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8/9/2019 Common Formulas in Civil Engineering
1/18
Cen
01+(n-l)cl
= az - = 03 --02
Sn=12)-(ai+ar,)= n
(201-1-(n-oct)
CXn
--air
n
- 1
sn=
1-r
r_a2
Q oz
M A T H E M A T IC S F O R M U L A S
EXPONENTS
X rn
xn
) Xm
-n
' " 1 1
X
(
X
)=
env)
()cy)
n
_
.
xn
91.1
X
9=
m -11
rn
9
FACTORING
b)
+b)(A + 9) =
>((
n
1, r
9
n
(X--(W,(+9) =
)(
2
-
y2
#y ) 1
=
X
2
4-2Xy +92
y) 1
= x
2
-2s9 +92
x'-t- y
3
= (x+y)(x2--xy+92)
y
3
-= (x- 9)(
x
+ % < 9 + Y 2 )
y)( 3+n) =
3x
+ ay +a)
,
+ay
2A
51 =
4AC
rats
o we o co .0 1
X
i
+x
2
--
-
1 >
lAC roast
cot wszucti
B
c
2 < 4,AC rook
at
i rc4Iwy
xi(x2)=
A T
BINOMIAL THEOREM
(X +9)n
r
th
-term
=
r1
Cm
X
in-rri
yni
v-I
Sec,F 7 7-
CHANGE -) a
y To
I
Se m, = n(n+1)(av e
ex0
S=V V=-S
t =-
nifovm moti
on
X * #
OF titzS
F
o
R A Jof3
1-4
R ATE
OF PoItsiG A J06
W O R K P R O 6 L e r v i g
_
y
X MINUTE HAND
CLOCK reo
6 L E M
(WET)
:=
FS
F
f= /
cc
Wcace
(A
REA AlioNG Ac)
Or
PAMicAr
(
=
45bub
Q1-ip
t
QFwC
FS
X 1 3 =
sub (e-a)
I KFINItTE
SLoPE
tan 0
=
N/0 g eefbi g e
-
stn
i
e
cos,
e n
f
sub
-Lctv
PS=
eepage,
2 f s c
,
t t4 slry8 cp
s/6
1(sot tan !!,
F t .
xec) nom
1.6
G
(s
tri 4 cas
1- cos
(/3 -4).1
cb =- ?)/I7C
P t Y t O k X
J
SAND
P
owO.G5 k0,
Y 14
c t ' A
0.2. )-1 -Eo 0, '1 Y H
STIFP CLAY
)I4
8/9/2019 Common Formulas in Civil Engineering
6/18
h
2
its_ a/a + x213
MIN - L
Mtts - P
X=
Mft -P
RacT
A SauARE
( Gw a tz A
AA)
MAX -
A
R E c T : A S a u A R E ( 6 1 6 -1 4 v e - e i m )
GYLtuoEizs
p
MAX
-V (Gtver4 : As)
M
I
N
-As (awel4
v)
Eox BLCCK
M A X - V (60/ 614 ; A s)
m - As (swer l:V)
9
r
MAX-
A
MAX
-A
9
r2: A
MAX - t
i
o -
V
V
cyL
VArE
MAX - A
x-
6/2
y VV2
MAX - L
1-2/'J
/3
4-$4
mm-cat,sE
sine=
1/ 3
L
x -3
MIN
-CAST
41ve
t4 :V
MAx-
y:
a t k i E g
: c o L T
cosT(
e40s)
(
9="cosr(ckcE)\
MAx -A : PAvAB otA
b = psmGo
0.-75
X .7-- 0,75 D
SAIA2A42
S nwN (---ECT / s-nFFECT
2 b
X =
MA X -A
y
s Q u A R E
STPONGeST /griPreSC
bsri
=
2X
MAX-A
h
AX -V
= A 1 - 2 7 -
y
=
MAXIMA
MII.1IMA
MAX
- 49
X
=raT)
M I N - L
L.-= -01+6
a o s e D - -
D= -h
ct.os EV
A C u B e
OPE1,17*
2-1-1
09eN IDP-
R E C T ( S S U A R E
W
I
-Se)
X
y
8/9/2019 Common Formulas in Civil Engineering
7/18
,DESIGN
( co m P u T E A s ,
GIVEN Mu)
O
ASSUME W4OLE FLANGE IS IN c.OM9QESSI01,1*.
T;,:
IF Ac Af
c
< t
004E0
0
Ass..x=075/3,
A s
-c
;
K.
A
s
E E D S c o r n ? .
A .F
a > t
0 2(
.
4.)( t
b w(
a
) = A c
0 FIND
:
a
Mu
= Mu,
-Fmu2
=.41c cil..)+ oc d-ti)
0.9 (0.tg
licAbba
04
)
2 (0,ci)61.2s-y.,1(t)(1,1)
bf
(a)=,
0 F IND ;
M u = (
PT i-i)
45Asfi
l
(
6 1 -
G R E G A,
fs=RgSs
T=AgCc
C
o.ssab
u s e
GIVEN Mu
Mu = fe
bri
z
(1-0.
5
q
to)
0
o
0 Et
FiNo
:
p
() As
bC1
8/9/2019 Common Formulas in Civil Engineering
9/18
B
T _ A M S
[pOLIBLY REINFORCU)1
1 A N A L Y S I S ( co m P LI T E
Mu
GIVEN As f
l
As)1
W r IZ O X I M AT E M E T H O D I
fs
=C y
fIRD:
nowt 0.15
:.-- 0.75
02 _91_
'f f3
acoi fy j
f5
P
e
. / 0 0 4 x l
C=-
- o.ssCG'ab
C
pss,3.1:--OSSCoic+1:)
FIND
Mn
=
a -
Mu
Z
r
@
A G C
63 0-
S 5
W
)
b 4
-
As'
(0
)0
C-081)
C) FIND:
says
,
04 cl
n
;Vgc
= Mn
c
, + M S
S
l
= (di) + Ls( -
= 0 . $
ci -1)
s
i Cs '
(31
c(dl)
-I-
0
Cs
1_,E.?cAGT METHOD1
FIKID:
Cc
0. ss fotab
C s
7
s Cs'
00.-_}3c,
-6'
Vs --
I
- GOO
- F 5 1 =
03S fc'
8/9/2019 Common Formulas in Civil Engineering
10/18
B E A M S
I D ou B L N F e lti F oR c e pi
1
DESI GN
(comeurE
AS
'AS , GIVEN /AU)
FiNo
As
(
O
ma
bci
=.
As, fy
C, assisclob
Fodota,T=c1
SoLve
c
e
Ma,
e
ri ld-e1-
2)
--=0.4i0AG,f90-2)
MO2.
mu
tvluz
(d(y)
-r_,0.410p.szcio-dl)
* FIND
A s 2
VEZI F1E1) TWAT
COMRLES.9014 VLEINIFOtreMMT
iS
NIEcAa
.g
AtzY see
s
Mu > Mu
8/9/2019 Common Formulas in Civil Engineering
11/18
de
7.=0 , SS
......
=if5
S
L.
:7
3
.c c
Og5
f
c 1
co
600
p
c
6d
Sft4GLY REIRFORCED
41ALYSIS
Mn
IM4
Kt = Ww
bc11 t-0.sqw)
Mu .7.: (1)Mn
.qo
r
CESEGI1/4 .1
I
s
c:7--
0.S5
ti)
=
Act)
c.
C
lA n
=T(d-1)=r- c(d-'3)
4)=0.0)0
Pes.c. ,4
AS
RaNcts stew f
p
f4
- F c
As
/I
n a)
,75
ft
-V4
ootsax
=
error. --
'
t
4 vmaK:
7
.
cjos,,,,
bd2(1-0-54o,)
D
OUI3LY
REINFORCED
ANALIStS
"T=.C.c.+Cs
Ca
(Mt4,/
vest Git4
[EXACT METHOD)
=
o .
ss fctab
Cs = A
G I fc s
w
0 0 0
c
v 4 c0
085fcs
Mn
= C,
G .
(d-4) + cs(d-co
mu= cpMn
= (19
velum ? DOUBLY RED4M :
tviuy
IL 0
Barb _
_ _
M E L - C O - E C K
:orD
1
"
u M ut
C
i
= (:),Ssfe A
b w
C
I
-_-+.ssic)-t 6132
OK!
,4
1)
T =Ag+ 9
e:"--P6k04
As zia
mio b,c1
1-
1
= CI
M u,
Mu/
At, Pmax bd
As
i
ft 4
C. = 0.8.5
Mu
i
=
T
i
( c l - - 9 i 7 )
Mu: Mu - t
i
u, 4)1'20 -
Tz-As2
fy
E j
=
A 5 , + A s 2
Tt
= Asz -F9
C I
= AsiTsi
T BEAMS
A m A u s e s t s
C =T
ft
A c
M a i