STRUCTURES
GENERAL
Terms, concepts
structural elements
purlin: roof beam usu. @ truss panel joints to avoid bending stress in top
chord
pile cap: transfers column load to piles
forces
force couple = equal but opposite forces
double shear: 2 shear planes (places of poss. shear failure ) as in bolts
shear stress in column pad depends on load, column, size & thickness of pad
(not reinf. steel)
matenal properties
E = modulus of elasticity = stress/strain (Hooke's law)
E for steel = 29, 000, 000 psi
E for Doug fir = 1,600,000 psi
E for conc. = 57,000√f'c (-->ult. strength after 28 days)
for A36 steel, Fb = 24 ksi if compression flange laterally supported
fy = 40 ksi for grade 40 steel, 60 ksi for grade 60 steel
joist girder designation: 60G10N14.4K
60 in. deep, 10 eq. spaces along girder, 14.4 kip load @ ea. panel point
rules of thumb
structural costs about 25% of total constr. cost
truss depth to span ratio 1:10 best
slab on grade 3-1/2 to 9"
max slump
sidewalk conc.: 4"
min. conc. coverage
3" @ footings against earth
1-1/2" interior columns
3/4" @ interior slabs
Characteristics of different structural-systems
folded plate
inclined planes function as deep beams
pretensioning: steel tensioned before conc. cast
no end anchorages
consider shrinkage of conc. & creep of conc. & steel
continuous beams
less Mmax, deflection
Mmax greater in end spans than in middle
flat plate
use where loads relatively light
deflection high
flat slab
round column w/ capital, drop panel
formulas
stress = P/A (unit axial stress)
bending stress: f = M/S
strain = D/L
deformation under axial load
Δ=PL/AE
coefficient of linear expansion n (per 1 degree )
Δ = nL Δ t
Max moment
Mmax = w1**2/8 uniform load simple beam
Mmax = Pl/4 concentrated load at center
moment of inertia I (in**4)
I = bd**3/12 for rectangular section
neutral axis: y bar = ΣAy/ΣA
Ix-x = Σ (Io + Ayn**2)
section modulus
S = I/c (in**3) (c = dist. from outer fiber to neut. axis)
S = M/Fb (allowable bending stress)
Area of wood beam
A = 3V/2Fv (V = max shear; Fv = allowable shear)
Tu = Asfy ultimate tensile strength of rebar
Trig
sin 30 = .5
cos 30 = .866
tan 30 = .577
sin 45 = .707
cos 45 = .707
tan 45 = 1
sin 60 = .866
cos 60 = .5
tan 60 = 1.732
columns
round conc. columns reinforcement
spiral - stronger
ties
K factor in column design
accounts for diffs in column end conditions
Kx unbraced length = Kl (effective length)
steel columns
slenderness ratio = l/r (radius of gyration)
circle, tube - most efficient shapes - resist buckling; material far from axis
base plate
non-shrink grout (1")
Fp = 0.35 f'c
f'c = 3000 psi --> Fp = 1050 psi
A=P/Fp
Beams
Preliminary beam sizes
depth (in.) = 1/2 span (ft)
weight (lb/ft) = 1.25 W (kips)
delta = depth (in)/10
most efficient way to minimize deflection: increase depth ( -->I)
stiffness calcs to check for ponding - double deflections
short beams + long girders = less material but more depth
long beams + short girders = more material but less depth
plate girders
large load
large span ~ 100
depth 3 to 6'
web stiffeners
composite beams
large load, span
wide beam spacing
optional welded plate @ bottom
4 to 6" conc. deck
open-web steel joists
spans > 60' bolted bridging
LH for floors: 18-48" d, 96' 1
DLH for roofs: 52- 72" d, 144' 1
J series 36,000 psi yield strength
H series 50,000 psi yield strength chord sections
either hot-rolled or cold-rolled steel
underslung or pitched
designation: nominal depth @ center + size of top chord section (e.g., 40 LH
10)
often provided w/ top chord extended ends --> cantilever
other one-way flexural systems
channel slab
box girder
double T - most common
two-way flexural systems
1/12 - 1/20 span/depth --> shallower
connections
F - friction type
impact loading
N - bearing, threads included
steel binds w/bolt
X - bearing, no threads
bolts
A307 (120 ksi)
A325 (44 ksi) most common
welds
radiographic inspection (x-rays) used to test welds
strength of weld based on shear strength thru throat
fillet weld throat = .707(size)
Fsw = 0.40 Fy base material
Fsw = 0.30Fy weld material
avoid welding rebar
conc. systems
ultimate strength = 1.4 DL + 1.7 LL (factored loads)
balanced beam: designed for simultaneous failure of conc. and steel
under-reinforced is better - warning cracks
compression steel - can help reduce depth of conc. beam
in top portion of beam - tied w/ stirrups to lower reinf.
prestressed conc. advantages
fewer cracks
corrosive atmosphere
stiffer
smaller
kelly ball test - for workability of conc. - less common than slump test
Foundations
spread footing
wall, grade beam
combined
at property line
cantilever footing ( also strap footing) @ property line
mat/raft
good for differential settlement
moves up and down w/water table
pile footing/caissons
drilled pier - bell @ bottom for bearing
site constr .
excavation
footing 6" @ natural grade
6" below frost line
backfill
clean, low shrink/swell, compacted
std. proctor compaction test
95% bldg.
90% parking lots
History
Perret- first to use reinf. conc. frame in hi-rise
Kahn- struct. eng. on Hancock, Sears Tower
Jenney- first skyscraper - Home Insurance Co. 1883
Maillart - Swiss eng. - bridges
LATERAL
retaining walls
resultant should fall in middle third of base
usu. designed to resist 30 lb/cf pressure
counterfort wall: retaining wall w/ bracing walls
hydrostatic pressure 62.4 lb/cf - pools, tanks
seismic force
Richter scale - each no. is about 32 times previous no.
lateral force, or shear at base V
V = ZIKCSW or V = ZICW/R
Z = zone factor
zone 0, z = 0
zone 1, z = 3/16
zone 2, z = 3/8
zone 3, z = 3/4
zone 4, z = 1
I = importance 1-1.5
assembly of over 300 --> I = 1.25
essential facilities (hospitals, fire, police) --> I = 1.5
K = lateral resisting type
moment resisting frames
resists by bending
most ductile
steel or conc.
ductile moment resisting space frame
shear walls
allowable shear for diff mat'ls -- table 25K
stiffest
braced frames
seismic force is dependent on stiffness of structure
K value from table 23T
.67 --> 2.5
ductile --> less ductile
bldgs > l60'h in zone 3 or 4 must have DMRSF resist 25%
C = accel. = 1/15√T (period (sec.)) or C = 1.25S/T**2/3 (1991 UBC)
T = .05h/√D
h = ht. of structure (ft)
D = dimension parallel to applied forces (ft)
for DMRSF bldgs., T = .10ON
N = no. of stories
long period --> flexible, low force
short period --> stiff, high force
drift = 1/500 h
S = subsoil condition - betw. 1-1.5
max when Tbldg = Tsoil
firm soil --> higher force
CS < 0.14 per UBC
W = total dead load incl. partitions
storage & warehouse include 25% live load also
distribution of base shear
force applied to any level x
Fx = (V -Ft)wx*hx/Σwh
Ft = force at top = .07TV < .25V
diaphragms
rigid, semi-rigid - transfers loads in proportion to rigidity of verticals
flexible, semi-flexible
drag strut - collects seismic load from diaphragm
parts of bldg: Fp = Z*I*Cp*Wp; Cp from table 23J - horiz force factor
Wind pressure
p = Ce*Cq*qs*I - all from UBC
Ce = exposure (based on height) - Table 23G
Cq = pressure coefficient - Table 23H
method 1 (normal force method)
method 2 (projected area method)
qs = wind stagnation pressure @ ht. 30'
from basic wind speed - table 23F
I = importance
assemblies, I = 1.15
others, I = 1