Engineering Calculation Spreadsheet

Item,Symbol,Value,Unit,Notes Bending stress and deflection check - simply supported steel beam under uniform load (Project: Warehouse mezzanine B2),,,, "NOT STAMPED OR CERTIFIED ENGINEERING. This sheet automates the formulas and inputs supplied by the user. It is not a professional engineering design, review or approval. All formulas, inputs, units and results must be independently verified by a qualified, licensed engineer before use in design, construction, fabrication or safety decisions.",,,, ,,,, INPUTS - edit the values in column C,,,, Uniform distributed load (service),w,2.5,kN/m,Given by customer (service load) Span (simply supported),L,6,m,Given by customer Steel modulus of elasticity,E,200,GPa,Given by customer Moment of inertia,I,8.36E-05,m^4,Given by customer Elastic section modulus,S,5.12E-04,m^3,Given by customer Allowable bending stress,sigma_allow,165,MPa,Given by customer Deflection limit denominator (allowable deflection = L/n),n,360,ratio,Given by customer (L/360) CALCULATIONS,,,, Maximum bending moment at midspan,M,=C6C7^2/8,kNm,M = wL^2/8 Maximum bending moment converted to Nmm,M_Nmm,=C141000000,Nmm,Conversion: 1 kNm = 1000000 Nmm Section modulus converted to mm^3,S_mm3,=C101000000000,mm^3,Conversion: 1 m^3 = 1000000000 mm^3 Bending stress (unrounded),sigma,=C15/C16,MPa,sigma = M/S (Nmm / mm^3 = N/mm^2 = MPa) Modulus of elasticity converted to MPa,E_MPa,=C81000,MPa,Conversion: 1 GPa = 1000 MPa = 1000 N/mm^2 Uniform load converted to N/mm,w_Nmm,=C61,N/mm,Conversion: 1 kN/m = 1 N/mm Span converted to mm,L_mm,=C71000,mm,Conversion: 1 m = 1000 mm Moment of inertia converted to mm^4,I_mm4,=C91000000000000,mm^4,Conversion: 1 m^4 = 1000000000000 mm^4 Maximum midspan deflection (unrounded),delta,=5C19C20^4/(384C18C21),mm,"delta = 5wL^4/(384EI) using N/mm, mm, MPa and mm^4" Allowable deflection (unrounded),delta_allow,=C20/C12,mm,delta_allow = L/360 (L in mm) FINAL RESULT: Maximum bending moment,M,"=ROUND(C14,3)",kNm,Rounded to 3 decimal places for display FINAL RESULT: Bending stress,sigma,"=ROUND(C17,3)",MPa,Rounded to 3 decimal places for display FINAL RESULT: Maximum midspan deflection,delta,"=ROUND(C22,3)",mm,Rounded to 3 decimal places for display FINAL RESULT: Allowable deflection,delta_allow,"=ROUND(C23,3)",mm,Rounded to 3 decimal places for display CHECKS,,,, Check 1 - Bending stress demand,sigma,=C17,MPa,Demand = sigma (unrounded value used in check) Check 1 - Allowable bending stress limit,sigma_allow,=C11,MPa,Limit = 165 MPa as given by customer Check 1 - Utilization ratio,U_b,=C29/C30,ratio,U_b = sigma/sigma_allow Check 1 - Utilization as percentage,U_b%,"=ROUND(C31100,3)",%,U_b% = U_b100 (rounded to 3 decimal places) Check 1 - Status,,"=IF(C29<=C30,""PASS"",""FAIL"")",,PASS if sigma <= sigma_allow Check 2 - Deflection demand,delta,=C22,mm,Demand = delta (unrounded value used in check) Check 2 - Allowable deflection limit,delta_allow,=C23,mm,Limit = L/360 as given by customer Check 2 - Utilization ratio,U_d,=C34/C35,ratio,U_d = delta/delta_allow Check 2 - Utilization as percentage,U_d%,"=ROUND(C36100,3)",%,U_d% = U_d100 (rounded to 3 decimal places) Check 2 - Status,,"=IF(C34<=C35,""PASS"",""FAIL"")",,PASS if delta <= delta_allow ,,,, NOTES & ASSUMPTIONS,,,, "Unit conversion: 1 kNm = 1000000 N*mm (row 15); 1 m^3 = 1000000000 mm^3 (row 16); 1 GPa = 1000 MPa (row 18).",,,, "Unit conversion: 1 kN/m = 1 N/mm (row 19); 1 m = 1000 mm (row 20); 1 m^4 = 1000000000000 mm^4 (row 21); 1 MPa = 1 N/mm^2.",,,, "Constants: 8, 5 and 384 come from the customer-supplied formulas; 100 converts ratios to percentages. No other numbers are hard-coded.",,,, "Assumption: the beam is simply supported with the uniform load w acting over the full span. Maximum moment and maximum deflection occur at midspan.",,,, "Assumption: w is the service (unfactored) load as stated. The same w is used for both the stress check and the deflection check. Confirm this matches the basis of your 165 MPa allowable stress.",,,, "Confirm: whether w includes beam self-weight and any other dead loads. The sheet does not add self-weight.",,,, "Confirm: I and S are about the same bending axis and match your actual steel section. These values were not checked against any section table.",,,, "Information: the inputs imply a distance to the extreme fibre of c = I/S = 163.3 mm (about 327 mm overall depth if the section is symmetric). Confirm this matches your section.",,,, "Assumption: linear elastic behaviour and small deflections, as implied by the supplied formulas.",,,, "Sign convention: all values are positive magnitudes. Deflection is taken as positive downward. Bending stress is the extreme-fibre magnitude (tension or compression).",,,, "Rounding: final results (rows 24 to 27) and utilization percentages are rounded to 3 decimal places. All intermediate values and the PASS/FAIL comparisons use unrounded values.",,,, "Limits: the 165 MPa allowable stress and the L/360 deflection limit were supplied by the customer. This sheet does not verify them against any code or standard.",,,, "Not included (not part of the supplied method): shear, lateral-torsional buckling, local web or flange effects, bearing at supports, connections and vibration. A licensed engineer should confirm whether these apply.",,,, "A PASS only means the computed value is within the limit entered on this sheet. It does not mean the design is safe, adequate or code compliant.",,,, "Made by a Donkley AI worker. AI can make mistakes; please review before you rely on it.",,,,