Beam To Column Connection: SHEAR PLATE SUBJECT TO SHEAR & AXIAL LOAD

This is an experimental program. Hope you will find this stuff useful.

I got the idea when an engineer friend and a former colleague asked me to create a web versions (via this blog) of the Connection Design Calculations that I used to do in Microsoft Excel and SMath Studio. I wrote the program in javascript both as pastime and learning exercise.

I will be writing and posting more like this connection design programs soon. With javascript, possibilities are just endless...

CONNECTION LAYOUT:

MEMBER SIZES:
Beam Size
Column Size
Connection Interface

SHEAR PLATE DATA:
Plate Thickness
Plate Placement (Is CENTERED On Beam?)
Steel Plate Grade

DISTANCES and SPACINGS:
First Bolt Distance from Top of Beam
Beam-Column Gap
Beam Edge Distance
Plate Vertical Edge Distance
Plate Horizontal Edge Distance
Bolt Vertical Spacing
Bolt Horizontal Spacing

BOLT INPUT DATA:
Bolt Diameter
Bolt ASTM Grade
Number of Bolt Columns
Number of Bolt Rows

WELD INPUT DATA:
Fillet Weld Size
Weld Class/Electrode

BEAM END LOADS:
Factored Vertical Load [KIP]	Vu
Factored Axial Load (Compression/Tension) [KIP]	Pu

***CANNOT PERFORM CALCULATIONS***

>>>Incomplete Input<<<

...Please fill-out required Data..

SOLUTION/DESIGN CALCULATIONS:

A.) GENERAL: • Reference: AISC - American Institute of Steel Construction Manual, 14th Edition • Design Method: LRFD - Load and Resistance Factor Design B.) DESIGN NOTES: The loading for this connection is a combination of SHEAR and AXIAL LOAD. As a result, the Tension Capacity for any "LIMIT STATE" is reduced by the presence of Shear, or vice versa. For design bolt tension in the presence of shear, the "INTERACTION" (combined stresses) is handled directly by the AISC Code equations. For other "LIMIT STATES" in combined stresses such as Bolt Bearing, Gross and Net Shear and Tension, and Block Shear and Tension Tearout, the effect of "INTERACTION" is handled by the use of the formula, P/Ra + (R/Rv)² = 1, as suggested from the following reference: "Combined Shear and Tension Stress" - by Subhash C. Goel, AISC Journal, 3rd Qtr.-1986. Alternately, the effect of "INTERACTION" can also be evaluated by the use of VON MISES' YIELD CRITERION formula, (P/Ra)² + 3(R/Rv)² = 1 Where: P = Connection Axial Load Ra = Design Axial Strength for the particular "Limit State" considered R = Connection Shear Load Rv = Design Shear Strength for the particular "Limit State" considered C.) LOAD: Vu = Factored Shear Load = 0.00 Kips Pu = Factored Axial Load = 0.00 Kips Ru = Factored Resultant Load = `sqrt(V_u^2 + P_u^2)` = 0.00 Kips D.) SHEAR PLATE & DISTANCES: tp = Thickness of Plate = 0.00 inches hp = Depth of Plate = 0.00 inches wp = Width of Plate = 0.00 inches Lev = Plate Vertical Edge Distance = 0.00 inches Leh = Plate Horizontal Edge Distance = 0.00 inches Leb = Beam Edge Distance = 0.00 inches E.) MATERIAL PROPERTIES: Fyp = Plate Yield Strength = 0.00 Ksi Fup = Plate Tensile Strength = 0.00 Ksi Fyb = Beam Yield Strength = 0.00 Ksi Fub = Beam Tensile Strength = 0.00 Ksi E = Modulus of Elasticity = 0.00 Ksi F.) BEAM PROPERTIES: Size = XX d = Beam Depth = 0.00 inches tw = Beam Web Thickness = 0.00 inches tf = Beam Flange Thickness = 0.00 inches kdet = Beam k-Detailing Dimension = 0.00 inches G.) BOLT DATA: Bolt Type: A325-N Designation: ¾"Ø - A325-N-STD db = Bolt Diameter = 0.00 inches N = Number of Bolt Rows = 00 M = Number of Bolt Columns = 00 Sn = Bolt Row Spacing = 0.00 inches Sm = Bolt Column Spacing = 0.00 inches ex = Load Eccentricity from Bolt C.G. = 0.00 inches Ø = Load Angle From Vertical = `ArcTan [(P_u)/(V_u)]` = 0.00 degrees C = Bolt Group Coefficient By IC Method = 0.00 `phi`vrn = Available Bolt Shear Strength AISC 14th Ed. [Table 7-3] = 0.00 Kips `phi`brn = Available Bolt Bearing Strength on Shear Plate/Beam Web = `0.75*min[(2.4*F_(ub)*t_w*d_b), (2.4*F_(up)*t_p*d_b)]` = 0.00 Kips H.) BOLT STRENGTH CHECK: `phi`Rn = Design Bolt Shear Strength AISC 14th Ed. [Eq. 7-19] = `C*min[phi_vr_n, phi_br_n]` = 0.00 Kips 0.00 Kips [OK] I.) BOLT BEARING on SHEAR PLATE under SHEAR and AXIAL TENSILE Load: » Bolt Bearing On Shear Plate Under Shear: Exterior Bolt: Lc = Clear Edge Distance = XXX inches `phi_er_n` = `0.75*min[1.2*L_c*t_p*F_(up); 2.4*d_b*t_p*F_(up)]` AISC 360-10 [Eq. J3-6a] = XXX Kips/Bolt Interior Bolt: Lc = Clear Distance Between Interior Bolts = XXX inches `phi_ir_n` = `0.75*min[1.2*L_c*t_p*F_(up); 2.4*d_b*t_p*F_(up)]` AISC 360-10 [Eq. J3-6a] = XXX Kips/Bolt Thus: `phiR_n` = Design Bearing Strength of Bolts = `M*[phi_er_n + (N-1)*phi_ir_n]` = 0.00 Kips > 0.00 Kips [OK] » Bolt Bearing On Shear Plate Under Axial Tensile Load: Exterior Bolt: Lc = Clear Edge Distance = XXX inches `phi_er_n` = `0.75*min[1.2*L_c*t_p*F_(up); 2.4*d_b*t_p*F_(up)]` AISC 360-10 [Eq. J3-6a] = XXX Kips/Bolt Interior Bolt: Lc = Clear Distance Between Interior Bolts = XXX inches `phi_ir_n` = `0.75*min[1.2*L_c*t_p*F_(up); 2.4*d_b*t_p*F_(up)]` AISC 360-10 [Eq. J3-6a] = XXX Kips/Bolt Thus: `phiR_n` = Design Bearing Strength of Bolts = `N*[phi_er_n + (M-1)*phi_ir_n]` = 0.00 Kips > 0.00 Kips [OK] » Check Bolt Bearing On Shear Plate Under Combined Load: P = x.xx Kips [Axial Load] Ra = x.xx Kips [Design Axial Strength] R = x.xx Kips [Shear Load] Rv = x.xx Kips [Design Shear Strength] Substitute to 'Subhash C. Goel' Interaction Equation: `[P/R_a] + [R/R_v]^2 <= 1.0` 1.00 = 1.00 [OK] Substitute to 'Von Mises Criterion' Interaction Equation: `[P/R_a]^2 + 3*[R/R_v]^2 <= 1.0` 1.00 = 1.00 [OK] J.) SHEAR PLATE YIELDING under SHEAR and AXIAL TENSILE Load: » Plate Shear Yielding: `phiR_n` = Design Shear Yield Strength AISC 360-10 [Eq. J4-3] = `0.6*F_(yp)*[t_p*h_p]` = 0.00 Kips > 0.00 Kips [OK] » Plate Tensile Yielding: `phiR_n` = Design Tensile Yield Strength AISC 360-10 [Eq. D2-1] = `0.9*F_(yp)*[t_p*h_p]` = 0.00 Kips > 0.00 Kips [OK] » Check Plate Yielding Under Combined Load: P = x.xx Kips [Axial Load] Ra = x.xx Kips [Design Axial Strength] R = x.xx Kips [Shear Load] Rv = x.xx Kips [Design Shear Strength] Substitute to 'Subhash C. Goel' Interaction Equation: `[P/R_a] + [R/R_v]^2 <= 1.0` 1.00 = 1.00 [OK] Substitute to 'Von Mises Criterion' Interaction Equation: `[P/R_a]^2 + 3*[R/R_v]^2 <= 1.0` 1.00 = 1.00 [OK] K.) SHEAR PLATE RUPTURE under SHEAR and AXIAL TENSILE Load: » Plate Shear Rupture: Anv = Net Cross-sectional Area subject to Shear = `t_p*[h_p-N*(d_b+0.125)]` = XXX in2 Thus: `phiR_n` = Design Shear Rupture Strength AISC 360-10 [Eq. J4-4] = `0.75*[0.6*F_(up)*A_(nv)]` = 0.00 Kips > 0.00 Kips [OK] » Plate Tensile Rupture: Ag = Gross Cross-sectional Area subject to Tension = `t_p*h_p` = XXX in2 An = Net Cross-sectional Area subject to Tension = `t_p*[h_p-N*(d_b+0.125)]` = XXX in2 Ae = Effective Cross-sectional Area subject to Tension = `A_n<=0.85*A_g` = XXX in2 Thus: `phiR_n` = Design Tensile Rupture Strength AISC 360-10 [Eq. D2-2] = `0.9*[F_(up)*A_e]` = 0.00 Kips > 0.00 Kips [OK] » Check Plate Rupture Under Combined Load: P = x.xx Kips [Axial Load] Ra = x.xx Kips [Design Axial Strength] R = x.xx Kips [Shear Load] Rv = x.xx Kips [Design Shear Strength] Substitute to 'Subhash C. Goel' Interaction Equation: `[P/R_a] + [R/R_v]^2 <= 1.0` 1.00 = 1.00 [OK] Substitute to 'Von Mises Criterion' Interaction Equation: `[P/R_a]^2 + 3*[R/R_v]^2 <= 1.0` 1.00 = 1.00 [OK] L.) PLATE BLOCK SHEAR and TENSION TEAR-OUT due to SHEAR and AXIAL TENSILE Load: » Plate Block Shear Strength: (consider L-Pattern Failure for combined stress) `U_(bs)` = XXX Agt = Gross Area with Tensile Resistance = `[(M-1)*S_m+L_(eh)]*t_p` = XXX in2 Ant = Net Area with Tensile Resistance = `A_("gt") - (M-0.5)*(d_b+0.125)*t_p` = XXX in2 Agv = Gross Area with Shear Resistance = `[h_p-L_(ev)]*t_p` = XXX in2 Anv = Net Area with Shear Resistance = `A_(gv)-(N-0.5)*(d_b+0.125)*tp` = XXX in2 Thus: `phiR_n` = Design Block Shear Strength AISC 360-10 [Eq. J4-5] = `0.75*min[(0.6*F_(up)*A_(nv)+U_(bs)*F_(up)*A_(nt)); (0.6*F_(yp)*A_(gv)+U_(bs)*F_(up)*A_(nt))]` = 0.00 Kips = 0.00 Kips [OK] » Plate Tension Tear_Out Strength: (consider L-failure Pattern for combined stress) `U_(bs)` = XXX Agv = Gross Area with Shear Resistance = `[(M-1)*S_m+L_(eh)]*t_p` = XXX in2 Anv = Net Area with Shear Resistance = `A_(gv)-(M-0.5)*(d_b+0.125)*t_p` = XXX in2 Agt = Gross Area with Tensile Resistance = `[h_p-L_(ev)]*t_p` = XXX in2 Ant = Net Area with Tensile Resistance = `A_("gt")-(N-0.5)*(d_b+0.125)*t_p` = XXX in2 Thus: `phiR_n` = Design Tensile Tear-Out Strength AISC 360-10 [Eq. J4-5] = `0.75*min[(0.6*F_(up)*A_(nv)+U_(bs)*F_(up)*A_(nt)); (0.6*F_(yp)*A_(gv)+U_(bs)*F_(up)*A_(nt))]` = 0.00 Kips > 0.00 Kips [OK] » Check Plate Combined Block Shear and Tension Tear-Out: P = x.xx Kips [Axial Load] Ra = x.xx Kips [Design Axial Strength] R = x.xx Kips [Shear Load] Rv = x.xx Kips [Design Shear Strength] Substitute to 'Subhash C. Goel' Interaction Equation: `[P/R_a] + [R/R_v]^2 <= 1.0` 1.00 = 1.00 [OK] Substitute to 'Von Mises Criterion' Interaction Equation: `[P/R_a]^2 + 3*[R/R_v]^2 <= 1.0` 1.00 = 1.00 [OK] M.) Beam Web BLOCK SHEAR and TENSION TEAR-OUT due to SHEAR and AXIAL TENSILE Load: » Beam Web Block Shear Strength: ** There is NO vertical block shear for this case. Shear PATH just runs into the flange. » Beam Web Tension Tear-Out Strength: (C-Pattern Failure) `U_(bs)` = XXX Agv = Gross Area with Shear Resistance = `2*[L_(eb)+(M-1)*S_m]*t_w` = XXX in2 Anv = Net Area with Shear Resistance = `A_(gv)-2*(M-0.5)*(d_b+0.125)*t_w` = XXX in2 Agt = Gross Area with Tensile Resistance = `[(N-1)*S_n]*t_w` = XXX in2 Ant = Net Area with Tensile Resistance = `A_("gt")-[(N-1)*(d_b+0.125)]*t_w` = XXX in2 Thus: `phiR_n` = Design Tensile Tear-Out Strength AISC 360-10 [Eq. J4-5] = `0.75*min[(0.6*F_(ub)*A_(nv)+U_(bs)*F_(ub)*A_(nt)); (0.6*F_(yb)*A_(gv)+U_(bs)*F_(ub)*A_(nt))]` = 0.00 Kips = 0.00 Kips [OK] N.) SHEAR PLATE under Combined COMPRESSION and BENDING: » Geometric Properties: K = Effective Length Factor = XXX L = Plate Unsupported Length = XXX inches r = Least Radius of Gyration = `[t_p/3.464]` = XXX inches Ag = Cross-sectional Area = `t_p * h_p` = XXX in2 Z = Plastic Section Modulus = `[t_p * h_p^2]/4` = XXX in3 » Evaluate Plate Strength: Fe = Elastic Critical Buckling Stress AISC 360-10 [Eq. E3-4] = `(pi^2*E)/[(K*L)/r]^2` = XXX Ksi Since Fe > 0.44Fy, therefore: Fcr = Elastic Critical Buckling Stress = `[0.658^(F_(yp)/F_e)]*F_(yp)` AISC 360-10 [Eq. E3-2] = `0.877*F_e` AISC 360-10 [Eq. E3-3] = XXX Ksi Pr = Required Axial Compressive Strength = Pu = XXX Kips Pcy = Available Axial Compressive Strength = `0.9*[F_(cr)*A_g]` AISC 360-10 [Eq. E3-1] = XXX Kips Mr = Required Flexural Strength = `V_u*L` = XXX Kip-in Mcx = Available Flexural Strength = `0.9*[F_(yp)*Z]` AISC 360-10 [Eq. E7-1] = XXX Kip-in Cb = Lateral-Torsional Buckling Modification Factor = XXX (assumed) For Doubly Symmetric Members in Single Axis Bending, the Interaction of Flexure and Compression in Column is controlled by the below equation: `P_r/P_(cy)*[1.5-0.5*P_r/P_(cy)]+[M_r/(C_b*M_(cx))]^2 <= 1.0` AISC 360-10 [Eq. H1-2] Substituting values to Interaction Equation H1-2, therefore: 1.00 = 1.00 [OK] O.) Plate to Column Flange WELD: FEXX = Tensile Strength of Weld = 0.00 Ksi ctfw = Column Flange Thickness = 0.00 inch wa = Assigned Fillet Weld Size = 0.00 inch wu = Useful weld based on Column Flange rupture @ weld zone AISC 14th Ed. [Eq. 9-2] = `(F_(ub)*[(ct_(fw))/16])/3.09` = 0.00 inch we = Effective Fillet Weld Size = `min[w_a, w_u]` = 0.00 inch Ø = Load Angle relative to Weld Line = `Arc tan[P_u/V_u]` = 0.00 radian = 0.00 degrees Vw = Available Shear Strength of Weld per linear inch = `0.75*[0.6*F_(EXX)*(1.0+0.50*sin^1.5theta)*0.707*w_e]` = 0.00 Kips/in Lw = Total Length of Fillet Weld (back-to-back) = 0.00 inches Thus: `phi`Rn = Design Shear Strength of Weld = `V_w*L_w` = 0.00 Kips > 0.00 Kips [OK] P.) Beam Web YIELDING due to AXIAL TENSILE Load: » Reference: ** 'YIELD LINE ANALYSIS OF A WEB CONNECTION IN DIRECT TENSION' by Richard H. Kapp, Second Quarter/1974, Engineering Journal/American Institute Of Steel Construction, 2nd Quarter 1974, Pages 38~41 » Required Dimensions: T = T-Dimension of Column Section = *** in w = Fillet Weld Size = *** in c = Distance between Inner Yield Lines, across the Member = `t_p + 2/3 * w` = *** in L = Distance between Inner Yield Lines, along the Member (Depth of Plate) = *** in b = Distance from inner Yield Line to Outer Yield Line across the member = `[T-c]/2` = *** in twc = Column Web Thickness = *** in Thus: `phiT_n` = Column Web Design Tensile Strength (Equation 5 - Yield Line Analysis of a Web Connection in Direct Tension) = `0.9*F_(yb)*t_(wc)^2*[L/b+ 4*sqrt(1+c/(2*b))]` = 0.00 Kips = 0.00 Kips [OK]