solutions for mechanics of materials assignment

7/21/2019 Solutions for Mechanics of materials assignment

1/14

Example.

AbeamisloadedandsupportedasshowninFig,P0.Useh"@to

compute

the

deflection:

w

(a)

at

a

point

midway

between

the

supports

(b)

at

the

right

end

of

the

beam.

V=yvL

(4=u),.t)*

tw[zL)'

/-/q)Drtu

ffi@

,.)

M

=

t'vL-

lL

-

wL(-

lz

Er

6=

0rL+

gnL

.t\

: @tr

2V

ET

+(-\M

L'\

Zt

,

D

Y71

*?L+

9Er

L';f

(

,^

-h/Lv

lS'a

.P

+


2/14

Find

the

maximum

deflection

of

the

cantilever

beam

1.

Using

discontinuity

function

method

2.

Using integration

method

k-

*r

3k

,

Finl{

ru.Ldooa-t

:

f,l(A

=-F

h/L'(r

-o7o+

EIffr=-#t4/L''l

+

Vrs

V

4


3/14

at

K>c

)

O=ff=c

o=

-o+opdt

=>

1r=a)

rft)

=

hCAurr'x'+#y3*

%G-gL>)

IW

tt,*=

4r=t

b{-

ft,"

4

-

+

H

)=

-,#

#

ok=r=

b

(-SwLz'

ry'

-

ygty)r

-

#

#'


4/14

Ip

l-

Find

the

maximum

defrection

of

the

cantirever

beam

1.

Using

discontinuity

function

method

2.

Using integration

method

-

t-{'-

'

{

C

F;^d

l*=

O

:

.a

h/L

t- ..: ,

t

-

.---

.'i:

i

'

1

t--'

t-

ra

cflao

u1-{

;

*/n=

/f

tz=

+

-0L+

T

Er

4-Y=

u/L*

w=

+:r

f

"tel

ra{


5/14


6/14

f=;^/

/t{etk'po

at

a

vn^(t/,nd,

Ef

;s

6t(ca,

z'tog

Uq

l.q

)

ue.Sty

t?nryQSa-h'8P'

re

3eo

(

/dftt)

L{00

3oo.

(

'l

J)'soo'8'YzM2

/vlr

=

LV0O'8

#42

(1;

9l*,=

/'rr

l',

=

tttt

ffi,

C"\

lvr)r-,r=

/4,

Y

lt-t-N)

=

+ '

mL

L"

/

ett6

n=

Vr)r,*(%)*,=

H

(n,pftr)=

,Flg

.)

=

n,f,

Gt)

-yA.

t$'r+')

ETL


7/14

W

Determine

the

reaction

force

at

support

A in

terms

of

p.

P:wL/4

(N)

I

Reltlo'u

ra//er

d*fU

a{ tp"

*t

WN/m

fuet

lq

6'e

ft-r,*tdfo^

z4r0.

W

R,t

^-*o(

anfurd(

w-

#-uH

t,=#=

a'#)'

u)

W=fi+l[r+6=P ,

-/'

-wTM

W=c

n;=W=#*t=Jlt


8/14

P(

Forthe

beam

and loading

shown,

use

double

integrati^rlmethod

to

determine

(a)the

equation

of

the

elastic

curve

for

the

se$ment

AB

of

the

beam,

(b)

the

deflection

midway

betlryeen

A

and

B,

and

(c)

the

slope

at

B.

Assume

that

El is

constant

for

the

beam.

-

TE=Od4r-*O

Z

fre

=o>>

8"=

ttL

, :;P

d

Vn

A

A

zn=Qz2

/fi"=&

-L

ZA/"=O:

/V

lY

=

-W'r

Z

fll

P

*ru*-l

+

wb'

-fl/c=

74

+

ry'

r-tffi=

$*ry-V

luffEre""''.

,-3

iyr(g4f

o'l

et

mf4

IA,

'

u'u

I

tt"teXrate:

Y

-

fi"4t^'

Pr

?

x

z

ffi

-

v,x'nY#-Ii+tt

v

7

6

7rl

#

+

lr

Y*Lz-


9/14

bo*n/,a,,

eooth'rtbog

e"t

K

>o,

[=o

0

=-0

+C

--O*Ct?

+C.

:)

Cr:O

shfL

*4

B:

IIJ

qt

>c=L

)

[=C

e=

#:M'*

wL{d'-

&(L)'+

c'L

11

-'

'-

w

Lj'-,

P

L'

,/^tt;J'r)rnu4.i7,

nwr ,- r

wL'n

f

"t*;J'*nn'Ju'

)r"

-

''

3

U\

Erv=

-4':'yTr"-

#'+

Kt-%"fr/

ffifl

d*t'+ft/tY-H-

TET

t,^rlT ry

'

vvb

Ji-

,?

4

frr'ZvEr

, -

tq-

PL3

r)r=Llz=

-

{Y='==

+

ffi'

{rET

)r-L

nt wLt

Pt

G.

-

--.-

/

lra-

ZV

Ef

DEI


10/14

W

2'

[zs.ptsl.fhs

bsam

depicted

below

has

a 2m

area

mome1l

of

inodia

"1"

equof

Zl

inch{

and

ic

made

of a

rnaterial

with

e

Young's

modurus

of 2g,ooo

iai.

-priase

crotisnnine:

a)

The

reacfion

force

at

point

c.

$pecify

if the

forcs

{s

up

or down

and

tfie

uR[s

userL

b)

Tho

reaction

moment

at

point

A.

Diagram

ff it

is

clockwise

or countscbdnalse

and

lhe

unltg

ussd

c)

The

displacement

et

point

D.

Spacify

if it

is

up

[+vl

or

dswn

[.v]

anO

sFsdfy

th

unlt*

usad.

(a)

Rc

=

Z,l?

/8,

{b)

[tlA=

7

v,=

-47{F

c'u,

'1"

**-rfr

I

7tt

i

1011

Qd^*

Ldc

{r=

Pd=

Pfza)3

/rtd

{g

;;)fr,^'."hr;2,

a,*,}

aaftru

/d#db

Le

wo,

...r

Jioo(tVJt)

J

14=

zooo(16'fl

,nPUp*slfzo,"

,o*-/tn

o4*

/afe

#lhortr*

*

Ll^;u,

f,r'o

-

7

WL:


11/14

,futrt

zo4/6'ft)

wt

Z

/Llfi

=C

s),/?'*zt?o,e'

z

va/

(b;1'

;

)

I,J

/

i

o"*

0",

=

wL

-g

vb\\

W-

tdET

--

P

L.,

7EI

zf

o,*:

{,/-%}=-

ry

Fc

2

EJ

lx,ro

0r=

9r*

*

Zcr

*

2cn

,

:

/?./

a

>

OOO

+1fl(7,

Ht

=

st.W[hP,tt)'=


12/14

W

-lhr:

sirnply

suppcrted

bcanr

slxrrvn

in

l;ig.

i

consists

uf'a

Wl0tt

r

Sg

stfucturill

*te*l

wide-tlangc

shapc

[li

=

200

(ip*l

/

,,

(rti.g ,

lt]n

mrn'1.

For

rhe

l*ading

shrr\4rn.

usc

*lisco*rinuir.v

ftutctions

io

compuls

ta)

the

dsl'lectirlt

,:tlthe

bemr

at

C

and

(b)

thc

dcflection

ul'the

lrc*nr

ar

J...

/,

Zh,=

o=)

Dr=

/Z(/cu,

0bl/

Z

Ft=

,7^

=//

/'4

&u

/t{r)

=

/6

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