Cantilever-si Units Final 022615

8/18/2019 Cantilever-si Units Final 022615

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Cantilever Beam Calculator - SI Units

Workbook Contents

Click on tabs at the bottom of the screen to access the following:

Note: For complicated loadings, the spreadsheets estimate the maximum m

the largest of these values. The actual maximum existing in the beam may

happens to occur between grid points. ou can reassure yourself that the di

deflection.

Copyright ! "c#raw$%ill #lobal &ducation %oldings, ''C. (ll rights reserved.

Tab 1. Contents )current tab*

Tab 2. +ingle concentrated load case

Tab 3. Two concentrated loads case

Tab 4. +ingle linearly$varying distributed load case

Tab 5. Two linearly$varying distributed loads case

Tab 6. +ingle concentrated moment load case

Tab . Two concentrated moments loads case

Tab !. Combined loads )concentrated force, moment, and linearly$varying lo

Tab ". nstructions on how to analy-e load cases not covered by Tabs $/

calculating the moment at 011 evenly spaced grid points along the beam an

small, by examining the moment diagram. +imilar statements hold for maxi


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ment by

iffer slightly, if it

ference is

d*

then selecting

um shear and


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+ingle Concentrated 'oad (cting at (ny 2oint Calculations

Calculation of "oment, +hear, 4eflection, and

&nter values in yellow cells only.

I # $ U T I # % &

In'ut In(ormation

'ength, ' 6 0.1 m

&lastic "odulus, & 6 11 #2a

"oment of nertia, 6 711111

'oad, 2 6 /11 kN

'ength, a 6 .1 m

) * S U + T S

)esults o( Calculation

"aximum moment 6 /,111

"aximum shear 6 /11 kN

"aximum deflection 6 //.//8 mm

/11 kN

$/,111

cm9

kN·m

Force reaction, 5 6

"oment reaction, " 6 kN·m


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-800.00

-700.00

-600.00

-500.00

-400.00

-300.00

-200.00

-100.00

0.00

S,ear iaram

/ 0m

0k#

-50.00

0.00

e(lection

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.

-9000.00

-8000.00

-7000.00

-6000.00

-5000.00

-4000.00

-3000.00

-2000.00

-1000.00

0.00

oment iaram

/ 0m

0k#.m


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e(lec-

S,ear oment tion

n / 0/ 0/ 0/

0m 0k# 0mm

1 1.11 1.11 1.11 $//./8

0 1.0 1.11 1.11 $/9./8

1.9 1.11 1.11 $/1./8

; 1.;7 1.11 1.11 $


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08 ./ $/11.11 $9.11 $0./8

1 .91 $/11.11 $;1.11 $1/.81

0 .= $/11.11 $907.11 $19.81

.79 $/11.11 $=0.11 $11.8

; .


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=7 7.


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8; 00.07 $/11.11 $


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$ + 3nits )e(erence

eactions

For a general discussion, including examples, of the

diagrams and deflections, see

*uations Use (or T,ese Calculations

The shear, moment, and deflection are given by the

in which the constants are defined by the boundary v

5oark?s Formulas for +tress and +train, &ight

Civil &ngineering (ll$n$@ne 2& &xam #uide:

"arksA +tandard %andbook for "echanical &n

+tandard %andbook for Civil &ngineers, Fifth

http://accessengineeringlibrary.com/browse/roarks-formulas-for-stress-and-strain-eighth-edition/c97800717424740800#Chap0800clnk58http://accessengineeringlibrary.com/browse/civil-engineering-all-in-one-pe-exam-guide-breadth-and-depth-second-edition/c9780071787727ch102#ch102lev1sec12http://accessengineeringlibrary.com/browse/marks-standard-handbook-for-mechanical-engineers-eleventh-edition/p2001147c9975_14001#p2001147c9975_20002http://accessengineeringlibrary.com/browse/standard-handbook-for-civil-engineers/p2000a1f599706_1001#p2000a1f59976_14001http://accessengineeringlibrary.com/browse/standard-handbook-for-civil-engineers/p2000a1f599706_1001#p2000a1f59976_14001http://accessengineeringlibrary.com/browse/marks-standard-handbook-for-mechanical-engineers-eleventh-edition/p2001147c9975_14001#p2001147c9975_20002http://accessengineeringlibrary.com/browse/civil-engineering-all-in-one-pe-exam-guide-breadth-and-depth-second-edition/c9780071787727ch102#ch102lev1sec12http://accessengineeringlibrary.com/browse/roarks-formulas-for-stress-and-strain-eighth-edition/c97800717424740800#Chap0800clnk58


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and

and the singularity functions are defined by

+ource: 5oarkAs Formulas for +tress and +tra

+ource: 5oarkAs Formulas for +tress and +train, &

.00

0

http://accessengineeringlibrary.com/browse/roarks-formulas-for-stress-and-strain-eighth-edition/c97800717424740800#Chap0800tbl8_1http://accessengineeringlibrary.com/browse/roarks-formulas-for-stress-and-strain-eighth-edition/c97800717424740800#d13087e27830http://accessengineeringlibrary.com/browse/roarks-formulas-for-stress-and-strain-eighth-edition/c97800717424740800#d13087e27830http://accessengineeringlibrary.com/browse/roarks-formulas-for-stress-and-strain-eighth-edition/c97800717424740800#Chap0800tbl8_1


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an *uations

alculation of shear and bending$moment

>uations,

lues,

&dition +ec. /.0

readth and 4epth, +econd &dition +ec. 01.0

gineers, &leventh &dition +ec. =..=

dition +ec. 7.=



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in, &ighth &dition +ec. /.0


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Two Concentrated 3ne>ual 'oads 2laced 3nsymmetricall

Calculation of "oment, +hear, 4eflectio


I # $ U T I # % &

In'ut In(ormation

'ength, ' 6 0 m


"oment of nertia, 6 711111

/11 kN

9.1 m

;11 kN

;.= m

) * S U + T S


"aximum moment 6


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$


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e(lec-

S,ear oment tion

n / 0/ 0/ 0/

0m 0k# 0mm

1 1.11 1.11 1.11 $0=.


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09 0.7/ 1.11 1.11 $0


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=0 7.0 $/11.11 $0787.11 $


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// 01.=7 $0011.11 $=/77.11 $=.8/

/8 01.7/ $0011.11 $=88/.11 $=.17

81 01./1 $0011.11 $70;1.11 $9.0

80 01.8 $0011.11 $77.11 $;.9;

8 00.19 $0011.11 $7;89.11 $.


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Calculations $ + 3nits

, and 5eactions

For a general discussion, inclu


*uations Use (or

The shear, , and moment, ",

5oark?s Formulas for

Civil &ngineering (ll$

"arksA +tandard %an

+tandard %andbook

The deflection e>uation can be

from the left end, with the defle

deflection e>uation for the sing

y)x* 6 yo)x, a

0, 2

0*



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)e(erences an *uations

ing examples, of the calculation of shear and bending$moment

T,ese Calculations

can be found similarly from superposition.

+tress and +train, &ighth &dition +ec. /.0

n$@ne 2& &xam #uide: readth and 4epth, +econd &dition +ec. 01.0

dbook for "echanical &ngineers, &leventh &dition +ec. =..=

for Civil &ngineers, Fifth &dition +ec. 7.=

found by superposing the deflection e>uation for the load 20, acting distance a0

ction e>uation for the load 2, acting distance ' $ a

from the left end. 3sing the

le concentrated load case )Tab D+ingle Conc 'oadD* gives

yo)x, ' $ a

, 2

*



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ork 8re


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+ingle 4istributed 'oad Calculations $ + 3nits



I # $ U T I # % &

In'ut In(ormation

'ength, ' 6 0.1 m


"oment of nertia, 6 711,111

71 kNm

91.1 kNm

;.1 m

8.1 m

+ T S


"aximum moment 6 9,/71 kNBm

"aximum shear 6 0,;=1 kN

cm9

'oad, w0 6

'oad, w 6

'ength, a0 6

'ength, a 6


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) * S "aximum deflection 6 01=.


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0.00 2.00 4.00 6.00 8.00 10.

-1600.00

-1400.00

-1200.00

/ 0m

-80.00

-60.00

-40.00

-20.00

0.00

e(lection

0mm

0.00 2.00 4.00 6.00 8.00 10.00

-6000.00

-5000.00

-4000.00

-3000.00

-2000.00

-1000.00

0.00

oment iaram

/ 0m

0k#7m


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e(lec-

S,ear oment tion

n / 0/ 0/ 0/

0m 0k# 0mm

1 1.11 1.11 1.11 $01=.


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1 .91 1.11 1.11 $/1.08

0 .= 1.11 1.11 $


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= 7.9 $88.;/ $9/.;1 $;8.7=

=; 7.;7 $;09.=1 $97=.0; $;/.9

=9 7.9/ $;8.81 $=1;.


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/9 01.1/ $87.17 $7/7.


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, and 5eactions

For a general discussion, in

diagrams and deflections, s

*uations Use (or

5oark?s Formulas fo

Civil &ngineering (ll$

"arksA +tandard %a

+tandard %andbook

For a distributed load begin

)x 6 '*, the shear, moment,



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in which the constants are d

and the singularity functions

where the value of the load

The shear, , and moment,

+ource: 5oarkAs For

+ource: 5oarkAs For

The deflection of the beam

superposition:

y)x* 6 yo)

12.00 14.00



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0 12.00 14.00

12.00 14.00


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.


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luding examples, of the calculation of shear and bending$moment

e

T,ese Calculations

+tress and +train, &ighth &dition +ec. /.0

n$@ne 2& &xam #uide: readth and 4epth, +econd &dition +ec. 01.0

dbook for "echanical &ngineers, &leventh &dition +ec. =..=

for Civil &ngineers, Fifth &dition +ec. 7.=

ing with the value wa at x 6 a and ending with the value w

' at the end of the beam

nd deflection are given by the e>uations,



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efined by the boundary values,

and

are defined by

t the end of beam is found from similar triangles to be

, can be found similarly from superposition.

ulas for +tress and +train, &ighth &dition +ec. /.0


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Two 4istributed 'oad Calculations $ + 3nits

Calculation of "oment, +hear, 4eflection, and 5


I # $ U T I #

% &

In'ut In(ormation

'ength, ' 6 0.1 m



1 kNm

71.1 kNm

1 m

; m

71 kNm

91.1 kNm

1.1 m

8.1 m

cm9

'oad, w0 6

'oad, w 6

'ength, a0 6

'ength, a 6

'oad, w; 6

'oad, w9 6

'ength, a; 6

'ength, a9 6


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) * S U + T S


"aximum moment 6 =,


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-1600.00

-1400.00

-1200.00

-1000.00

-800.00

-600.00

-400.00

-200.00

0.00

/ 0m

0k#

-60.00

-40.00

-20.00

0.00

e(lection

0.00 2.00 4.00 6.00 8.00 10.00 1 2.00 1 4.00

-7000.00

-6000.00

-5000.00

-4000.00

-3000.00

-2000.00

-1000.00

0.00

oment iaram

/ 0m

0k#7m


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e(lec-

S,ear oment tion

n / 0/ 0/ 0/

0m 0k# 0mm

1 1.11 1.11 1.11 $0;/.9

0 1.0 $1.09 $1.10 $0;7.=0

1.9 $1.=/ $1.1= $0;9.


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0/ .07 $97.77 $;;.=8 $01


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=1 7.11 $;71.11 $


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/ 8./9 $87/.7 $;0


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)e(eren

actionsFor a general discussion, including examples, of


*uations Use (or T,ese Calculation

where

5oark?s Formulas for +tress and +train, &

Civil &ngineering (ll$n$@ne 2& &xam #ui

"arksA +tandard %andbook for "echanic

+tandard %andbook for Civil &ngineers, F

The deflection e>uation can be found by superposingle distributed load case )Tab D+ingle 4ist 'oa

y)x* 6 yo)x, a

0, w

0, w

0* $ y

o)x, a

0 E a

, w

E yo)x,a

0 E a

E a

;, w

;, w

;9* $ y

o)x,



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and

The shear, , and moment, ", can be found simil

0


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es an *uations

he calculation of shear and bending$moment

ighth &dition +ec. /.0

de: readth and 4epth, +econd &dition +ec. 01.0

l &ngineers, &leventh &dition +ec. =..=

ifth &dition +ec. 7.=

a; G 1

sing the deflection e>uation for a distributed load given for thed*:

, w0

*

0 E a

E a

; E a

9, w

9, w

;9*



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arly from superposition.


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Work 8re


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+ingle Concentrated "oment (cting at (ny 2oint Calculations $

Calculation of "oment, +hear, 4eflection, and 5e


I # $ U T I # % &

In'ut In(ormation

'ength, ' 6 0.1 m



,111 kNBm

'ength, a 6 9.1 m

) * S U + T S


"aximum moment 6 ,111 kNBm

"aximum shear 6 1 kN

"aximum deflection 6 017.77< mm

1 kN

cm9

"oment, "C 6

Force reaction, 5 6


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,111 kNBm"oment reaction, " 6

0.00 2.00 4.00 6.00 8.00 10.00 12.00

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

S,ear iaram

/ 0m

0k#

0.00 2.00 4.00 6.00 8.00 10.00 12.00

0.00

500.00

1000.00

1500.00

2000.00

2500.00

oment iaram

0k#7m


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8 0.1/ 1.11 1.11 8.<

01 0.1 1.11 1.11 81.7<

00 0.; 1.11 1.11 /8.1<

0 0.99 1.11 1.11 /


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90 9.8 1.11 111.11 90.


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3nits )

ctions

For a general discussion, including exampl


*uations Use (or T,ese Calcul

The shear, moment, and deflection are giv

5oark?s Formulas for +tress and +t

Civil &ngineering (ll$n$@ne 2& &x

"arksA +tandard %andbook for

+tandard %andbook for Civil &ngin



262/407

in which the constants are defined by the b

and

and the singularity functions are defined b

+ource: 5oarkAs Formulas for +tres

+ource: 5oarkAs Formulas for +tress a

14.00

14.00



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e(erences an *uations

es, of the calculation of shear and bending$moment

ations

n by the e>uations,

rain, &ighth &dition +ec. /.0

m #uide: readth and 4epth, +econd &dition +ec. 01.0

echanical &ngineers, &leventh &dition +ec. =..=

ers, Fifth &dition +ec. 7.=



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oundary values,

s and +train, &ighth &dition +ec. /.0


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Two Concentrated 3ne>ual "oments 2laced 3nsymmetrical



I #

$ U T I # % &

In'ut In(ormation

'ength, ' 6 0.1 m



,111 kNBm

9.1 m

=,111 kNBm

=.1 m

T S


"aximum moment 6


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) * S U

"aximum deflection 6 ;19.=/; mm

1 kN


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e(lec-

S,ear oment tion

n / 0/ 0/ 0/0m 0k# 0mm

1 1.11 1.11 1.11 ;19.=/

0 1.0 1.11 1.11 ;11.9/

1.9 1.11 1.11 87.;/

; 1.;7 1.11 1.11 8./

0k#·m

0.00 2.00 4.00 6.00 8.00 10.00

0.00

1000.00

2000.00

3000.00

/ 0m

0.00 2.00 4.00 6.00 8.00 10.00

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

e(lection

/ 0m

0mm


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9 1.9/ 1.11 1.11 //.0/

= 1.71 1.11 1.11 /9.1/

7 1.


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;7 9.; 1.11 111.11 0=


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7/ /.07 1.11


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011 0.11 1.11


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ly Calculations $ + 3nits

, and 5eactions

For a general discu

diagrams and defle

The deflection e>u

left end, with the de

e>uation for the sin


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The shear, , and

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12.00 14.00


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ssion, including examples, of the calculation of shear and bending$moment

ctions, see

*uations Use (or T,ese Calculations

5oark?s Formulas for +tress and +train, &ighth &dition +ec. /.0

Civil &ngineering (ll$n$@ne 2& &xam #uide: readth and 4epth, +econd &dition +ec. 01.0

"arksA +tandard %andbook for "echanical &ngineers, &leventh &dition +ec. =..=

+tandard %andbook for Civil &ngineers, Fifth &dition +ec. 7.=

tion can be found by superposing the deflection e>uation for the moment "0, acting distance

flection e>uation for the moment ", acting distance ' $ a

from the left end. 3sing the deflecti

gle concentrated load case )Tab D+ingle Conc "omentD* gives

y)x* 6 yo)x, a

0, "

0* E y

o)x, ' $ a

, "

*



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oment, ", can be found similarly from superposition.


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0 from the

on

http://accessengineeringlibrary.com/browse/civil-engineering-all-in-one-pe-exam-guide-breadth-and-depth-second-edition/c9780071787727ch102#ch102lev1sec12


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Combined 'oad Calculations $ + 3nits

Calculation of "oment, +hear, 4eflection, and 5


I # $ U T I

# % &

In'ut In(ormation

'ength, ' 6 0.1 m



1 kNm

91.1 kNm

1 m

0 m

,111 kNBm

9.1 m

'oad, 2 6 /11 kN

=.1 m

cm9

'oad, w0 6

'oad, w 6

'ength, a0 6

'ength, a 6

"oment, "C

'ength, a; 6

'ength, a9 6


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) * S U + T S


"aximum moment 6


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0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00

-2500.00

-2000.00

-1500.00

-1000.00

-500.00

/0m

0k#

-80.00

-60.00

-40.00

-20.00

0.00e(lection

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00

-10000.00

-8000.00

-6000.00

-4000.00

-2000.00

0.00

2000.00

4000.00

oment iaram

/ 0m

0k#7m


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e(lec-

S,ear oment tion

n / 0/ 0/ 0/

0m 0k# 0mm

1 1.11 1.11 1.11 $00


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1 .91 $=


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= 7.9 $;/8.;/ 0081.01 $=7.07

=; 7.;7 $919.=1 009.9< $=9.


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/9 01.1/ $0/07.17 $;/


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)e(eren

actions

For a general discussion, including examples, of


*uations Use (or T,ese Calculation

where

5oark?s Formulas for +tress and +train, &

Civil &ngineering (ll$n$@ne 2& &xam #ui

"arksA +tandard %andbook for "echanic

+tandard %andbook for Civil &ngineers, F

The deflection e>uation can be found by superpo

D+ingle Conc 'oadD*, a concentrated moment yo"

D+ingle 4ist 'oadD*:

y)x* 6 yoF

)x, ' $ a9, 2* E y

o")x,

$ yow

)x, a0 E a

, w

, w

0*



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es an *uations

he calculation of shear and bending$moment

ighth &dition +ec. /.0

de: readth and 4epth, +econd &dition +ec. 01.0

l &ngineers, &leventh &dition +ec. =..=

ifth &dition +ec. 7.=

sing the deflection e>uations for a concentrated force yoF

)Tab

)Tab D+ingle Conc "omentD*, and a distributed load yow

)Tab

a;, "

C* E y

ow)x, a

0, w

0, w

0*



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arly from superposition.


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Work 8re


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;eneral +oain Case

f you encounter a loading case that is not covered by one of the worksheets in this

then you can still easily analy-e the beam by using superposition. 'et?s illustrate the

5emember to use D2aste +pecialaluesD. ou will then have something lik

o- e(lec-

S,ear ment tion

n / 0/ 0/ 0/1 1 1 1 $.1/;;;;

0 1.0 $= $1.= $.1=1/9

1. $= $0 $.11/9

o- e(lec-

S,ear ment tion

n / 0/ 0/ 0/1 1 1 1 $.1/;;;;

0 1.0 $= $1.= $.1=1/9 1. $= $0 $.11/9

o- e(lec-

S,ear ment tion

n / 0/ 0/ 0/1 1 1 1 $;.;807<

0 1.0 $


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you can use &xcel?s plotting and formatting capabilities to put the results in t

for your needs.

case simply by adding the maximum moments for the individual load cases,

combined load case by examining the list of moments for the combined loadlargest one.

Copyright ! "c#raw$%ill #lobal &ducation %oldings, ''C. (ll rights reserved.

Warnin


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orkbook,

procedure by

the following:

re the steps:

eam for 'oad0.

a blank worksheet.

have three tables of results:

Documents

Cantilever-si Units Final 022615