ten reinforced concrete construction Concrete Concrete Materials Concrete Construction columns beams slabs domes footings

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1 APPLIED ACHITECTURAL STRUCTURES: STRUCTURAL ANALYSIS AND SYSTEMS DR. ANNE NICHOLS SPRING 018 lecture ten Concrete columns beams slabs domes ootings reinorced concrete construction Reinorced Concrete Construction 1 Applied Architectural Structures F01abn Reinorced Concrete Construction F009abn Concrete Construction cast-in-place tilt-up prestressing post-tensioning Concrete Materials low strength to weight ratio relatively inexpensive Portland cement aggregate water Reinorced Concrete Construction 3 F009abn Reinorced Concrete Construction 4 1

2 Concrete Materials reinorcement deormed bars prestressing strand stirrups development length anchorage splices Concrete Materials ire resistance most ire-resistive structural material low rate o penetration retains strength i exposure not too long stable to F internally loses 50% ater that no toxic umes cover necessary to protect steel Reinorced Concrete Construction 5 F009abn Reinorced Concrete Construction 6 Concrete Beams types reinorced precast prestressed shapes rectangular, I T, double T s, bulb T s box spandrel Concrete Beams deormation camber (elastic) hogging sagging shrinkage strain x 10-6 about -3 years creep strain ~3 times elastic strain about -3 years Reinorced Concrete Construction 7 Reinorced Concrete Construction 8

3 Concrete Beams shear vertical horizontal combination: tensile stresses at 45 bearing crushing Copyright Kirk Martini Concrete Beam Design composite o concrete and steel American Concrete Institute (ACI) design or ailure strength design (LRFD) service loads x load actors concrete holds no tension ailure criteria is yield o reinorcement ailure capacity x reduction actor actored loads < reduced capacity concrete strength = c Reinorced Concrete Construction 9 F009abn Reinorced Concrete Construction 10 Behavior o Composite Members plane sections remain plane stress distribution changes Transormation o Material n is the ratio o E s E n E1 eectively widens a material to get same stress distribution Ey R Ey R 1 1 E1 E Reinorced Concrete Construction 11 Reinorced Concrete Construction 1 3

4 Stresses in Composite Section with a section transormed to one material, new I stresses in that material are determined as usual stresses in the other material need to be adjusted by n n c s E E 1 I I E E steel concrete My transormed Myn transormed Reinorced Concrete - stress/strain Reinorced Concrete Construction 13 Reinorced Concrete Construction 14 Reinorced Concrete Analysis or stress calculations steel is transormed to concrete concrete is in compression above n.a. and represented by an equivalent stress block concrete takes no tension steel takes tension orce ductile ailure Reinorced Concrete Construction 15 Location o n.a. ignore concrete below n.a. transorm steel same area moments, solve or x Reinorced Concrete Construction 16 x bx nas ( d x) 0 4

5 T sections n.a. equation is dierent i n.a. below lange h x h b h x x h ( ) 0 bw nas d x Reinorced Concrete Construction 17 b w h Applied Architectural Structures b w h ACI Load Combinations* 1.4D 1.D + 1.6L + 0.5(L r or S or R) 1.D + 1.6(L r or S or R) + (1.0L or 0.5W) 1.D + 1.0W + 1.0L + 0.5(L r or S or R) 1.D + 1.0E + 1.0L + 0.S 0.9D + 1.0W 0.9D + 1.0E Reinorced Concrete Construction 18 Applied Architectural Structures *can also use old ACI actors F01abn Reinorcement deormed steel bars (rebar) Grade 40, F y = 40 ksi Grade 60, F y = 60 ksi - most common Grade 75, F y = 75 ksi US customary in # o 1/8 longitudinally placed bottom top or compression reinorcement spliced, hooked, terminated... Reinorced Concrete Construction 19 Applied Architectural Structures Reinorced Concrete Design stress distribution in bending h A s b d Wang & Salmon, Chapter 3 Reinorced Concrete Construction 0 x C a= NA 1 c T actual stress 0.85 c a/ C T Whitney stress block 5

6 Force Equations C = 0.85 c ba T = A s y where c = concrete compressive strength a = height o stress block 1 = actor based on c c = location to the n.a. b = width o stress block y = steel yield strength A s = area o steel reinorcement Reinorced Concrete Construction 1 a= 1 c 0.85 c a/ T C c (0.05) Equilibrium T = C M n = T(d-a/) d = depth to the steel n.a. with A s a = A s y 0.85 c b M u M n = 0.9 or lexure* M n = T(d-a/) = A s y (d-a/) Reinorced Concrete Construction d a= 1 c 0.85 c a/ 0.5 * 0.65 ( t y) 0.65 (0.005 ) T y F008abn C Over and Under-reinorcement over-reinorced steel won t yield under-reinorced steel will yield reinorcement ratio A s bd use as a design estimate to ind A s, b, d max is ound with steel (not bal ) *with steel 0.005, = 0.9 Reinorced Concrete Construction 3 A s or a given Section several methods guess a and iterate 1. guess a (less than n.a.).. cba As 0 85 y 3. solve or a rom M u As M u a d As y 4. repeat rom. until a rom 3. matches a in. Reinorced Concrete Construction 4 y h A s b d a d 0.85 c a/ a C A s y 6

7 A s For Given Section (cont) chart method Wang & Salmon Fig R n vs. 1. calculate M bd. ind curve or c and y to get 3. calculate A s and a simpliy by setting h = 1.1d R n n Shear in Concrete Beams lexure combines with shear to orm diagonal cracks horizontal reinorcement doesn t help stirrups = vertical reinorcement Reinorced Concrete Construction 5 Reinorced Concrete Construction 6 ACI Shear Values V u is at distance d rom ace o support shear capacity: where b w means thickness o web at n.a. shear stress (beams) = 0.75 or shear c c c is in psi Vc c bwd λ or lightweight materials shear strength: V s is strength rom stirrup reinorcement Stirrup Reinorcement shear capacity: Av ytd Vs 8 c bwd s A v = area in all legs o stirrups s = spacing o stirrup may need stirrups when concrete has enough strength! Reinorced Concrete Construction 7 Reinorced Concrete Construction 8 7

8 Required Stirrup Reinorcement spacing limits Concrete Delections elastic range I transormed E c (with c in psi) normal weight concrete (~ 145 lb/t 3 ) E 57, 000 c c concrete between 90 and 155 lb/t 3 Ec w 1.5 c 33 cracked I cracked E adjusted c Reinorced Concrete Construction 9 Applied Architectural Structures F01abn Reinorced Concrete Construction 30 Delection Limits relate to whether or not beam supports or is attached to a damageable nonstructural element need to check service live load and long term delection against these Prestressed Concrete impose a longitudinal orce on a member in order to withstand more loading until the member reaches a tensile limit L/180 L/40 L/360 L/480 roo systems (typical) live loor systems (typical) live + long term supporting plaster live supporting masonry live + long term Reinorced Concrete Construction 31 Reinorced Concrete Construction 3 8

9 Prestressed Concrete pretensioned reinorcement bonded post-tensioned bonded or unbonded end bearing Prestressed Concrete high strength tendons grade 50 grade 70 precast concrete premade in a position other than its inal position in the structure Reinorced Concrete Construction 33 Reinorced Concrete Construction 34 Prestressed Concrete axial prestress (e=0) Prestressed Concrete axial prestress (e0) M(w) M(w) P A I t Mc t g P Mc b b A I g t - top b - bottom c - distance to iber I g - gross cross section inertia P Pec Mc P ec Mc t Ig P ecb Mc 1 A r I t t t t 1 A Ig Ig A r P Pec Mc b b b A Ig Ig g b ( remember r I ) A Reinorced Concrete Construction 35 Reinorced Concrete Construction 36 9

10 Prestressed Concrete Prestressed Concrete E F G r 7. 5 c D C Design load (DL+LL) (w i ) 0 B Sel weight A - areas o design importance Reinorced Concrete Construction 37 Reinorced Concrete Construction 38 Composite Beams concrete in compression steel in tension shear studs Continuous Beams reduced size reduced moments moments can reverse with loading patterns need top & bottom reinorcement sensitive to settlement Reinorced Concrete Construction 39 Reinorced Concrete Construction 40 10

11 Approximate Depths Concrete Columns columns require ties or spiral reinorcement to conine concrete (#3 bars minimum) minimum amount o longitudinal steel (4 bars minimum) Reinorced Concrete Construction 41 Reinorced Concrete Construction 4 Concrete Columns eective length in monolithic casts must be ound with respect to stiness o joint not slender when Concrete Columns *not braced Reinorced Concrete Construction 43 Reinorced Concrete Construction 44 11

12 Concrete Columns P o no bending P c = 0.65 or ties with P n = 0.8P o c = 0.70 or spirals with P n = 0.85P o P u c P n nominal axial capacity: o presumes steel yields concrete at ultimate stress 0.85 ( A A ) c g st y A st Columns with Bending eccentric loads can cause moments moments can change shape and induce more delection (P-) P Reinorced Concrete Construction 45 Reinorced Concrete Construction 46 Columns with Bending or ultimate strength behavior, ultimate strains can t be exceeded concrete y steel E P reduces with M s Columns with Bending need to consider combined stresses Pn P o M M 1 plot interaction diagram n o Reinorced Concrete Construction 47 Reinorced Concrete Construction 48 1

13 Concrete Floor Systems types & spanning direction Concrete Floor Systems Reinorced Concrete Construction 49 Reinorced Concrete Construction 50 Concrete Floor Systems one-way and two-way moments lexure design as T-beams (+/- M) increase o 10% V c permitted slabs need steel eective width is smallest o L/4 b w + 16t center-to-center o beams One-way Joists standard stems.5 to 4.5 slab ~30 widths reusable orms Reinorced Concrete Construction 51 Reinorced Concrete Construction 5 13

14 One-way Two-way Joists Joists wide pans domed pans 5, 6 up 3, 4 & 5 light loads & long spans one-leg stirrups Reinorced Concrete Construction 53 Reinorced Concrete Construction 54 Construction Supervision proper placement o all reinorcement welding splices mix design slump in-situ strength cast cylinders cylinder cores i needed Reinorced Concrete Construction 55 14

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