Fastening plate design Peikko Group FASTENING PLATE CALCULATIONS Date: 26th Oct 2017 Fastening plate design CONTENT: 1. General 1.1Applied Standards 1.2Materials 1.3Safety Factors 1.4Load Combinations 1.5Enviromental Conditions 2. Dimensions 3. Design of Plates 3.1 Steel strength in tension 3.2 Concrete breakout strength in tension 3.3 Pullout strength 3.4 Steel strength in shear 3.5 Pryout strength 3.6 Concrete breakout strength in shear 3.7 Interaction strength 3.8 Plate bending strength 4. Results Peikko Group Fastening plate design 1 Peikko Group GENERAL Fastening plates for Wylfa Nuclear project. Connection will be welded connection between the structures. 1.1 APPLIED STANDARDS Loading combinations should follow ASCE7-10 Design of base plates shall be by AISC 360-10 LRFD Design of anchor bolts shall be by ACI 318M-2011 Appendix-D 1.2 MATERIALS EN 10025-2:2004– Hot rolled structural steel, non-alloy quality steel, for general purpose. S355J2+N - Plate EN ISO-13918 – Welding Studs and Ceramic Ferrules for Arc Stud Welding ISO/TR15608 – Welding Guidelines for Metallic Materials Grouping System Headed Studs – SD1 (fy=350MPa; fu=450MPa) ACI318M-11 – Building Code Requirements for Structural Concrete Minimum compressive strength of concrete – 35 mPa (Cylinder) Minimum compressive strength of concrete – 45 mPa (Cube) 1.3 SAFETY FACTORS Safety factors for different materials as listed below: Plate Yield strength Tensile strength Safety factor S355 fy fu Ø 355 MPa 500 MPa 0.9 Fastening plate design Studs Yield strength Tensile strength Modulus of elasticity Safety factor - tension Safety factor - shear Concrete Compressive strength Maximum strain Safety factor Safety factor 1.4 Peikko Group ISO/TR 15608 SD1 fy 350 MPa fu 450 MPa Es 200000 MPa Ø 0.75 Ø 0.65 fc' εc Ø Ø 35 MPa 0.003 0.75 0.7 (Condition A –ACI318M-11) (Pullout&Pryout) LOAD COMBINATIONS Loading combinations should follow ASCE 7-10 and ACI318M-11 instructions for the applicable loading cases. ULS factored loading combinations should be compared to the LRFD capacities of the fastening plates. Capacities has been designed as per static loads, in case of seismic or dynamic loads additional requirements in ACI 318M-11 should be considered. 1.5 ENVIROMENTAL CONDITIONS Corrosion and fire resistance hasn’t been considered in the calculations. This should be taken into account according to the project requirements. 2 DIMENSIONS Fastening plate dimensions are following the Figure 1 instructions. Fastening plate design Peikko Group Figure 1. Fastening plate dimensions 3 DESIGN OF PLATES Strengths in different cases has been calculated in chapters 3.1 – 3.8. In these strengths additional reinforcement hasn’t been taken into account but concrete strengths can be increased by adding additional reinforcement. 3.1 Steel strength of anchors in tension Steel strength of single anchor can be obtained as follows: Where Ase fy = = Cross-section area of stud = Yield strength of the stud ∙ Steel strength of group of anchors can be obtained as follows: Fastening plate design Where Ø n Peikko Group ∅ =∅∙ = Safety factor of stud = number of studs ∙ 3.2 Concrete breakout strength in tension Concrete breakout strength is calculated for anchors in tension. All the anchors has been expected to be loaded equally with tension force. Concrete edge distance has not been considered and it should be > 1.5 ∙ ℎ . Concrete breakout strength for group of anchors can be obtained as follows: Where ANc ANco Ψec,N E’n Ψed,N Ψc,N Nb hef fc’ kc ∅ = ∙ ∙ , , ∙ , ∙ = Total projected area = (3ℎ + ) ∙ (3ℎ + ) = Maximum projected area of single anchor = 9ℎ = Factor for eccentricity = = Eccentricity of load = Factor for concrete edge effect = > 1.5ℎ = Factor for concrete cracking = 1.0 (cracked concrete) = Basic concrete breakout strength = ∙ ∙ℎ . = Effective anchor height = Concrete grade = Factor for anchors = 10 (cast-in anchors) 3.3 Pullout strength Pullout strength of single anchor can be obtained as follows: Where Ψc,p Np Abrg = , ∙ = Factor for concrete cracking = 1.0 (cracked concrete) = Pullout strength = 8 ∙ ∙ = Cross-section of the head with shaft excluded Fastening plate design Peikko Group Pullout strength of group of anchors can be obtained as follows: Where Ø ∅ =∅∙ ∙ = Safety factor for concrete in pullout 3.4 Steel strength of anchors in shear Steel strength for the single anchor in shear can be obtained as follows: = 0.6 ∙ ∙ Steel strength for group of anchors in shear can be obtained as follows: Where Ø ∅ =∅∙ ∙ = Safety factor of stud in shear 3.5 Pryout strength of anchors Pryout strength of the anchor can be obtained as follows: Where kcp Ncbg Ø ∅ =∅∙ ∙ = Pryout factor for anchors = 2 (if h ef ≥65mm) = Concrete breakout strength (see chapter 3.2) = Safety factor for pryout 3.6 Concrete breakout strength for shear Embedded plates has been assumed to be in the middle of the structure where edge distance is not limiting the capacity due to his concrete breakout strength in shear will not govern the calculation and can be ignored. Fastening plate design Peikko Group 3.7 Interaction strength Interaction strength is applied as per ACI318M-11 trilinear approach as shown in Figure 2 below: If If If ∅ ∅ ∅ ≤ 0.2 full strength in tension shall be permitted ≤ 0.2 full strength in shear shall be permitted > 0.2 for the governing strength in shear and in tension then: ∅ + ∅ ∅ > 0.2 for the governing strength ≤ 1.2 Figure 2. Trilinear approach where ØNn = MIN (Nsag;Ncbg;Npng) ØV n = MIN (Vsag;Vcpg) 3.8 Plate bending strength Plate bending resistance is based on the assumed yield line distance from the anchors. Yield line will occur in the side of the profile. Fastening plate design Peikko Group Yield line can occur either parallel to L and B dimensions in that case 2 or more bolts will cause the bending for the plate or it can be from the corner in that case 1 bolt will cause the bending of the plate. Yield line theories and dimensions are shown in Figure 3. Figure 3. Yield line theories Distances x1;x2;x3 from the yield lines can be obtained as follows: = Where h s1 s2 = = −ℎ 2 −ℎ 2 −ℎ 2 + −ℎ 2 = Attached profile size (square) = Spacing of outermost studs parallel to L = Spacing of outermost studs parallel to B In case where the yield line occurs to the corner of the plate length of yield line can be obtained as follows: Where L B = Plate length = Plate width = 2∙ −ℎ 2 +2∙ −ℎ 2 Fastening plate design Peikko Group Max tension force for single stud which plate is able to transfer can be obtained as follows: Where t fy nL nB Ø ØNsa = ( ∙ ∙ ∙∅ ∙ ∙ ∙∅ ; ; 4∙ ∙ 4∙ ∙ ∙ 4∙ ∙ ∙∅ ;∅ ) = Plate thickness = Yield strength of plate = Number of studs in row parallel to L = Number of studs in row parallel to B = Safety factor for plate = Steel strength of stud (see chapter 3.1) Max tension force for group of anchors which plate is able to transfer can be obtained as follows: ∅ = ∙