ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2014 lecture twenty one concrete construction: http:// nisee.berkeley.edu/godden materials & beams Concrete Beams 1
Concrete Beam Design composite o concrete and steel American Concrete Institute (ACI) design or maximum stresses limit state design 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 Concrete Beams 2
Concrete Construction cast-in-place tilt-up prestressing post-tensioning Concrete Beams 3 http://nisee.berkeley.edu/godden
Concrete low strength to weight ratio relatively inexpensive Portland cement aggregate water hydration ire resistant creep & shrink Concrete Beams 4
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 (nominal) bottom top or compression reinorcement spliced, hooked, terminated... Concrete Beams 5
Behavior o Composite Members plane sections remain plane stress distribution changes E 1 1 1 Concrete Beams 6 E y E E 2 2 2 y
Transormation o Material n is the ratio o E s n E E 1 eectively widens a material to get same stress distribution 2 Concrete Beams 7
Stresses in Composite Section with a section transormed to one material, new I n E E 2 1 E E steel concrete stresses in that material are determined as usual stresses in the other material need to be adjusted by n c s I I My transormed Myn transormed Concrete Beams 8
Reinorced Concrete - stress/strain Concrete Beams 9
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 Concrete Beams 10
Location o n.a. ignore concrete below n.a. transorm steel same area moments, solve or x bx x 2 na s ( d x) 0 Concrete Beams 11
T sections n.a. equation is dierent i n.a. below lange h h b w b w b h x h 2 x h b w x h 2 na s ( d x) 0 Concrete Beams 12
ACI Load Combinations* 1.4D 1.2D + 1.6L + 0.5(L r or S or R) 1.2D + 1.6(L r or S or R) + (1.0L or 0.5W) 1.2D + 1.0W + 1.0L + 0.5(L r or S or R) 1.2D + 1.0E + 1.0L + 0.2S 0.9D + 1.0W 0.9D + 1.0E *can also use old ACI actors Concrete Beams 13
Reinorced Concrete Design stress distribution in bending h A s b d C x a= 1 x NA T 0.85 c a/2 T C actual stress Whitney stress block Wang & Salmon, Chapter 3 Concrete Beams 14
Force Equations C = 0.85 cba T = A s y where a= 1 x 0.85 c a/2 C c = concrete compressive strength T a = height o stress block 1 = actor based on c x = location to the n.a. b = width o stress block y = steel yield strength A s = area o steel reinorcement Concrete Beams 15
Equilibrium T = C M n = T(d-a/2) d = depth to the steel n.a. d a= 1 x 0.85 c a/2 C with A s a = A s y 0.85 b c T M u M n = 0.9 or lexure M n = T(d-a/2) = A s y (d-a/2) Concrete Beams 16
Over and Under-reinorcement over-reinorced steel won t yield under-reinorced steel will yield reinorcement ratio As ρ bd http://people.bath.ac.uk/abstji/concrete_video/virtual_lab.htm use as a design estimate to ind A s,b,d max is ound with steel 0.004 (not bal ) Concrete Beams 17
A s or a Given Section several methods guess a and iterate 1. guess a (less than n.a.) 2. A s. 0 85 y ba c 3. solve or a rom M u = A s y (d-a/2) a 2d M A s u y 4. repeat rom 2. until a rom 3. matches a in 2. Concrete Beams 18
A s or a Given Section (cont) chart method Wang & Salmon Fig. 3.8.1 R n vs. 1. calculate R n M bd n 2 2. ind curve or c and y to get 3. calculate A s and a simpliy by setting h = 1.1d Concrete Beams 19
Reinorcement min or crack control required not less than A s-max : typical cover 1.5 in, 3 in with soil bar spacing 3 c As ( bd) y 200 As ( bd ) y a 1 ( 0. 375d ) spacing cover Concrete Beams 20
Approximate Depths Concrete Beams 21