculated crack growth versus life cycle for a stress range of 124 MPa (18 ksi) (1/2 σys). The remaining life N, calculated by the equation for the life of the propagating crack in (1) above, is 207,700 cycles. If the structure operates 10,000 times per year, then the remaining life of the girder is: 207,700 = 20.8 years 10,000 Critical crack length (determined by Equation 6-2) is a function of external loading as shown in Figure 7-7b. Figure 7-7c shows the fatigue life for stress ranges varying from 124 MPa (18 ksi) to 186 MPa (27 ksi) calculated using the crack growth equation with variable stress and acr. The remaining life of the girder flange containing a 3-mm (1/8-in.) initial crack is shown in the figure as a function of stress. b. Double-edge crack. A girder flange containing double-edge cracks is shown in Figure 7-8. The crack growth curves were calculated for stress ranges varying from 69 to 138 MPa (10 to 20 ksi). The same integration procedure as used for the single-edge crack case is employed for calculating the fatigue life. A 3-mm 7-14 EM 1110-2-6054 1 Dec 01 Figure 7-6. A single-edge cracked girder (1 in. = 2.54 cm) 7-15 EM 1110-2-6054 1 Dec 01 Figure 7-7. Curves for fatigue life of a flange with a single-edge crack (1 in. = 2.54 cm; 1 ksi = 6.89 MPa) 7-16 EM 1110-2-6054 1 Dec 01 (1/8-in.) initial crack length is also assumed in this case. The predicted crack growth curve for stress range of 124 MPa (18 ksi) is shown in Figure 7-9a. Figure 7-9b shows the relationship between stress and critical crack length. The remaining life of the girder flange plate for various stress ranges is also shown in Figure 7-9c. c. Surface crack. Figure 7-10 shows a crack assumed to have initiated in the diagonal bracing member from a surface crack at the corner of the bracket. It is assumed that the crack propagated through the thickness of the bracing member and then grew toward the edge of the flange plate. A single-edge crack condition similar to the first example case was developed. The fracture and fatigue analysis of this example consists of three propagation steps. (1) The first step is to analyze the crack propagation of a hemispheric surface crack having an initial radius of 1.6 mm (1/16 in.). When the surface crack breaks through the surface on the other side of the plate (i.e., the radius of hemispheric crack becomes the same as the plate thickness of 9.5 mm (3/8 in.)), a through-thickness crack condition is reached. (2) The second step is to analyze crack growth of a plate containing a through-thickness crack. Once the through-thickness crack reaches the edge of the plate, the single-edge crack condition is developed. (3) The third step is to analyze crack growth of the edge crack. The total remaining life of the diagonal bracing member from the initial hemispheric surface crack can be determined by adding the three propagation lives. The calculated crack growth curve for a stress range of 124 MPa (18 ksi) is shown in Figure 7-11a. The total remaining life and critical crack length are also shown in Figure 7-11b and c for stress ranges varying from 69 to 138 MPa (10 to 20 ksi). d. Inspection schedule. The inspection schedule can be determined from the fatigue life curve of the single-edge crack in the primary member. The maximum stress range is assumed as 124 MPa (18 ksi). The procedure is shown in the following steps. (1) Determine critical crack length: acr = 2.26 cm (0.89 in.) (paragraph 7-4a) (2) Determine crack length when repair is needed (Figure 6-23): ar = 2.26/2 = 1.13 cm (0.45 in.) (FS = 2.0) (3) Determine fatigue life from fatigue life N versus crack length a curve: N = 160,000 cycles; 160,000/10,000 = 16 years (10,000 cycles/year) Therefore, the girder should be inspected within 16 years after the initial crack (ai = 3 mm (1/8 in.)) was found. 7-5. Structural Steels Used on Older Hydraulic Steel Structures Steel standards for the period when many hydraulic steel structures were constructed are of interest from both a structural evaluation and a repair and maintenance standpoint. In a structural evaluation, the characteristics of corrosion resistance, fracture resistance, crack propagation rate, and stability of properties with seasonal temperature changes are considered important parameters. The weldability of steels is also of interest since welding will likely be considered for repair and maintenance procedures even for riveted structures. However, at the time the gates were constructed, these properties probably were not determined or even much considered. 7-18 EM 1110-2-6054 1 Dec 01 Figure 7-9. Curves for fatigue life of a flange with a double-edge crack (1 in. = 2.54 cm; 1 ksi = 6.89 MPa) 7-19 EM 1110-2-6054 1 Dec 01 Figure 7-10. A stiffening member with a crack (1 in. = 2.54 cm) 7-20 EM 1110-2-6054 1 Dec 01 Figure 7-11. Curves for fatigue life of a stiffening member with a surface crack (1 in. = 2.54 cm; 1 ksi = 6.89 MPa) 7-21 EM 1110-2-6054 1 Dec 01 a. Structural steel standards. (1) In the 1930's when many hydraulic steel structures were designed and built, several structural steels were commonly in use. In the mid-1930's, structural steel could have been either ASTM A7-33T or ASTM A9-33T steel (Ferris 1953). A7 steel was generally regarded at the time as a steel for bridges, whereas A9 steel was a steel for buildings. The primary differences between the two were that A7 steel had a lower maximum allowable phosphorus content and had a limit on sulfur content compared with A9 steel. A7 steel also was restricted to open-hearth or electric-furnace production and excluded the older acid-bessemer production. These compositional and production restrictions suggest that A7 bridge steel was recognized as the premium steel of the two. For a brief period (1932-33), structural steel also could have been supplied as ASTM A140 steel, which was a tentative replacement for both A7 and A9 steels (Ferris 1953). (2) Steel identified as silicon steel on design drawings is mostly likely ASTM A94-25T structural silicon steel. This was a high-strength steel with a specified minimum silicon content that attained its high strength (minimum yield point of 310 MPa (45 ksi) and tensile strength of 552 to 655 MPa (80 to 95 ksi)) through a high level of carbon (0.44 percent maximum). It also had limits on its phosphorus and sulfur contents. (3) An important characteristic of the early steels, regardless of whether they were A7, A9, A140, or A94 silicon steel, is that they had either no specified level or a high level of carbon in their composition. Consequently, the carbon level was either not rigorously controlled or was moderately high, with the result that the steels probably had and have only poor to fair weldability. The specification for A94 structural silicon steel specifically limits welding and specifies a preheat condition when welding must be done. Of course, the steels were being used for riveted structures, so weldability was not then a concern to designers. But it needs to be considered for weld repairs or maintenance contemplated today. (4) In 1939, A7 and A9 were consolidated into a single specification, A7 steel (ASTM A7-39) for bridges and buildings, which then became the single specification for structural steel. In 1954 a new structural steel for welding, A373 steel, was introduced (ASTM A373-58T). Both A7 and A373 steels were consolidated in 1965 into one specification, A36 steel (ASTM A36-60T), which is the basic structural steel today and is used for both welded and bolted applications. b. Rivet steel standards. (1) Rivet steel was not typically specified by steel grade, but only as structural steel, carbon steel, or as rivets. However, the allowable shear stress for power-driven rivets was occasionally identified as 82.7 MPa (12 ksi), and the allowable bearing stress as 165.4 MPa (24 ksi). Until 1932, rivet steel was included in the ASTM A7 and A9 specifications, but with lower yield and tensile strengths than structural steel (Ferris 1953). However, in 1932, ASTM A141 was issued as a tentative specification for structural rivet steel, with somewhat more enhanced strength requirements than earlier. More restrictive diameter tolerances were included in a 1936 tentative revision. Until 1949, rivet yield strength was specified as one-half times the tensile strength or not less than 193 MPa (28 ksi). In 1949, the yield strength for A141 rivet steel was changed to 193 MPa (28 ksi) minimum (Ferris 1953). In 1960, A141 rivet steel was incorporated into the new tentative A36 steel specification (ASTM A36-60T). (2) In 1936, a new tentative specification, ASTM A195, was issued for high-strength structural rivet steel, for rivets produced from structural silicon steel (ASTM A195-36T). As opposed to A141 rivet steel, A195 rivet steel had carbon, manganese, silicon, and copper requirements. In addition, A195 rivet steel yield strength was specified as one-half times the tensile strength or not less than 262 MPa (38 ksi). A195 steel rivets were to be used with A94 structural silicon steel, although the use of A141 steel rivets may have continued. 7-22