Lecture Example. Steel Deck (info from Vulcraft Steel Roof and Floor Deck Manual)

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Rhoda Stewart
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1 1 / 8 Geometry beam span L 40 ft Steel Wide Flange Beam: beam spacing s beam 10 ft F y 50 ksi construction live load LL construc 20 psf row 148 live load LL 150 psf unit weight of concrete UW conc 145 pcf concrete compressive strength f' c 3 ksi Steel Deck (info from Vulcraft Steel Roof and Floor Deck Manual) length of deck sheet L sheet 40 ft weight of slab wt slab 44 psf number of spans for deck N spans 4.0 = L sheet / s beam weight of deck wt deck 2.82 psf Deck 1.5VLR18 SDI max. unshored clear span max_span 10.1 ft >= s beam TRUE width of rib at top w top 4.25 in max. LL max_ll 164 psf >= LL TRUE width of rib at bottom w bot 3.5 in total slab depth h slab 4 in width of stiffening "bump" w bump 0 in rib depth h ribs 1.5 in rib spacing s rib 6 in slab thickness t slab 2.5 in = h slab - h ribs Design Summary After Composite Action Meets Design Criteria checked TRUE stud_position = middle of rib in these calculations stud_position_rating = weak N studs = 40 0 Before Composite Action % composite = 90% M u <= M n TRUE 195 k-ft 611 k-ft M u <= M n TRUE 611 k-ft 897 k-ft V u <= V n TRUE 19.5 k 232 k V u <= V n TRUE 61.1 k 232 k 0.8 factor accounts for partial DL = 0.65 in = 0.8 * D LL <= LL_max TRUE rotational restraint at beam ends 1.29 in 1.33 in

2 2 / 8 Before Composite Action: Wide Flange Properties: factored uniform distributed load u 973 plf beam 76 plf = 1.2 * ( ( wt slab + wt deck ) * s beam + beam ) * LL construc * s beam A 22.3 in 2 d 18.2 in moment due to factored loads M u 195 k-ft = u /1000 * L^2 / 8 b f 11 in shear due to factored loads V u 19.5 k-ft = u /1000 * L / 2 t f 0.68 in t w in available flexure strength M p 611 k-ft = 0.9 * F y * Z x /12 h w in = d - 2 * t f available shear strength V n 232 k see Appendix 1 t f 0.68 in I x 1330 in 4 Available Shear Strength from Studs, V' avail strength of stud F u_stud 65 ksi maximum stud diameter stud_max 0.75 in with formed steel deck AISC I8.2c(1)(2), pg stud diameter stud 0.75 in cross-sectional area of stud A sa in 2 = PI() * stud^2 / 4 Z x 163 in 3 coefficient to account for group effe R g 1 for one stud welded in a steel deck rib with deck oriented perp. to beam AISC I8.2a, pg Default: stud_position middle of rib AISC pg e mid_ht_center 1.56 in = 1/2 * (w top + w bot ) / 2 - w bump /2 - stud / 2 - IF( w bump > 0, stud /2, 0 ) rating weak = IF( e mid_ht_center < 2, "weak", "strong" ) specified stud position Specified: stud_position middle of rib rating weak coefficient to account for position R p 0.60 = IF( stud_position = "weak", 0.6, IF( stud_position = "strong", 0.75, NA() ) ) Q n_max 17.2 k = R g * R p * A sa * F u_stud modulus of elasticity of conc. E c 3024 ksi = UW conc^1.5 * SQRT( f' c ) Q n 21.0 k = 0.5 * A sa * SQRT( f' c * E c ) shear strength of one stud Q n 17.2 k = MIN( Q n_max, Q n )

3 3 / 8 Available Shear Strength from Studs, V' avail -cont'd N studs along beam N studs_avail 40 = ROUNDDOWN( L / 2 / ( s rib /12 ), 0 ) between M = 0 and Mmax req'd stud shear strength V' req'd_full 765 k = MIN( C slab, T beam ) see values below for full composite action N studs_full 45 = ROUNDUP( V' req'd_full / Q n, 0 ) specified num. studs N studs 40 = MIN( N studs_avail, N studs_full ) available shear strength along bea V' studs 689 k = Q n * N studs_avail between M = 0 and Mmax % composite 90% = V' studs / V' req'd_full After Composite Action: u 3053 plf = 1.2 * ( ( wt slab + wt deck ) * s beam + beam ) * LL * s beam M u 611 k-ft = u /1000 * L^2 / 8 V u 61.1 k-ft = u /1000 * L / 2 effective flange width b eff 120 in = MIN( L / 4, s beam ) * 12 AISC I3.1a, pg 88 Limiting horizontal force on beam Limiting Horizontal Force, F LIMIT between M = 0 and Mmax max poss. Comp. force in slab C slab_max 765 k = 0.85 * f' c * t slab * b eff max poss. Tension force in beam T beam_max 1115 k = F y * A V' studs 689 k = V' studs limiting horizontal force F LIMIT 689 = MIN( C slab_max, T beam_max, V' studs ) NA in top flang (see Appendix 2) M n 997 k-ft M n 897 k-ft = 0.9 * M n V n 232 k ( shear strength of beam only)

4 4 / 8 Deflection dead loads D klf = ( ( wt slab + wt deck ) * s beam + beam ) / 1000 deflection due to dead loads D 0.81 in = 5 / 384 * L /12 * ( L *12 )^4 / ( * I x ) moment of inertia I comp 3175 in 4 (see Appendix 3) of composite section I x 1330 in 4 C s 765 k = MIN( C slab_max, T beam_max ) V' studs 689 k I eqiuv 3081 in 4 = I x + SQRT( MIN( 1, V' studs / C s ) ) * ( I comp - I x ) AISC Eqn. C-I3-4, pg I eff 2311 in 4 = 0.75 * I eqiuv AISC C I3.2, pg service live load L 1.50 klf = LL/1000 * s beam deflection due to live load L 1.29 in = 5 / 384 * L /12 * ( L *12 )^4 / ( * I eff ) limiting live load deflection L/ in = L *12 / 360

5 5 / 8

6 6 / 8 Appendix 1: Available Shear Strength, Vn F y 50 ksi t w in E 29,000 ksi h/t w 37.8 d 18.2 in k v 5 =IF(h/t w <260,5,NA()) TP =2.24*SQRT(E/F y ) TP =1.1*SQRT(k v *E/F y ) TP =1.37*SQRT(k v *E/F y ) IF Then C v = And v = h/t w <= TP1 TRUE TP1 < h/t w <= TP2 FALSE TP2 < h/t w <= TP3 FALSE =1.1*SQRT(k v *E/F y )/h/t w 0.90 TP3 < h/t w FALSE =1.51*E*k v /((h/t w )^2*F y ) 0.90 C v v 1.00 V n k =0.6*F y *d*t w *C v v V n k = v *V n Appendix 2: Plastic Moment, Mn all of beam is in tension NA is in slab FALSE = IF( F LIMIT = T beam, TRUE, FALSE ) a 3.64 in = T beam / ( 0.85 * f' c * b eff ) M k-ft = T beam * ( d / 2 + h slab - a / 2 ) /12 only part of beam is in tension ELSE area of one flange A F 7.48 in 2 area of web A W 7.16 in 2

7 7 / 8 Appendix 2: Plastic Moment, Mn -cont'd if NA is in the top flange NA in top flange TRUE = IF( AND( NOT( NA is in slab ), F LIMIT > F y * A W ), TRUE, FALSE ) depth of top flange in comp. h C 0.38 in = ( t f - ( F LIMIT / F y - ( A F + A W ) ) / b f ) / 2 comp. force in top flange C TF 208 k = F y * h C * b f b eff tension force in top flange T TF 166 k = F y * ( t f - h C ) * b f tension force in web T W 358 k = F y * A W tension force in bot. flange T BF 374 k = F y * A F F beam 689 k = T BF + T W + T TF - C TF h slab d t f t w h c t slab t rib NA depth of comp. zone in slab a 2.25 in = F beam / ( 0.85 * f' c * b eff ) mom. Arm for top flange comp. d C_TF 3.06 in = h C / 2 + h slab - a / 2 mom. Arm for top flange ten. d T_TF 3.40 in = ( t f - h C ) /2 + h C + h slab - a / 2 mom. Arm for web d W 12.0 in =h w /2 + t f + h slab - a/2 moment arm for bot. flange d BF 20.7 in = t f / 2 + h w + t f + h slab - a/2 M k-ft = ( T BF * d BF + T W * d W + T TF * d T_TF - C TF * d C_TF ) /12 b f NA is in web FALSE = AND( NOT( NA is in slab ), NOT( NA in top flange ) ) depth of web in compression h C in = ( h w - ( F LIMIT / ( F y * t w ) ) ) / 2 C TF 374 k = F y * A F C W -166 k = F y * h C * t w T W 524 k = F y * ( h w - h C ) * t w T BF 374 k = F y * A F F beam 689 = T BF + T W - C W - C TF a 2.25 in = F beam / ( 0.85 * f' c * b eff ) d TF 3.21 in = t f / 2 + h slab - a / 2 d C_W in = h C / 2 + t f + h slab - a / 2 d T_W 8.1 in = ( h w - h C ) / 2 + h C + t f + h slab - a / 2 d BF 20.7 in = t f / 2 + h w + t f + h slab - a / 2 M k-ft = ( C TF * d TF + C W * d C_W + T W * d T_W + T BF * d BF ) / 12 M n 997 k-ft = IF( NA is in slab, M 1, IF( NA in top flange, M 2, IF( NA is in web, M 3, NA() ) ) )

8 8 / 8 Appendix 3. Transformed Section b eff / n d slab y slab y comp y beam modular ratio n 9.59 = / E c Reference Axis slab beam Total area of section A 31 in 2 = b eff / n * t slab A 22.3 in 2 A 54 in 2 distance from bottom of beam y in = d + h slab - t slab /2 y 9.1 in y in to centroid of section centroid of compos. Section y comp 16.0 in = Ay / A Ay in 3 = A * y Ay in 3 Ay 858 in 3 mom. Inertia about own centroid I' 16.3 in 4 = 1/12 * b eff / n * t slab^3 I' 1330 in 4 distance from section centroid d 4.93 in = y - y bar d 6.92 in to composite centroid I' + A d in 4 I' + A d in 4 I' + A d in 4

AISC LRFD Beam Design in the RAM Structural System

AISC LRFD Beam Design in the RAM Structural System Model: Verification11_3 Typical Floor Beam #10 W21x44 (10,3,10) AISC 360-05 LRFD Beam Design in the RAM Structural System Floor Loads: Slab Self-weight: Concrete above flute + concrete in flute + metal