Product Technical Guides : US-EN Cast-In Anchor Channel Fastening Technical Guide | Page 158

1. Anchor Channel Systems 2. HAC Portfolio 3. HAC Applications V ns Nominal steel strength of anchor channel loaded in shear (lowest value of V sa , V sc , and V sl ), lbf (N) V ns,a nominal shear strength for steel failure of anchor or connection between anchor and channel (lowest value of V sa and V sc ), lbf (N) V sa,x,seis nominal seismic shear steel strength in longitudinal channel axis of a single anchor, lbf (N) V sc,y nominal shear strength of connection between one anchor bolt and the anchor channel, lbf (N) factored shear load on anchor channel, lbf (N) V aua factored shear load on a single anchor of the anchor channel, lbf (N) V aua,i factored shear load on anchor i of the anchor channel, lbf (N) V sua factored shear load on a channel bolt, lbf (N) α exponent of interaction equation α ASD conversion factor for allowable stress design α ch,N factor to account for the influence of channel size on concrete breakout strength in tension [-] ψ cp,N modification factor for anchor channels to control splitting ψ ed,N modification factor for edge effect on concrete breakout strength for anchors loaded in tension [-] ψ g,Nb modification factor to account for influence of bearing area of neighboring anchors on concrete blowout strength for anchors loaded in tension [-] ψ h,Nb modification factor to account for influence of member thickness on concrete blowout strength for anchors loaded in tension [-] Tension Loads: Calculation of t-bolt loads induced by tension loads and bending moments acting on the fixture per elastic theory involves the following assumptions (Fig. 7.2.7.1) a) T  he fixture remains plane (flat) under the influence of internal forces. In order to warrant this supposition, the fixture must be sufficiently stiff and must be in contact with the base material. A stiff fixture may be assumed if under the design actions, the stresses in the fixture are smaller than the design resistance of the fixture material. The stiff fixture assumption corresponds to the Bernoulli hypothesis in reinforced concrete design, wherein plane cross-sections are assumed to remain plane. b) I  n the part of the fixture subjected to compression, t-bolts do not act in either tension or compression. c) T  he stiffness of all t-bolt in a group are identical. The t-bolt stiffness is directly proportional to the area of the stressed cross-section and the modulus of elasticity of the steel. The stiffness of the concrete is characterized by its elastic modulus and the stressed area. Consequently, the calculation of the tension forces in the t-bolts corresponds to how one determines the tension resultant in the reinforcing bars of a reinforced concrete member. However, in contrast to strength design of reinforced concrete members, we assume here that the response of the concrete and steel elements remains linear elastic. Figure 7.2.7.2 — Distribution of shear forces in an anchor group Example of connections in which all t-bolts participate in resisting the shear load. In most cases, elastic analysis yields satisfactory results and is recommended. It should be noted, however, that the assumption of anchor load linearly proportional to *the magnitude of the applied load and the distance from the neutral axis of the group is valid only if the attachment (e.g. baseplate) is sufficiently stiff in comparison to the axial stiffness of the t-bolts. Note: Assuming a rigid base plate condition, Hilti’s PROFIS Anchor channel analysis and design software performs a simplified finite element analysis to establish anchor load distribution on an elastic basis. ψ h,V modification factor to account for influence of member thickness on concrete edge breakout strength for anchors channels loaded in shear [-] ψ s,N modification factor to account for influence of location and loading of neighboring anchors on concrete breakout strength for anchor channels loaded in tension [-] ψ s,Nb modification factor to account for influence of location and loading of neighboring anchors on concrete blowout strength for anchor channels loaded in tension [-] ψ s,V modification factor to account for influence of location and loading of neighboring anchors on concrete edge breakout strength for anchor channels loaded in shear [-] Figure 7.2.7.1 — Distribution of forces predicted by elastic theory in an t-bolt group subjected to tension force and bending moment. α M factor to account for the influence of restraint of fixture on the flexural strength of the channel bolt [-] 158 Cast-In Anchor Channel Product Guide, Edition 1 • 02/2019 159 V ua ψ co,V modification factor for corner effects on concrete edge breakout strength for anchor channels loaded in shear [-] In calculating the distribution of shear loads through a fixture to the t-bolts of a group positioned away from an edge, it is assumed that all t-bolts exhibit the same shear stiffness. Additionally, it is generally assumed that all t-bolts participate in accommodating the shear loads (Fig. 7.2.7.2). It is assumed that the shear load acts at the center of gravity of the group of t-bolts. When the shear load acts eccentrically, the forces in the anchors should be calculated taking into account equilibrium conditions based on steel design principles. V ss nominal strength of channel bolt in shear, lbf (N) ψ co,Nb modification factor for corner effects on concrete blowout strength for anchors loaded in tension [-] Shear Loads: V sl,x,seis nominal seismic shear steel strength in longitudinal channel axis of connection between channel bolt and channel lips, lbf (N) ψ co,N modification factor for corner effects on concrete breakout strength for anchors loaded in tension [-] 14. Design Example V sl,y,seis nominal seismic shear steel strength perpendicular to the channel axis of the local bending of the channel lips, lbf (N) ψ c,V modification factor to account for influence of cracked or uncracked concrete for concrete edge breakout strength [-] The forces on a t-bolt can generally be determined using general principles of structural mechanics. In doing so, the displacement of the t-bolt is usually assumed to be small (i.e negligible). The distribution of forces acting on a fixture of a t-bolt group to the individual t-bolt of the group can be calculated with elastic theory. 13. Field Fixes V sl,x nominal shear steel strength in longitudinal channel axis of connection between channel bolt and channel lips, lbf (N) ψ c,Nb modification factor to account for influence of cracked or uncracked concrete on concrete blowout strength [-] Determination of t-bolt forces acting on anchor channels 12. Instructions for Use V sl,y nominal shear steel strength perpendicular to the channel axis of the local bending of the channel lips, lbf (N) ψ c,N modification factor to account for influence of cracked or uncracked concrete on concrete breakout strength [-] 7.2.7 LOAD DISTRIBUTION 11. Best Practices V sc,x,seis nominal seismic shear strength in longitudinal channel axis of connection between one anchor bolt and the anchor channel, lbf (N) α v,seis,x adjustment factor for seismic loading (x-direction, in longitudinal channel axis) 10. Design Software V sc,y,seis nominal seismic shear strength perpendicular to the channel axis of connection between one anchor bolt and the anchor channel, lbf (N) α v,seis,y adjustment factor for seismic loading (y-direction, perpendicular to the channel axis) 9. Special Anchor Channel Design V sc,x nominal shear strength in longitudinal channel axis of connection between one anchor bolt and the anchor channel, lbf (N) α ch,V factor to account for the influence of channel size and anchor diameter on concrete edge breakout strength in shear (lbf 0.5 /in) 0.33 (N 0. 5/mm 0.33 ) 8. Reinforcing Bar Anchorage V sa,y,seis nominal seismic shear steel strength perpendicular to the channel axis of a single anchor, lbf (N) λ Modification factor for sand-lightweight concrete in accordance with Section 8.6.1 of ACI 318-08 and 318-11 or Section 19.2.4 of ACI 318-14 7. Anchor Channel Design Code V sa,x nominal shear steel strength in longitudinal channel axis of a single anchor, lbf (N) 6. Loading V sa,y nominal shear steel strength perpendicular to the channel axis of a single anchor, lbf (N) 5. Base material shear loads) or V ca (anchor channels with anchor reinforcement to take up shear loads) and V cp ) 4. Design Introduction