E-TN-CBD-AISC-ASD89-008

©COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 COMPOSITE BEAM DESIGN AISC-ASD89 Technical Note Beam Shear Checks This Technical Note describes how the program checks the beam end reaction for shear for AISC-ASD89 composite beam design. The program performs two checks for beam end shear. The first is based on the allowable shear stress specified in AISC-ASD89 Specification Section F4. If the beam does not pass this shear stress check, the program indicates that the beam is inadequate. This shear check is described in the section entitled "Shear Stress Check." The second check the program performs is based on the allowable shear rupture (block shear) specified in AISC-ASD89 Specification Section J4. This check is completed based on several built-in assumptions about bolt size, bolt spacing, cope depth, etc. If the beam does not pass this shear rupture check, the program does not indicate that the beam is inadequate. Instead, it issues a design warning message in the output that the block shear may be high for the beam. This shear check is described in the section entitled "Shear Rupture Check" in this Technical Note Shear Stress Check Typical Case For h/tw ≤ 380 Fy the allowable shear stress is shown in Equation 1, which is the same as AISC-ASD89 Specification Equation F4-1. Fv = 0.40 Fy where, Fv Fy = = Allowable shear stress, ksi. Beam yield stress, ksi. Eqn. 1 The shear stress to which Equation 1 applies is calculated using Equation 2. Shear Stress Check Page 1 of 8 Equation 3 is based on AISC-ASD89 Specification Equation F4-2 with kv set equal to 5. = Beam web thickness. in.Composite Beam Design AISC-ASD89 Beam Shear Checks fv = where. = Cope depth at top of beam. in.34 Fy (h t w ) 2 Fy 2. = Shear stress. d fv tw Note: The top and bottom copes are internally calculated by the program and reported in the long. = Beam end shear at the inside end of the rigid end offset along the length of the beam (if the offset exists). ksi.8 Eqn. = Beam depth. Slender Web For h/tw > 380 Fy the allowable shear stress is that shown in Equation 3. in. See the section entitled "Copes" later in this Technical Note for more information on beam copes. Note that Equation 2 is based on the full depth of the beam minus the top and bottom copes. kips. See the following section titled "Copes" for information on how the program determines the assumed copes. 3 when Cv ≤ 0. F v = Cv where Cv = 45. 3a Shear Stress Check Page 2 of 8 .89 ≤ 0. The copes are internally calculated by the program and are reported in the printed output. 2 = Cope depth at bottom of beam. in.and short-form printed output.40Fy Eqn.000 * 5. Cbot Ctop V ( V d − C bot − C top t w ) Eqn.34. If the depth of Beam A is greater than the depth of Beam B minus the bottom flange thickness of Beam B minus 1/4". If a beam. the following copes are assumed in Beam A. 4b Note that Equation 4 is based on the clear distance between the flanges of the beam minus any portion of the top and bottom copes that extends into this clear distance. call it Beam B. the depth of the cope at the bottom of Beam A is equal to the depth of Beam A minus the depth of Beam B plus the bottom flange thickness of Beam B plus 1/4". note that the value of h/tw is limited by the requirements for a noncompact web. by default. 3b The shear stress to which Equation 3 applies is calculated using Equation 4. ! " Copes Page 3 of 8 . 4a Eqn. fv = (d − V * C bot − C* top t w ) Eqn. Copes The program calculates the default beam copes as follows: ! If the beam frames into a column or a brace. 4 where C*bot = maximum of Cbot or tf bot C*top = maximum of Ctop or tf top Eqn.34 when Cv > 0. non-slender web case. See "Noncompact Section Limits for Webs" in Technical Note Width-to-Thickness Checks Composite Beam Design AISC-ASD89 for more information. call it Beam A. This is different from the typical.Composite Beam Design AISC-ASD89 Beam Shear Checks Cv = 190 h tw 5. Finally.8 Fy Eqn. no cope is assumed at either the top or the bottom of the beam. frames into another beam. as shown in Figure 1: " The depth of the cope at the top of Beam A is equal to the thickness of the Beam B top flange plus 1/4". 2. Several assumptions are required for the program to perform this check. with actual beam sections assigned to all elements. and thus the cope dimensions for the beam were calculated based on an older design section for the girder. A single row of 7/8" diameter bolts is assumed. They include: 1. This illustrates that the design is an iterative process. You must cycle through your design and analysis several times before you get final results. Shear Rupture Check dA . that is. you may see different results. Shear Rupture Check The program checks for shear rupture based on AISC-ASD89 Specification Section J4. The reason for this is that the beam may have been designed before the girder.Composite Beam Design AISC-ASD89 Beam Shear Checks tf-top + 1/4" tf-top Beam B Beam A tf-bot + 1/4" dB tf-bot Figure 1: Default Beam Copes Important note: In some cases when you use auto select section lists and you compare the cope dimensions reported in the output with the cope dimensions calculated using the above-described method considering the current design sections for the beam and the girder. The bolt spacing is assumed to be 3 inches. Also you should always run one final design check with all auto select section lists removed. The shear rupture check is only performed at the end of a beam if the top flange of the beam is coped at that end.d + f-bot + 1/4" B t dA Page 4 of 8 . For welded sections. Standard bolt holes are assumed.5 inches.5" ≤ T < 19. is equal to d -2k.5" 25. which is tabulated in the AISC manual.5" 19.5" 12. in. Shear Rupture Check Page 5 of 8 . 6.5" 6. = Thickness of beam top flange.Composite Beam Design AISC-ASD89 Beam Shear Checks 3.1 inch.5" ≤ T < 25. is 1. lv.5" 22. 4.tf-bot . tf-bot tf-top Table 1: Assumed Number of Bolts Based on Beam T Dimension T Dimension Range T < 6. in. in.5" ≤ T < 16. is 1.5 Assumed Number of Bolts Shear rupture not checked 2 3 4 5 6 7 8 9 10 5. = Thickness of beam bottom flange. the T dimension. For rolled sections.5" 9. The number of bolts assumed is based on the T dimension of the beam as shown in Table 1.5" ≤ T < 12. where.5 inches. The distance from the center of the top bolt hole to the top edge of the beam web (at the cope). lh.5" 28.5" ≤ T < 22.5" T ≥ 31. in.5" ≤ T < 28. the program assumes that the T dimension equals d . The distance from the center of any bolt hole to the end of the beam web.5" 16.5" ≤ T < 9.tf-top . = Distance from outside face of rolled beam flange to toe of web fillet. The diameter of the bolt hole is assumed to be 15/16".5" ≤ T < 31. d k = Beam depth. 2. See Figure 2 for an illustration of the assumptions in items 1. = Minimum specified tensile strength of structural steel. in2.30 Fu Ans + 0. kips. = Net area along the shear plane. Agt. 6 and 7. Vall = 0. is given by Equation 6. 6 Page 6 of 8 3” typ. The allowable shear rupture stress is calculated based on shear fracture along the shear plane and tension yield along the tension plane.5" Figure 2: Illustration of Shear Rupture Assumptions and Terms 7.5" Shear plane Tension plane lh = 1. 5. Eqn. in2. Agt = lh tw Shear Rupture Check Eqn. The allowable beam shear (end reaction) based on shear rupture is calculated using Equation 5. ksi. See Equation 7.Composite Beam Design AISC-ASD89 Beam Shear Checks lv = 1. 5 Ans Fu Vall The gross area along the tension plane.60 Fy Agt where. . Agt = Gross area along the tension plane. = Allowable shear at end of beam. See Equation 6. in." If the beam does not satisfy the shear rupture check. the program prints a design warning message in the output. The shear rupture (block shear) check specified in AISC-ASD89 Specification Section J4 is performed as described in the section above entitled "Shear Rupture Check. lh = The distance from the center of a bolt hole to the end of the beam web. only a warning suggesting you should check shear rupture (block Limitations of Shear Check Page 7 of 8 . Ans = [lv + 3(n . The program assumes this distance to be 1. Eqn. Vall.1) . 2. is less than the beam end reaction. tw The net area along the shear plane. lv = The distance from the center of the top bolt hole to the top edge of the beam web (at the cope). as shown in Figure 2. = Beam web thickness.Composite Beam Design AISC-ASD89 Beam Shear Checks where.5 inches. 1. Limitations of Shear Check Following are some limitations of the program check for beam end shear in the Composite Beam Design postprocessor. No check is made for shear on the net section considering the bolt holes. in. Ans.5)] tw where. in. = Beam web thickness. unitless.0. is given by Equation 7. You cannot specify transverse web stiffeners. = The number of bolts as determined from Table 1. The program assumes this distance to be 1. as shown in Figure 2. except as noted in the following item 3.5 inches.(15/16)(n . 7 n tw If the allowable shear at the end of the beam. in. 3. The program does not fail the beam because it does not pass the shear rupture check. as described in AISC-ASD89 specification Chapter G is not considered. Tension field action.Composite Beam Design AISC-ASD89 Beam Shear Checks shear) is issued in the output. Limitations of Shear Check Page 8 of 8 . 4.