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Reference Formulas - Elements of Architectural Structures - Lecture Notes, Study notes of Structural Design and Architecture

AMET University Structural Design and Architecture

Reference Formulas, Ultimate, Allowable, Beam Shear, Bolt Shear, Weld Shear, Compression, Without Stirrups, Beam Diagrams, With Stirrups are some points of this lecture. Its Elements of Architectural Structures handout.

Typology: Study notes

2011/2012

Uploaded on 12/22/2012

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1

Reference Formulas

0

x

F



cos2ABBAC 222 

 180)radians(π

0

y

F



sin

C

sin

B

sin

A

a

acbb

2

4

x2



0M

H

O

sin 



bmxy



cosFFx

H

A

cos 



12

xx

yy

m







sinFFy

A

O

tan 



A

Ax

x



)(

ˆ

22 yx FFF 

drp



 2





 n

iiiy AxAxQ

1

x

y

F





tan

4

2

2d

rA





A

Ay

y



)(

ˆ

FdM

dtlWA 





 n

iiix AyAyQ

1

2

s

m

9.81 g 

lAlhWV 

2

AdII 

2

1

0att)(v)t(s 

mgF

2

AdII c

w

dx

dV 

A

I

r

xxdx ˆ

V

dx

dM 

w

V

xA



yydy ˆ

2

m

N

Pa 

2

s

mkg

N



NF





Pa,kPa 00011 

2

in

lb

psi 

2

in

kip

ksi 

2

11 m

kN

kPa 

lbkip 10001

ftin 112 

PaMPa 6

101

PaGPa 9

101

mmm10001

A

P

fc

allowable

ultimate

S.F 

L







e

tA

P

or

A

P

f

td

P

A

P

fv



Ef 

td

P

A

P

fp

J

T

fv







E

L

f





I

My

fy

Ib

VQ

favev 



A

P

fv2



c

I

S

A

V

fv2

3

max 



for a rectangle

AE

PL





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Reference Formulas

 Fx^0 C^ A B 2ABcos

2 2 2    π (radians)^180 

 Fy^0

  sin

C

sin

B

sin

A

a

b b ac

x

2    

 M^0

H

O

sin  y mxb

Fx F cos

H

A

cos 

2 1

x x

y y

m

Fy Fsin

A

O

tan 

A

xA

x

2 2 F  Fx F y

p 2 r d 



n

i

Q (^) y xA xiAi

1

x

y

F

tan 

4

2 2 d A r

A

yA

y

M Fd A Wltd 



n

i

Qx yA yiAi

1

2 s

g 9.81m V WhlAl

2 I I Ad

2 2 s( t)v( 0 )t^1 at F^ mg I I Ad^2  c 

w dx

dV 

A

I

r  dx ^ xˆx

V

dx

dM 

w

V

x  A d^ y ^ yˆy

2 m

N

Pa  2 s

kg m N

 F^ N

1 kPa  1 , 000 Pa 2 in

psi lb 2 in

kip ksi 

m

kPa  kN 1 kip  1000 lb^12 in^ ^1 ft

MPa Pa

6 1  10 GPa Pa

9 1  10 1 m^ ^1000 mm

A

P

fc  allowable

ultimate F .S L

e

t A

P

or A

P

f 

td

P

A

P

fv   f^ ^ E

td

P

A

P

f (^) p   J

T

fv

  E

L

f

 

I

My f (^) y  Ib

VQ

f (^) v ave A

P

fv 2

c

I

S 

A

V

fv

 max ^ for a rectangle

AE

PL

S

M

I

Mc f (^) b max 

t d

V

A

V

f

web w

v max ^ for an^ I^ beam  T (^  T ) L

b

req F

M

S 

E

f (^) x

y z

     T (  T )

w A W V W tA

p I

VQ

nF

connectedarea connector  

3 2 2

3 1 1 1 1 2 1 2 3 2

wL w L M L M LL M L  

3 2 2

2 2 2

3 1 1

2 M 1 L 1 2 M 2 L 1 L 2 M 3 L 2 P 1 L 1 n n PL n n

x I

VQ

V

T longitudinal   L

L

fv G

2 c 1 ab

T

 max 

c abG

TL

3 2

JG

TL

2 3

(^1) ab

T

 max 

ab G

TL

3 3

1

3 3

1 ii

max max bt

Tt

t a

T

max 2

  ^ 

i (^) i

i

t

s

t

TL

2

4 a

3 3

1 G bi ti

TL



 

EI

M

R

  dx

EI

M (x)

2 n b 3

PU PL γ LPD γ D Pn 1.4(D F)

1.2D  1.6(LrorSorR)

(Lor0.8W)

Le Kl

1.2(D  FT)1.6(LH)

0.5(LrorSorR)

1.2D 1.6WL

0.5(LrorSorR)

2

r

L

π EA

L

π EI

P

e e

cr

AISC – ASD:

a^ n

R

c

e C

r

l

2

r

Kl

E

F.S.

F

cr a



2

r

L

E

f

e

cr



y

c

F

E

C

2

c

e C

r

l

F.S.

F

C

r

Kl

F

y

c

a

2

I

Mc

A

P

f max 

Pn = FcrAg

3

c

e

c

e

C

r

L

C

r

L

F.S.

 =1.67 (bending)

b

a

F

f

F

f^ ^ =1.67 (beam shear)

P

c n

u



10 9

8 . M

M

P

ny

y

nx

x

n























 =2.00 (bolt shear) 

I

M z

I

M y

A

P

f

max

1 2

 =2.00 (weld shear)

P

c n

u



10 2

. M

M

P

ny

y

nx

x

n

























 =1.50 (bearing)

F

f

F

f

F

f

by

bx

a

a     =1.67 (compression)

AISC-LRFD:^ b^0.^9

M u bMn 0. 9 FyZ S

Z

k 

y

p

f

M

Z 

M (^) ult MpfyAiyifyZ

y

p y

F

E

L  1. 76 r

2

max

w L M

equivalent 

Vu v( 0. 6 FywAw)v  1. 0 trial limit

toobig Ireq' d I 

 

2

r

KL

E

Fe



Pu c FcrAg c 0. 90 Fe  0. 44 Fy y

F

Fcr. F

e

y

Pn(max (^) end)(N 2. 5 k)Fywtw

Fe  0. 44 Fy Fcr  0. 877 Fe

Pn(max (^) interior)(N 5 k)Fywtw  1. 0

Ru t FyAg t 0. 9

P

c n

u



M

P

b ny

uy

b nx

ux

c n

u

075    Ru t FuAe t.

Ru  0. 6 FEXXTl  0. 75

P

c n

u



M

P

b ny

uy

b nx

ux

c n

u

2

M

Cm

g

s An Ag Aofallholes t 4

(P P )

C

B

u e

m

2

1

r

Kl

EA

Pe



Ae AnU Ru ( 0. 6 FuAnvUbsFuAnt 0. 6 FyAgvUbsFuAnt)  0. 75

Masonry:

Fb fm ^13  2

f b(kd) A f

m x s 2

2 f bd jk M

m m 

plain:Fv  1. 5 fm v (^) m F  f without stirrups Fv  3 fmwith stirrups

f b faFt h’/r  99  

2

r

h

Pa fmAn AstFs

fa fbFb h’/r > 99  

2

h

r

Pa fmAn AstFs

P

M

e 1  h’/r  99

2

r

h Fa. fm h’/r > 99

2 70

(^25) 



h

r Fa fm

Reference Diagrams

Reference Beam Diagrams

-^ 25%

W =

wl

2

Reference Diagrams

(tensile strain of 0.

)

Reference Diagrams

Available Strength of Fillet Welds

per inch of weld ( S)

Weld Size

(in.)

E60XX

(k/in.)

E70XX

(k/in.)

16

3 3.58 4.

¼ 4.77 5.

16

(^5) 5.97 6.

8

(^3) 7.16 8.

16

(^7) 8.35 9.

½ 9.55 11.

8

5 11.93 13.

¾ 14.32 16.

(not considering increase in throat with

submerged arc weld process)

Reference Diagrams

Reference Formulas - Elements of Architectural Structures - Lecture Notes, Study notes of Structural Design and Architecture

Related documents

Partial preview of the text

Download Reference Formulas - Elements of Architectural Structures - Lecture Notes and more Study notes Structural Design and Architecture in PDF only on Docsity!

 Fx^0 C^ A B 2ABcos

 Fy^0

  sin

C

B

A

 M^0

H

O

sin  y mxb

Fx F cos

H

A

cos 

x x

y y

m

Fy Fsin

A

O

tan 

A

xA

x

p 2 r d 

F

F

A

yA

y

M Fd A Wltd 

I

V

w

V

x  A d^ y ^ yˆy

N

A

P

P

P

P

A

P

fv   f^ ^ E

P

A

P

T

  E

L

I

VQ

P

c

I

S 

A

V

fv

 max ^ for a rectangle

AE

PL

S

M

I

t d

V

A

V

f

v max ^ for an^ I^ beam  T (^  T ) L

M

S 

E

w A W V W tA