SEC Flashcards
FRICTION f
mu N
IMPENDING MOTION tan theta
f/N or mu
PARABOLIC CABLES highest point
lowest point
max tension
min tension
PARABOLIC CABLES s
integral from leftmost to rightmost of lowest point
SQRT (1+(Wx/To)^2) dx
CENTROIDS Icg
summ Ix + summ Ad^2
CENTROIDS Ix or Iy
Icgx + Aybar^2
or
Icgy + Axbar^2
Icg triangle
bh^3 / 36
Icg circle
D^4*pi/64
Icg trapezoid
h(2a+b) / (3*(a+b))
STRESS
P/A
DEFORMATION triangle
Afd/AE
STRAIN epsilon
deformation / original dimension
MODULUS OF ELASTICITY E
stress / strain
GAMMA STEEL
77kN/m^3
SHEAR STRESS fv
V/nAparallel
BEARING STRESS fp
P/Aperpendicular
TORSIONAL SHEAR STRESS tau
Tp/J
DEFORMATION theta
TL/JG
J FOR SOLID CIRCLES
D^4pi / 32
J FOR HOLLOW CIRCLES
pi(Do^2 - Di^2) /32
FLEXURAL/BENDING STRESS fb
Mc/I
SHEAR STRESS IN BEAMS fv
VQ/Ib
MAX SHEAR STRESS IN TRIANGLES AND RECTANGLES
3V/2A
MAX SHEAR STRESS IN CIRCLES
4V/3A
MOVING LOADS
Centerline of Resultant and largest at centerline of beam
Resultant is sandwiched by the 2 largest point loads
INFLUENCE LINE OF REACTIONS
1 at chosen reax 0 at other
INFLUENCE LINE OF SHEAR AT MIDSPAN
-a/L b/L at midspan
INFLUENCE LINE OF BENDING AT MIDSPAN
ab/L
RADIUS OF CURVATURE p
EI/M
M constant through the length
MAX DEFORMATION for SS full UDL
5wL^4/384EI @midspan
MAX DEFORMATION for Fixed-Fixed full UDL
wL^4/384EI @midspan
MAX DEFORMATION for SS point load at midspan
PL^3/48EI
3 MOMENT EQUATION
MAL1 + 2MB(L1+L2) + MCL2 + [(summ(Pa / L1) * (L1^2 - a^2)] + [(summ(Pb / L2) * (L2^2 - b^2)] = 6EI (h1/L1 + h2/L2)
DOUBLE INTEGRATION METHOD
UDL touches cut
Cut at near supps
SLOPE DEFLECTION METHOD
Mab=FEMab (fixed-fixed)
FEM= Pnf^2/L^2
VIRTUAL WORK METHOD
Forces due to actual, forces due to virtual
L F U AR FUL/AR
RCD Tension T
Asfy steel yielding
Asfs SNY
RCD C
0.85f’c Acompression
RCD MnSRB
phy [T(d-a/2)] or phy [C(d-a/2)]
*Take moment about T or C
RCD MnDRB
C1(d-a/2) + C2(d-d’)
*Take moment about T
YIELD STRESS TENSION STEEL fs
600*(d-c)/c
YIELD STRESS COMPRESSION STEEL
600*(c-d’)/c
fs:phy range
400:0.65 to 1000:0.9
RHO p
As/bd
RHO MAX pmax
least of 0.025
and
0.85f’cB1*3/7fy
C-C between rebars vertical
C-C between rebars horizontal
least 25mm or db
least 25mm or db or 4/3 dagg
TBEAMS beff
least of c-c spacing of beams
bw+16t
bw+ L/4
T < Cflange
T > Cflange
doesnt need help
needs help
RUPTURE MODULUS fr
0.62lambdaSQRT(f’c)
and
Mcrctens/Igross
As’ converted to concrete
As converted to concrete
(2n-1)As’
nAs
Ix OF RECTANGLE ABOUT ITS BASE
bh^3/3
Econcrete
4700*SQRT(f’c)
NOMINAL SHEAR CAP Vn
Vc+Vs
NOMINAL CONCRETE SHEAR CAP
0.17lambda*SQRT(f’c)bwd
RCD ULTIMATE SHEAR FORCE Vu
0.75Vn
SPACING IN BEAMS s
Avdfyh/Vs
Vu < 0.5phyVc
No shear reinforcement required
0.5phyVc < Vu < phyVc
minimum reinforcement
least of
0.062bws*SQRT(f’c)/fyh and
0.35bws/fyh
phyVc <Vu
design spacing
if Vs<2Vc, least of 600mm and d/2
if Vs>2Vc, least of 300mm and d/4
Vs cannot ____ 4Vc
exceed, else use 4Vc in design
hmin SS
l/20
hmin 1end cont
l/24
hmin both end cont
l/28
hmin cantilever
l/10
SLAB THICKNESS h
hmin(1.65-0.003wc)[0.4+(fy/700)]
SLAB MINIMUM AREA Asmin
for fy>=420, 0.002Ag
for fy<420, least of
0.0014Ag
0.0018Ag*420/fy
SLAB NUMBER OF BARS n
As/Ab
SLAB SPACING s
least of
b/n usually 1000/n
3h or 5h(forT&S)
450mm
EFFECTIVE BEARING CAP qeff
P/A
ALLOWABLE BEARING CAP qa
qc+qs+qsur+qe
FOOTING BEAM SHEAR Vu
quAsheared topview
FOOTING ALLOWABLE BEAM SHEAR STRESS Tau ab
Vu/0.75Bd
Allowable: 0.17 * lambda * SQRT(f’c)
FOOTING PUNCHING SHEAR Vu
quApunchedoff topview
FOOTING ALLOWABLE PUNCHING SHEAR STRESS Tau
Vu/0.75bod
Allowable: 0.33 * lambda * SQRT(f’c)
FOOTING BENDING MOMENT Mu
qu * Abended * moment arm
(moment abt face of column)
PILE REACTION Rn
Pu/n +- My/summ x^2
PILE Vubeam
summ forces y where max shear was generated
PILE Vupunch
summ forces y @ column punched only or summ forces y @ whole footing remaining forces
FOOTING Mu
Take moment about face of column with max set of reactions
YOGA Pg
0.6FyAg
Anet correction
s^2*t/4g
FONA Pnet
0.5FuAn
BEARING Pp
1.2Fu*Aperpendicular
SHEAR Pv
FvAparallel
WELDS Fallow
0.3Fu
Aweld
0.707wL
BENDING IN STEEL BEAMS ASD
Fbx=0.66Fy
Fby=0.75Fy
fb=M/S
BENDING IN STEEL BEAMS LRFD
Fb=phyFy usually 0.9Fy
fb= Mu/Z
SHAPE FACTOR
Z/S
SHEARING IN STEEL BEAMS ASD
Fv=0.4Fy
fv=V/Aweb
SHEAR STRESS IN STEEL BEAMS LRFD
Fv=phyFy usually 0.75Fy
W kN/m in ASD
DL+LL
Wu kN/m LRFD
1.2DL+1.6LL
MAX SHEAR IN SS UDL
wL/2
SLENDERNESS RATIO SR
kL/r
RADIUS OF GYRATION r
SQRT(I/A)
k pinpin
k pinfix
k fixfix
1.0
0.7
0.5
LIMITING SLENDERNESS RATIO Cc
if < SR
if > SR
SQRT [(2pi^2E) / Fy]
LONG COLUMN
INTERMEDIATE COLUMN
STEEL LAMBDA
SR/Cc
INTERMEDIATE COLUMN Fa
(1-0.5lambda^2)Fy/Fs
FS Intermediate Columns
5/3 + 3LAMBDA/8 - LAMBDA^3/8
LONG COLUMN Fa
12Epi^2/23SR^2
PCD STRESS NORMAL STRESS sigmaN
-P/A +- Mpsc/I +-Mloadc/I
PCD MOMENT M
Losses * Pps * e
CLASS AA RATIO
4000 psi, 1C:1.5S:3G
CLASS A RATIO
3500 psi, 1C:2S:4G
CLASS B RATIO
3000 psi, 1C:2.5S:5G
CLASS C RATIO
2500 psi, 1C:3S:6G
VOLUME MULTIPLIER
1.54
WATER CEMENT RATIO
W/C
