BASIC ENGINEERING CALCULATIONS (ASD)

FLEXURE DESIGN

FLEXURE–the available flexural strength, Mn/Ω must be greater than Required Strength, Ma

Ma ≤ Mn/Ω

Ω = Safety Factor for given loading type (or limit state) --- Ωb = 1.67 for Bending

ELASTIC FLEXUREf = Mc/I = Mmax/S

Sreqd = Mmax/fMn = MCR = SXfy

PLASTIC FLEXUREf = M/A

Mn = Mp = ZXfy

SLENDERNESS PARAMETERSFLB, λ = bf/2tf (FLANGE LOCAL BUCKLING)WLB, λ = h/tw (WEB LOCAL BUCKLING)LTB, λ = Lb/ry (LATERAL-TORSIONAL BUCKLING)Ma = Beam Bending Moment (Maximum Service Load Moment)MCR = Elastic Moment (the second-highest nominal Flexural Strength – when λ = λR) = FCRS = 0.7FySx

Mn = Nominal Moment Capacity (Nominal Flexural Strength – Must be divided by Ω for ASD Capacity)MP = Plastic Moment (the highest possible nominal Flexural Strength – for braced & compact members) = FYZMy = Yield Momentλ = Width-Thickness Ratio (dividing line is λP --- if λ < λP, the section is compact and MP can be used)∆ = DeflectionL, l = SpanI = Moment of InertiaLb = Unbraced Length (Lb≤Lp for a properly braced member)SX = Elastic Section Modulus about the x-axis = I/c

Rectangle: S = bd2/6Solid Round: S = πd3/32Tube: S = [bodo

3-bIdI3]/6d

ZX = Plastic Section Modulus about the x-axis Rectangle: Z = bd2/4Solid Round: Z = d3/6Tube: Z = [do

3-dI3]/6

E = Modulus of Elasticity =29,000 ksi for common steelsFy = Yield Stress of Steel (36ksi for A36 Steels)FCR =- Elastic Critical Buckling Stress (determined by equations)IX = Moment of Inertia about x-axisCb = Lateral-Torsional Buckling Modification FactorLb = Unbraced LengthJ = Torsional Constant

COMMON ENGINEERING EQUATIONS

Plastic Moment Capacity, MP = FyZx, so Mp/Ω = FyZx/1.67 = 0.6FyZx

Elastic Moment Capacity, Mr = FySx, so Mr/Ω = FySx/1.67 = 0.6FySx

Shear Strength, Vn = 0.6FyAw so Vn/Ω = 0.6FyAw/1.50 = 0.4FyAw

SIMPLE BEAM, UNIFORM LOAD (FROM 13TH EDITION TABLE 3-23)

VMAX = wl/2 MMAX = wl2/2∆ = 5wl4/384EI

SIMPLE BEAM, CONCENTRATED LOAD AT CENTER (FROM 13TH EDITION TABLE 3-23)

VMAX = P/2 MMAX = Pl/4∆ = Pl3/48EI

SIMPLE BEAM, CONCENTRATED LOAD (FROM 13TH EDITION TABLE 3-23)

WELD STRENGTH

ALLOWABLE STRENGTH– for ASD, the allowable strength, Rn/Ω must be greater than the Required Strength, Ra

Ra≤ Rn/Ω

Ω = Safety Factor for given loading type (or limit state)

WELDSThe allowable strength of welds shall be the lower value of:

1) Base Material Strength (Rn = FBMABM)2) Weld Metal Strength (Rn = FWAW)

FW = Nominal Strength of the Weld Metal per Unit Area (ksi) = 0.60FEXX

FBM = Nominal Strength of the Base Metal per Unit Area (ksi) = 0.60Fu

AW = Effective Area of the Weld (in2)ABM = Effective Area of the Base Metal (in2)

FEXX = ultimate strength of welding electrode,(ksi) = Fu (weld metal)(cos 45°)(1/16”)Fu = ultimate strength of base metal

Using ASD Table J2.5 (16.1-99), for allowable strength of welds in shear (the most conservative case of all weld loading), FBM or FW = 0.60 FEXX

Rn/Ω = 0.60FEXX/2.00 = 0.30FEXX = 0.30 (FyEXX)(sin 45°)(1/16”) = (0.30)(70ksi)(0.707)(1/16”)Note: (sin 45°)(1/16”) = effective throat for 1/16” leg of weld = WORST CASE

Rn/Ω =0.928k/in of weld leg for longitudinally loaded fillet (worst case)

Rn/Ω =1.392k/in of weld leg for transversely loaded fillet(increased loading angle strength = 1+0.5sin 1.5 Ѳ) = 1.5 for Ѳ = 90°

BOLT STRENGTH

ALLOWABLE STRENGTH(ASD) - allowable strength, rn/Ω must be greater than the Required Strength, Ra

ra≤ rn/Ω

BOLTS IN SIMPLE BEARING CONNECTIONSThe allowable sheara strength, rn of BOLTS in simple bearing connections is as follows:

rn = FnvAb* (# of shear planes) with Ω = 2.00

Fnv = Nominal Shear strength of fastener (ASD Table J3.2) = 0.50Fu (threads excluded) = 0.40Fu (threads included)

Ab = Area of bolt (unthreaded body area only)

Fnv values for common bolts: Using ASD Table J3.2 (16.1-104),A325X bolts (threads excluded) = 60 ksiA325N bolts (threads included) = 48 ksiA307 bolts = 24 ksiA36 Threaded Rod = 14.4 ksi

So, for a ¾” A325 bolt in simple bearing, threads included,rn = FnvAb = (48 ksi) (π (.375”)2) = (48)(0.44178) = 21.21k

rn/Ω = 21.21/2 = 10.6k

rn/Ω =10.6k/BOLT (A325N)(SINGLE SHEAR)rn/Ω =13.3k/BOLT (A325X)(SINGLE SHEAR)rn/Ω =5.30k/BOLT (A307)(SINGLE SHEAR)

(SEE ASD TABLE 7-1)

for a ¾” A36 Threaded Rod in double shear, threads included,rn = FnvAb = 0.40FuAb = (0.4)(36 ksi) (π (.375”)2) = (14.4)(0.44178) = 6.36k

rn/Ω = 6.36/2 = 3.18k

rn/Ω =3.18k/A36 THREADED ROD (SINGLE SHEAR, THREADS INCLUDED)

BOLTS IN SLIP-CRITICAL CONNECTIONS

rn = µDnhscTbNs with Ω = 1.5 (designed at serviceability limit state) Ω = 1.76 (designed at required strength level)

rn/Ω =6.28k/BOLT (A325SC, CLASS A)(SINGLE SHEAR – SSH, SERVICIABILITY)rn/Ω =5.38/BOLT (A325SC, CLASS A)(SINGLE SHEAR – SSH, STRENGTH LIMIT)

(SEE ASD TABLE 7-3)

WEDGE ANCHOR DESIGN

AVAILABLE STRENGTH– for ASD, the available strength, Rn/Ω must be greater than the Required Strength, Ra

Ra≤ Rn/Ω

Ω = Safety Factor for given loading type (or limit state) = 4