common formulas in civil engineering

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


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


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


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'


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


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

common formulas in civil engineering

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