Walls Flashcards
ductility formula
ultimate / yield
lp
equivalent length of plastic hinge
- lower bound approximation: lp = h/2
yield strain
= fy / Es
yield curvature
= 2 ey / lw
- function of the yield strain of the steel
- not a function of section geometry
- nothing to do with strength
estimate of wall neutral axis
k = 0.25 c = klw = lw / 4
Determining structural ductility factor
- longest wall yields and reaches max ductility first
- max drift targeting is limited by ductility of longest wall
- ductility demand on other walls decreases as length of wall decreases
- structural response determined by summing wall responses
benefit of lower stiffness
smaller loads
benefit of bigger stiffness
smaller drifts
columns of different height
- same hc = same yield curvature
- taller column = larger yield displacement
- shortest column = highest local ductility demand
- shortest column sets structural ductility factor
columns of different depths
- smaller columns = higher yield curvature and therefore displacement
- column with largest depth = greatest local ductility demand
- deepest column sets structural ductility factor
estimation of effective flange width
- width of wall flanges in tension or compression is reduced because of the effects of shear lag
- based on the number of rebars put into strain
- moment applied - web in shear - transferred into C/T in flanges
- as moment increases and so too the associated tension in the flange, the section of flange resisting increases
- for nominal bending tension flange: hw + bw (26.6 degrees or 1:2)
- reduced width in compression flange after loaded in tension - less contact further away from web
- can’t close cracks unless very high axial load
- compression: 0.3hw + bw
- for overstrength this is conservative, so consider 45 degrees for tension
coupling effect
typically provides 40-60% of overturning capacity
two types of coupling beams
- conventionally reinforced
- diagonally reinforced cage
advantage of diagonally reinforced cage
concrete not needed outside of diagonals -
can put service ducts there
basketing
to keep wedges of concrete formed in diagonal cage from falling out
simplifying assumption for wall design
- assume all steel yielding in tension or compression
- percentage difference less than 1%
ultimate curvature
0.003 / c
flexural overstrength factor
= Mo / Me
maximum credible earthquake
- structures are designed for the DBE but should be capable of resisting a larger earthquake
- NZ standards may design a maximum credible earthquake (MCE) in the future
- for now MCE taken as 2.0 x ULS actions
- not OK to fail after ULS
Comments on Singly Reinforced Walls
- should be avoided
- 150mm thick walls are TOO THIN
- cant get reinforcement in
- anti-buckling reinforcement should also be provided over central region for yielding walls
Thin walls with Drossbach
- need to have transfer stirrups like columns
- properly detailed end of wall that look like mini-columns
- anchor floor starters and other embedments properly
- anchor horizontal bars in boundary elements
Comments on Precast Panel Slices
- walls roughened to min of 5 mm to prevent slipping/sliding
- failure of lap splices observed where drossbach ducts were not confined
- drossbach ducts cause stress concentrations at panel joints
- Drossbach ducts should be fully confined by stirrups
- clamp bars to drossbach and ensure bond maintained
- panel splices must allow for de-bonding of reinforcement
Comments on concrete strength
- higher than in lab testing
- code equations based on lab testing (different behaviour to concrete in buildings)
- min. reinforcement requirements may be insufficient
- min steel is to ensure fan cracking: bar yields and elongates
- if real life concrete»_space;> stronger than lab testing : no fan cracking
- case studies showed failure of bars in walls and inelastic capacity of bars exhausted
order of most likely strained elements
- walls
- beams
- columns
Comments on distribution of reinforcement
- large cracks where insufficient reinforcing to form fan crack pattern
- results in high strain demands on reinforcing
- walls with even distribution of steel develop extremely high strain demands on the bars at the extreme fibres
- can lead to significant strain hardening or fracture of the bars under ‘elastic’ loads
RECOMMEND: - lump reinforcing steel at the ends of the walls and distribute minimum steel through the central portion
effect of neutral axis on ductility
longer neutral axis = significantly less ductility
reason for boundary elements
- ductile walls tend to buckle
- boundary elements (flanges) provide adequate flexural rigidity at end of wall section
lapping in PPHZ
must stagger laps
- ensure fan cracking still occurs and not horizontal crack at lap
- no more than 1/3 steel lapped at same levels
effect of size of penetrations in wall
- smaller penetration = greater shear capacity between walls
- therefore larger tension/compression forces in wall
- therefore higher overturning capacity
three failure modes for walls
flexure, shear, sliding
- avoid sliding by roughening cold joints to 5 mm
- likely combined flexural shear failure
Effect of penetration size on coupled walls
- larger penetrations means less depth in coupling beam and therefore reduced shear capacity
- less load transferred into axial loads in walls
- reduces coupling effect
- also need to be careful of zipper effect
Diagonally reinforced cages
- cages designed as mini-columns, with 6db stirrups
- need to extend 1.5 Ld into wall to anchor
- basketing extending 100-150 mm into walls to prevent diagonal wedges of concrete falling out
- advantage of services placement
Boundary Elements
- ends of walls: 0.15 lw
- designed like columns
- more steel required in BE (0.5 sqrt(f’c) / fy ) than in middle of wall (0.25 sqrt(f’c) / fy )
- more steel in BE to ensure multiple cracks form
- cracking steel runs full height of wall to prevent big horizontal crack forming at top and allow for higher modes
- can use enlarged boundary elements (flanges) to provide flexural rigidity to ductile walls
- steel lumped in ends of walls
- lapping staggered
Shear Requirements
- horizontal rebar fully anchored at ends of walls
- vertical spacing <= lw/5, 3t, or 450 mm
- horizontal spacing <= lw/3, 3t or 450 mm
- limit nominal shear stress to prevent diagonal compression failure in potential plastic hinge region
<= (0.2f’c or 8MPa)
Antibuckling
- common issue observed in Canterbury earthquakes was localised failure of reinforcing bars
- need cross ties to hold stirrups and rebars in to prevent buckling, cover spalling and contain concrete core
double the strength halve the ductility - fallacy
- traditional view based on force-based approach which uses equal displacement rule
- suggests that by doubling the strength through using more rebars, the ductility would half
- in reality, changing the number of bars has no impact on the yield displacement
- the stiffness of the section increases, but the ductility remains the same
- only things that affect ductility: yield strain of steel and length of wall
