CHECK STRESS ON DECK BASED ON SDI REQUIREMENTS

Transcription

1 ANALYSIS OF NON-COMPOSITE CONCRETE SLAB ON METAL DECK Lab #7 Question #2 A 6" total depth lightweight concrete slab with compressive strength of 3000psi is placed simply supported on a galvanized steel 3C22 deck. Determine construction load stresses in the steel deck for a clear span of 6 feet. Does the deck meet the SDI criteria for construction loads? If the steel deck is not adequate, select an appropriate one. Based on the ACI strength criteria, select the required reinforcement to carry a service live load of 120 psf. Assume reinforcing mesh will be placed directly on top of the deck. Look at the "Maximum Construction Spans" Table for SDI criteria with D = 6" Construction Loads should meet allowables for a 6 simple span For a non-composite slab, the slab only needs to carry the superimposed live load CHECK STRESS ON DECK BASED ON SDI REQUIREMENTS Page 36 of manual Figure 1 1 span condition L:= 6 Define loads W1 = slab weight + deck weight W1 := 43 psf Chart on pg 30 W2 = 20 psf construction load W2 := 20 psf Sec 3.2a P1 = 150 lb concentrated load P1 := 150lb Sec 3.2a Allowable Stress on deck Pg 32, Section 3.2a Fy := 33 ksi pg 31 Fb allow := 0.6 Fy Fb allow = 19.8ksi or 36 ksi (whichever is less) Case 1 positive moment M1 := ( 0.25 P1 L) W1 L 2 12 M1 = lb*in S p := in^3 pg 31 Positive Moment Stress M1 fb 1 := fb S p = ksi fb 1 = ksi < Fb allow = 19.8ksi OK 1

2 Case 2 positive moment M2 := ( 1.5W1 + W2) L 2 12 M2 = 4563 lb*in S p = in^3 Positive Moment Stress M2 fb 2 := fb S p = ksi fb 2 = ksi < Fb allow = 19.8ksi OK Stresses on steel deck are ok CHECK DEFLECTION BASED ON SDI REQUIREMENTS Figure 2, pg 36 & Sec 3.2b pg 32 L = 6 Given Values E := psi I := in^4 pg 31 Allowable deflection of steel deck based on wet concrete and steel deck allow := min L12 180, 0.75 allow = 0.4 in W1 L 4 1 := = in EI 1 = in < allow = 0.4 OK CHECK FLEXURAL DESIGN OF SLAB BASED ON ACI 318 Known Values 3C22 Steel Deck h := 3 in Height of slab D:= 6 in thickness above deck t := D h t = 3 in Undraped WWF reinforcement distance from comp face to reinf. d1 := t d1 = 3 in compression top 2

3 Maximum Moments due to superimposed loads w := 120 psf Given in problem statement The value from the chart is a service live load - Must use load factors to determine maximum moment Load factor for live load ll := 1.7 Simple Span Positive Moment ll w L 2 Mu p := Mu 8 p = 918 lb- Find moment capacity of slab (per foot width) Flexure Positive Moment - Compression on Top, Tension on Bottom Known Values Area of steel (per foot) As := in^2 Pg 30 Yield of Steel fy := 60 ksi Conc comp. strength f c := 3 ksi width b := 12 in Sum of forces in horizontal direction = 0 C=T C = 0.85*f.c*a*b Find value of a T = As*fy As fy a1 := a1 = in compression zone in concrete 0.85 f c b Sum of moments = 0 Sum moments about C a1 Force T1 := As fy Distance z1 := d1 z1 = in 2 3

4 Nominal Positive Moment Capacity of Slab Mn1 := T1 z1 Mn1 = k-in Factored Nominal Capacity φ := 0.9 ACI 318 factor for flexure 1000 φmn1 := φ Mn1 φmn1 = lb 12 Compare Maximum Positive Moment and Factored Nominal Moment Mu p = 918 lb- < φmn1 = lb- OK #3) Design of Steel Joists Select a LH series joist for a 60 clear span roof. The joists are spaced 8 apart and must support a 50 psf live load plus a 15 psf superimposed dead load. To control ponding, the live load deflection is limited to L/250. Determine the required diagonal bridging size member and number of rows of bridging. Service Loads Tributary Area of joists trib := 8 Superimposed Dead Load DL := 15 psf dl := DL trib dl = 120 lbf Live Load LL := 50 psf ll := LL trib ll = 400 lbf Initially estimate weight of truss for calculations self := 10 lbf Total service load w total := dl + ll + self w total = 530 lbf Steel Joists Guide From economical joist guide in vulcra catalog, numbers in red print for live load values will limit deflections to L/360. If some different limit is sought, multiply figures in red by ratio of old limit to new limit table := 360 given := 250 table ratio := ratio = 1.44 given 4

5 From page 107, Length = 60 + (12in) = 61 Choose a section w total 530 lbf ll = w live := w ratio live = lbf Try 44LH13 self := 25 lbf from charts w tot.allow := 579 lbf w live.allow := 405 lbf Total load on truss w tot := dl + ll + self w tot = 545 lbf < w tot.allow = 579 lbf OK Live Load Check Factor up the allowable live load from chart by ratio calculated previously ll = 400 lbf < ratio w live.allow = lbf OK Use 44LH13 Section Select Bridging D:= 44 in Value in chart is highlighted in blue = use diagonal bridging for joists For LH series use charts on pg 43 for bracing requirements Use chart titled "Maximum joist spacing for diagonal bracing" because our span is over 60 The spacing of our trusses is 8'-0" with a joist depth of 44" Select from chart 1 1/2" x 7/64" angle - this is good for a spacing of 9'-3" ( we are less than this so OK) Use chart for maximum spacing of lines of bridging ( pg 43) For section #13 - max spacing is 16'-0" If 3 rows of bridging ( 4 spaces) 60 4 = 15 < 16 OK Solution: 44LH13 with 3 rows of bridging spaced at 15' bridging is 1 1/2" x 1 1/2" x 7/64" angle 5