8/18/2019 Cantilever-si Units Final 022615
1/407
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
8/18/2019 Cantilever-si Units Final 022615
2/407
ment by
iffer slightly, if it
ference is
d*
then selecting
um shear and
8/18/2019 Cantilever-si Units Final 022615
3/407
+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
8/18/2019 Cantilever-si Units Final 022615
4/407
0.00 2.00 4.00 6.00 8.00 10.00 12.00 14
-900.00
-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
8/18/2019 Cantilever-si Units Final 022615
5/407
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 $
8/18/2019 Cantilever-si Units Final 022615
6/407
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
; .
8/18/2019 Cantilever-si Units Final 022615
7/407
=7 7.
8/18/2019 Cantilever-si Units Final 022615
8/407
8; 00.07 $/11.11 $
8/18/2019 Cantilever-si Units Final 022615
9/407
8/18/2019 Cantilever-si Units Final 022615
10/407
8/18/2019 Cantilever-si Units Final 022615
11/407
8/18/2019 Cantilever-si Units Final 022615
12/407
$ + 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
8/18/2019 Cantilever-si Units Final 022615
13/407
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
8/18/2019 Cantilever-si Units Final 022615
14/407
8/18/2019 Cantilever-si Units Final 022615
15/407
8/18/2019 Cantilever-si Units Final 022615
16/407
8/18/2019 Cantilever-si Units Final 022615
17/407
8/18/2019 Cantilever-si Units Final 022615
18/407
8/18/2019 Cantilever-si Units Final 022615
19/407
8/18/2019 Cantilever-si Units Final 022615
20/407
8/18/2019 Cantilever-si Units Final 022615
21/407
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.=
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
8/18/2019 Cantilever-si Units Final 022615
22/407
in, &ighth &dition +ec. /.0
8/18/2019 Cantilever-si Units Final 022615
23/407
8/18/2019 Cantilever-si Units Final 022615
24/407
8/18/2019 Cantilever-si Units Final 022615
25/407
8/18/2019 Cantilever-si Units Final 022615
26/407
8/18/2019 Cantilever-si Units Final 022615
27/407
8/18/2019 Cantilever-si Units Final 022615
28/407
8/18/2019 Cantilever-si Units Final 022615
29/407
8/18/2019 Cantilever-si Units Final 022615
30/407
8/18/2019 Cantilever-si Units Final 022615
31/407
8/18/2019 Cantilever-si Units Final 022615
32/407
8/18/2019 Cantilever-si Units Final 022615
33/407
8/18/2019 Cantilever-si Units Final 022615
34/407
8/18/2019 Cantilever-si Units Final 022615
35/407
8/18/2019 Cantilever-si Units Final 022615
36/407
8/18/2019 Cantilever-si Units Final 022615
37/407
8/18/2019 Cantilever-si Units Final 022615
38/407
8/18/2019 Cantilever-si Units Final 022615
39/407
Two Concentrated 3ne>ual 'oads 2laced 3nsymmetricall
Calculation of "oment, +hear, 4eflectio
&nter values in yellow cells only.
I # $ U T I # % &
In'ut In(ormation
'ength, ' 6 0 m
&lastic "odulus, & 6 11 #2a
"oment of nertia, 6 711111
/11 kN
9.1 m
;11 kN
;.= m
) * S U + T S
)esults o( Calculation
"aximum moment 6
8/18/2019 Cantilever-si Units Final 022615
40/407
$
8/18/2019 Cantilever-si Units Final 022615
41/407
e(lec-
S,ear oment tion
n / 0/ 0/ 0/
0m 0k# 0mm
1 1.11 1.11 1.11 $0=.
8/18/2019 Cantilever-si Units Final 022615
42/407
09 0.7/ 1.11 1.11 $0
8/18/2019 Cantilever-si Units Final 022615
43/407
=0 7.0 $/11.11 $0787.11 $
8/18/2019 Cantilever-si Units Final 022615
44/407
// 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 $.
8/18/2019 Cantilever-si Units Final 022615
45/407
8/18/2019 Cantilever-si Units Final 022615
46/407
8/18/2019 Cantilever-si Units Final 022615
47/407
8/18/2019 Cantilever-si Units Final 022615
48/407
8/18/2019 Cantilever-si Units Final 022615
49/407
8/18/2019 Cantilever-si Units Final 022615
50/407
8/18/2019 Cantilever-si Units Final 022615
51/407
Calculations $ + 3nits
, and 5eactions
For a general discussion, inclu
diagrams and deflections, see
*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*
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
8/18/2019 Cantilever-si Units Final 022615
52/407
12.00 14.00
12.00 14.00
8/18/2019 Cantilever-si Units Final 022615
53/407
2.00 14.00
8/18/2019 Cantilever-si Units Final 022615
54/407
8/18/2019 Cantilever-si Units Final 022615
55/407
8/18/2019 Cantilever-si Units Final 022615
56/407
8/18/2019 Cantilever-si Units Final 022615
57/407
8/18/2019 Cantilever-si Units Final 022615
58/407
8/18/2019 Cantilever-si Units Final 022615
59/407
8/18/2019 Cantilever-si Units Final 022615
60/407
8/18/2019 Cantilever-si Units Final 022615
61/407
8/18/2019 Cantilever-si Units Final 022615
62/407
8/18/2019 Cantilever-si Units Final 022615
63/407
)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
*
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
8/18/2019 Cantilever-si Units Final 022615
64/407
8/18/2019 Cantilever-si Units Final 022615
65/407
8/18/2019 Cantilever-si Units Final 022615
66/407
8/18/2019 Cantilever-si Units Final 022615
67/407
8/18/2019 Cantilever-si Units Final 022615
68/407
8/18/2019 Cantilever-si Units Final 022615
69/407
8/18/2019 Cantilever-si Units Final 022615
70/407
8/18/2019 Cantilever-si Units Final 022615
71/407
8/18/2019 Cantilever-si Units Final 022615
72/407
8/18/2019 Cantilever-si Units Final 022615
73/407
8/18/2019 Cantilever-si Units Final 022615
74/407
8/18/2019 Cantilever-si Units Final 022615
75/407
8/18/2019 Cantilever-si Units Final 022615
76/407
8/18/2019 Cantilever-si Units Final 022615
77/407
8/18/2019 Cantilever-si Units Final 022615
78/407
8/18/2019 Cantilever-si Units Final 022615
79/407
8/18/2019 Cantilever-si Units Final 022615
80/407
ork 8re
8/18/2019 Cantilever-si Units Final 022615
81/407
8/18/2019 Cantilever-si Units Final 022615
82/407
8/18/2019 Cantilever-si Units Final 022615
83/407
8/18/2019 Cantilever-si Units Final 022615
84/407
8/18/2019 Cantilever-si Units Final 022615
85/407
8/18/2019 Cantilever-si Units Final 022615
86/407
8/18/2019 Cantilever-si Units Final 022615
87/407
+ingle 4istributed 'oad Calculations $ + 3nits
Calculation of "oment, +hear, 4eflectio
&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, 6 711,111
71 kNm
91.1 kNm
;.1 m
8.1 m
+ T S
)esults o( Calculation
"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
8/18/2019 Cantilever-si Units Final 022615
88/407
) * S "aximum deflection 6 01=.
8/18/2019 Cantilever-si Units Final 022615
89/407
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
8/18/2019 Cantilever-si Units Final 022615
90/407
e(lec-
S,ear oment tion
n / 0/ 0/ 0/
0m 0k# 0mm
1 1.11 1.11 1.11 $01=.
8/18/2019 Cantilever-si Units Final 022615
91/407
1 .91 1.11 1.11 $/1.08
0 .= 1.11 1.11 $
8/18/2019 Cantilever-si Units Final 022615
92/407
= 7.9 $88.;/ $9/.;1 $;8.7=
=; 7.;7 $;09.=1 $97=.0; $;/.9
=9 7.9/ $;8.81 $=1;.
8/18/2019 Cantilever-si Units Final 022615
93/407
/9 01.1/ $87.17 $7/7.
8/18/2019 Cantilever-si Units Final 022615
94/407
8/18/2019 Cantilever-si Units Final 022615
95/407
8/18/2019 Cantilever-si Units Final 022615
96/407
8/18/2019 Cantilever-si Units Final 022615
97/407
8/18/2019 Cantilever-si Units Final 022615
98/407
8/18/2019 Cantilever-si Units Final 022615
99/407
8/18/2019 Cantilever-si Units Final 022615
100/407
8/18/2019 Cantilever-si Units Final 022615
101/407
8/18/2019 Cantilever-si Units Final 022615
102/407
8/18/2019 Cantilever-si Units Final 022615
103/407
8/18/2019 Cantilever-si Units Final 022615
104/407
, and 5eactions
For a general discussion, in
diagrams and deflections, s
*uations Use (or
5oark?s Formulas fo
Civil &ngineering (ll$
"arksA +tandard %a
+tandard %andbook
For a distributed load begin
)x 6 '*, the shear, moment,
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
8/18/2019 Cantilever-si Units Final 022615
105/407
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
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#d11290e27780http://accessengineeringlibrary.com/browse/roarks-formulas-for-stress-and-strain-eighth-edition/c97800717424740800#d11290e27780http://accessengineeringlibrary.com/browse/roarks-formulas-for-stress-and-strain-eighth-edition/c97800717424740800#Chap0800tbl8_1
8/18/2019 Cantilever-si Units Final 022615
106/407
0 12.00 14.00
12.00 14.00
8/18/2019 Cantilever-si Units Final 022615
107/407
12.00 14.00
8/18/2019 Cantilever-si Units Final 022615
108/407
8/18/2019 Cantilever-si Units Final 022615
109/407
8/18/2019 Cantilever-si Units Final 022615
110/407
.
8/18/2019 Cantilever-si Units Final 022615
111/407
8/18/2019 Cantilever-si Units Final 022615
112/407
8/18/2019 Cantilever-si Units Final 022615
113/407
8/18/2019 Cantilever-si Units Final 022615
114/407
8/18/2019 Cantilever-si Units Final 022615
115/407
8/18/2019 Cantilever-si Units Final 022615
116/407
8/18/2019 Cantilever-si Units Final 022615
117/407
8/18/2019 Cantilever-si Units Final 022615
118/407
8/18/2019 Cantilever-si Units Final 022615
119/407
8/18/2019 Cantilever-si Units Final 022615
120/407
8/18/2019 Cantilever-si Units Final 022615
121/407
)e(erences an *uations
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,
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
8/18/2019 Cantilever-si Units Final 022615
122/407
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
8/18/2019 Cantilever-si Units Final 022615
123/407
8/18/2019 Cantilever-si Units Final 022615
124/407
8/18/2019 Cantilever-si Units Final 022615
125/407
8/18/2019 Cantilever-si Units Final 022615
126/407
8/18/2019 Cantilever-si Units Final 022615
127/407
8/18/2019 Cantilever-si Units Final 022615
128/407
8/18/2019 Cantilever-si Units Final 022615
129/407
8/18/2019 Cantilever-si Units Final 022615
130/407
8/18/2019 Cantilever-si Units Final 022615
131/407
8/18/2019 Cantilever-si Units Final 022615
132/407
8/18/2019 Cantilever-si Units Final 022615
133/407
8/18/2019 Cantilever-si Units Final 022615
134/407
8/18/2019 Cantilever-si Units Final 022615
135/407
8/18/2019 Cantilever-si Units Final 022615
136/407
8/18/2019 Cantilever-si Units Final 022615
137/407
8/18/2019 Cantilever-si Units Final 022615
138/407
8/18/2019 Cantilever-si Units Final 022615
139/407
8/18/2019 Cantilever-si Units Final 022615
140/407
8/18/2019 Cantilever-si Units Final 022615
141/407
8/18/2019 Cantilever-si Units Final 022615
142/407
8/18/2019 Cantilever-si Units Final 022615
143/407
8/18/2019 Cantilever-si Units Final 022615
144/407
8/18/2019 Cantilever-si Units Final 022615
145/407
8/18/2019 Cantilever-si Units Final 022615
146/407
8/18/2019 Cantilever-si Units Final 022615
147/407
8/18/2019 Cantilever-si Units Final 022615
148/407
8/18/2019 Cantilever-si Units Final 022615
149/407
8/18/2019 Cantilever-si Units Final 022615
150/407
8/18/2019 Cantilever-si Units Final 022615
151/407
8/18/2019 Cantilever-si Units Final 022615
152/407
8/18/2019 Cantilever-si Units Final 022615
153/407
8/18/2019 Cantilever-si Units Final 022615
154/407
8/18/2019 Cantilever-si Units Final 022615
155/407
Two 4istributed 'oad Calculations $ + 3nits
Calculation of "oment, +hear, 4eflection, and 5
&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, 6 711,111
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
8/18/2019 Cantilever-si Units Final 022615
156/407
) * S U + T S
)esults o( Calculation
"aximum moment 6 =,
8/18/2019 Cantilever-si Units Final 022615
157/407
0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.0
-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
8/18/2019 Cantilever-si Units Final 022615
158/407
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.
8/18/2019 Cantilever-si Units Final 022615
159/407
0/ .07 $97.77 $;;.=8 $01
8/18/2019 Cantilever-si Units Final 022615
160/407
=1 7.11 $;71.11 $
8/18/2019 Cantilever-si Units Final 022615
161/407
/ 8./9 $87/.7 $;0
8/18/2019 Cantilever-si Units Final 022615
162/407
8/18/2019 Cantilever-si Units Final 022615
163/407
8/18/2019 Cantilever-si Units Final 022615
164/407
8/18/2019 Cantilever-si Units Final 022615
165/407
8/18/2019 Cantilever-si Units Final 022615
166/407
8/18/2019 Cantilever-si Units Final 022615
167/407
8/18/2019 Cantilever-si Units Final 022615
168/407
8/18/2019 Cantilever-si Units Final 022615
169/407
8/18/2019 Cantilever-si Units Final 022615
170/407
8/18/2019 Cantilever-si Units Final 022615
171/407
8/18/2019 Cantilever-si Units Final 022615
172/407
8/18/2019 Cantilever-si Units Final 022615
173/407
8/18/2019 Cantilever-si Units Final 022615
174/407
8/18/2019 Cantilever-si Units Final 022615
175/407
8/18/2019 Cantilever-si Units Final 022615
176/407
8/18/2019 Cantilever-si Units Final 022615
177/407
8/18/2019 Cantilever-si Units Final 022615
178/407
8/18/2019 Cantilever-si Units Final 022615
179/407
)e(eren
actionsFor a general discussion, including examples, of
diagrams and deflections, see
*uations Use (or T,ese Calculation
where
5oark?s Formulas for +tress and +train, &
Civil &ngineering (ll$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,
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
8/18/2019 Cantilever-si Units Final 022615
180/407
and
The shear, , and moment, ", can be found simil
0
8/18/2019 Cantilever-si Units Final 022615
181/407
8/18/2019 Cantilever-si Units Final 022615
182/407
8/18/2019 Cantilever-si Units Final 022615
183/407
8/18/2019 Cantilever-si Units Final 022615
184/407
8/18/2019 Cantilever-si Units Final 022615
185/407
8/18/2019 Cantilever-si Units Final 022615
186/407
8/18/2019 Cantilever-si Units Final 022615
187/407
8/18/2019 Cantilever-si Units Final 022615
188/407
8/18/2019 Cantilever-si Units Final 022615
189/407
8/18/2019 Cantilever-si Units Final 022615
190/407
8/18/2019 Cantilever-si Units Final 022615
191/407
8/18/2019 Cantilever-si Units Final 022615
192/407
8/18/2019 Cantilever-si Units Final 022615
193/407
8/18/2019 Cantilever-si Units Final 022615
194/407
8/18/2019 Cantilever-si Units Final 022615
195/407
8/18/2019 Cantilever-si Units Final 022615
196/407
8/18/2019 Cantilever-si Units Final 022615
197/407
8/18/2019 Cantilever-si Units Final 022615
198/407
8/18/2019 Cantilever-si Units Final 022615
199/407
8/18/2019 Cantilever-si Units Final 022615
200/407
8/18/2019 Cantilever-si Units Final 022615
201/407
8/18/2019 Cantilever-si Units Final 022615
202/407
8/18/2019 Cantilever-si Units Final 022615
203/407
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*
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
8/18/2019 Cantilever-si Units Final 022615
204/407
arly from superposition.
8/18/2019 Cantilever-si Units Final 022615
205/407
8/18/2019 Cantilever-si Units Final 022615
206/407
8/18/2019 Cantilever-si Units Final 022615
207/407
8/18/2019 Cantilever-si Units Final 022615
208/407
8/18/2019 Cantilever-si Units Final 022615
209/407
Work 8re
8/18/2019 Cantilever-si Units Final 022615
210/407
8/18/2019 Cantilever-si Units Final 022615
211/407
8/18/2019 Cantilever-si Units Final 022615
212/407
8/18/2019 Cantilever-si Units Final 022615
213/407
8/18/2019 Cantilever-si Units Final 022615
214/407
8/18/2019 Cantilever-si Units Final 022615
215/407
8/18/2019 Cantilever-si Units Final 022615
216/407
8/18/2019 Cantilever-si Units Final 022615
217/407
8/18/2019 Cantilever-si Units Final 022615
218/407
8/18/2019 Cantilever-si Units Final 022615
219/407
8/18/2019 Cantilever-si Units Final 022615
220/407
8/18/2019 Cantilever-si Units Final 022615
221/407
8/18/2019 Cantilever-si Units Final 022615
222/407
8/18/2019 Cantilever-si Units Final 022615
223/407
8/18/2019 Cantilever-si Units Final 022615
224/407
8/18/2019 Cantilever-si Units Final 022615
225/407
8/18/2019 Cantilever-si Units Final 022615
226/407
8/18/2019 Cantilever-si Units Final 022615
227/407
8/18/2019 Cantilever-si Units Final 022615
228/407
8/18/2019 Cantilever-si Units Final 022615
229/407
8/18/2019 Cantilever-si Units Final 022615
230/407
8/18/2019 Cantilever-si Units Final 022615
231/407
8/18/2019 Cantilever-si Units Final 022615
232/407
8/18/2019 Cantilever-si Units Final 022615
233/407
8/18/2019 Cantilever-si Units Final 022615
234/407
8/18/2019 Cantilever-si Units Final 022615
235/407
8/18/2019 Cantilever-si Units Final 022615
236/407
8/18/2019 Cantilever-si Units Final 022615
237/407
8/18/2019 Cantilever-si Units Final 022615
238/407
8/18/2019 Cantilever-si Units Final 022615
239/407
8/18/2019 Cantilever-si Units Final 022615
240/407
8/18/2019 Cantilever-si Units Final 022615
241/407
8/18/2019 Cantilever-si Units Final 022615
242/407
8/18/2019 Cantilever-si Units Final 022615
243/407
8/18/2019 Cantilever-si Units Final 022615
244/407
8/18/2019 Cantilever-si Units Final 022615
245/407
8/18/2019 Cantilever-si Units Final 022615
246/407
8/18/2019 Cantilever-si Units Final 022615
247/407
8/18/2019 Cantilever-si Units Final 022615
248/407
8/18/2019 Cantilever-si Units Final 022615
249/407
8/18/2019 Cantilever-si Units Final 022615
250/407
8/18/2019 Cantilever-si Units Final 022615
251/407
+ingle Concentrated "oment (cting at (ny 2oint Calculations $
Calculation of "oment, +hear, 4eflection, and 5e
&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, 6 711,111
,111 kNBm
'ength, a 6 9.1 m
) * S U + T S
)esults o( Calculation
"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
8/18/2019 Cantilever-si Units Final 022615
252/407
,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
8/18/2019 Cantilever-si Units Final 022615
253/407
8/18/2019 Cantilever-si Units Final 022615
254/407
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 /
8/18/2019 Cantilever-si Units Final 022615
255/407
90 9.8 1.11 111.11 90.
8/18/2019 Cantilever-si Units Final 022615
256/407
8/18/2019 Cantilever-si Units Final 022615
257/407
8/18/2019 Cantilever-si Units Final 022615
258/407
8/18/2019 Cantilever-si Units Final 022615
259/407
8/18/2019 Cantilever-si Units Final 022615
260/407
8/18/2019 Cantilever-si Units Final 022615
261/407
3nits )
ctions
For a general discussion, including exampl
diagrams and deflections, see
*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
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
8/18/2019 Cantilever-si Units Final 022615
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
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
8/18/2019 Cantilever-si Units Final 022615
263/407
14.00
8/18/2019 Cantilever-si Units Final 022615
264/407
8/18/2019 Cantilever-si Units Final 022615
265/407
8/18/2019 Cantilever-si Units Final 022615
266/407
8/18/2019 Cantilever-si Units Final 022615
267/407
8/18/2019 Cantilever-si Units Final 022615
268/407
8/18/2019 Cantilever-si Units Final 022615
269/407
8/18/2019 Cantilever-si Units Final 022615
270/407
8/18/2019 Cantilever-si Units Final 022615
271/407
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.=
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
8/18/2019 Cantilever-si Units Final 022615
272/407
oundary values,
s and +train, &ighth &dition +ec. /.0
8/18/2019 Cantilever-si Units Final 022615
273/407
8/18/2019 Cantilever-si Units Final 022615
274/407
8/18/2019 Cantilever-si Units Final 022615
275/407
8/18/2019 Cantilever-si Units Final 022615
276/407
8/18/2019 Cantilever-si Units Final 022615
277/407
8/18/2019 Cantilever-si Units Final 022615
278/407
8/18/2019 Cantilever-si Units Final 022615
279/407
8/18/2019 Cantilever-si Units Final 022615
280/407
8/18/2019 Cantilever-si Units Final 022615
281/407
Two Concentrated 3ne>ual "oments 2laced 3nsymmetrical
Calculation of "oment, +hear, 4eflectio
&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, 6 711,111
,111 kNBm
9.1 m
=,111 kNBm
=.1 m
T S
)esults o( Calculation
"aximum moment 6
8/18/2019 Cantilever-si Units Final 022615
282/407
) * S U
"aximum deflection 6 ;19.=/; mm
1 kN
8/18/2019 Cantilever-si Units Final 022615
283/407
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
8/18/2019 Cantilever-si Units Final 022615
284/407
9 1.9/ 1.11 1.11 //.0/
= 1.71 1.11 1.11 /9.1/
7 1.
8/18/2019 Cantilever-si Units Final 022615
285/407
;7 9.; 1.11 111.11 0=
8/18/2019 Cantilever-si Units Final 022615
286/407
7/ /.07 1.11
8/18/2019 Cantilever-si Units Final 022615
287/407
011 0.11 1.11
8/18/2019 Cantilever-si Units Final 022615
288/407
8/18/2019 Cantilever-si Units Final 022615
289/407
8/18/2019 Cantilever-si Units Final 022615
290/407
8/18/2019 Cantilever-si Units Final 022615
291/407
8/18/2019 Cantilever-si Units Final 022615
292/407
8/18/2019 Cantilever-si Units Final 022615
293/407
8/18/2019 Cantilever-si Units Final 022615
294/407
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
8/18/2019 Cantilever-si Units Final 022615
295/407
The shear, , and
12.00 14.00
8/18/2019 Cantilever-si Units Final 022615
296/407
12.00 14.00
12.00 14.00
8/18/2019 Cantilever-si Units Final 022615
297/407
8/18/2019 Cantilever-si Units Final 022615
298/407
8/18/2019 Cantilever-si Units Final 022615
299/407
8/18/2019 Cantilever-si Units Final 022615
300/407
8/18/2019 Cantilever-si Units Final 022615
301/407
8/18/2019 Cantilever-si Units Final 022615
302/407
8/18/2019 Cantilever-si Units Final 022615
303/407
8/18/2019 Cantilever-si Units Final 022615
304/407
8/18/2019 Cantilever-si Units Final 022615
305/407
8/18/2019 Cantilever-si Units Final 022615
306/407
8/18/2019 Cantilever-si Units Final 022615
307/407
)e(erences an *uations
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
, "
*
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
8/18/2019 Cantilever-si Units Final 022615
308/407
oment, ", can be found similarly from superposition.
8/18/2019 Cantilever-si Units Final 022615
309/407
8/18/2019 Cantilever-si Units Final 022615
310/407
8/18/2019 Cantilever-si Units Final 022615
311/407
8/18/2019 Cantilever-si Units Final 022615
312/407
8/18/2019 Cantilever-si Units Final 022615
313/407
8/18/2019 Cantilever-si Units Final 022615
314/407
8/18/2019 Cantilever-si Units Final 022615
315/407
8/18/2019 Cantilever-si Units Final 022615
316/407
8/18/2019 Cantilever-si Units Final 022615
317/407
8/18/2019 Cantilever-si Units Final 022615
318/407
8/18/2019 Cantilever-si Units Final 022615
319/407
8/18/2019 Cantilever-si Units Final 022615
320/407
0 from the
on
http://accessengineeringlibrary.com/browse/civil-engineering-all-in-one-pe-exam-guide-breadth-and-depth-second-edition/c9780071787727ch102#ch102lev1sec12
8/18/2019 Cantilever-si Units Final 022615
321/407
8/18/2019 Cantilever-si Units Final 022615
322/407
8/18/2019 Cantilever-si Units Final 022615
323/407
8/18/2019 Cantilever-si Units Final 022615
324/407
8/18/2019 Cantilever-si Units Final 022615
325/407
8/18/2019 Cantilever-si Units Final 022615
326/407
8/18/2019 Cantilever-si Units Final 022615
327/407
8/18/2019 Cantilever-si Units Final 022615
328/407
8/18/2019 Cantilever-si Units Final 022615
329/407
8/18/2019 Cantilever-si Units Final 022615
330/407
8/18/2019 Cantilever-si Units Final 022615
331/407
8/18/2019 Cantilever-si Units Final 022615
332/407
8/18/2019 Cantilever-si Units Final 022615
333/407
Combined 'oad Calculations $ + 3nits
Calculation of "oment, +hear, 4eflection, and 5
&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, 6 711,111
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
8/18/2019 Cantilever-si Units Final 022615
334/407
) * S U + T S
)esults o( Calculation
"aximum moment 6
8/18/2019 Cantilever-si Units Final 022615
335/407
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
8/18/2019 Cantilever-si Units Final 022615
336/407
e(lec-
S,ear oment tion
n / 0/ 0/ 0/
0m 0k# 0mm
1 1.11 1.11 1.11 $00
8/18/2019 Cantilever-si Units Final 022615
337/407
1 .91 $=
8/18/2019 Cantilever-si Units Final 022615
338/407
= 7.9 $;/8.;/ 0081.01 $=7.07
=; 7.;7 $919.=1 009.9< $=9.
8/18/2019 Cantilever-si Units Final 022615
339/407
/9 01.1/ $0/07.17 $;/
8/18/2019 Cantilever-si Units Final 022615
340/407
8/18/2019 Cantilever-si Units Final 022615
341/407
8/18/2019 Cantilever-si Units Final 022615
342/407
8/18/2019 Cantilever-si Units Final 022615
343/407
8/18/2019 Cantilever-si Units Final 022615
344/407
8/18/2019 Cantilever-si Units Final 022615
345/407
8/18/2019 Cantilever-si Units Final 022615
346/407
8/18/2019 Cantilever-si Units Final 022615
347/407
8/18/2019 Cantilever-si Units Final 022615
348/407
8/18/2019 Cantilever-si Units Final 022615
349/407
8/18/2019 Cantilever-si Units Final 022615
350/407
8/18/2019 Cantilever-si Units Final 022615
351/407
8/18/2019 Cantilever-si Units Final 022615
352/407
8/18/2019 Cantilever-si Units Final 022615
353/407
8/18/2019 Cantilever-si Units Final 022615
354/407
8/18/2019 Cantilever-si Units Final 022615
355/407
8/18/2019 Cantilever-si Units Final 022615
356/407
8/18/2019 Cantilever-si Units Final 022615
357/407
)e(eren
actions
For a general discussion, including examples, of
diagrams and deflections, see
*uations Use (or T,ese Calculation
where
5oark?s Formulas for +tress and +train, &
Civil &ngineering (ll$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*
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
8/18/2019 Cantilever-si Units Final 022615
358/407
8/18/2019 Cantilever-si Units Final 022615
359/407
8/18/2019 Cantilever-si Units Final 022615
360/407
8/18/2019 Cantilever-si Units Final 022615
361/407
8/18/2019 Cantilever-si Units Final 022615
362/407
8/18/2019 Cantilever-si Units Final 022615
363/407
8/18/2019 Cantilever-si Units Final 022615
364/407
8/18/2019 Cantilever-si Units Final 022615
365/407
8/18/2019 Cantilever-si Units Final 022615
366/407
8/18/2019 Cantilever-si Units Final 022615
367/407
8/18/2019 Cantilever-si Units Final 022615
368/407
8/18/2019 Cantilever-si Units Final 022615
369/407
8/18/2019 Cantilever-si Units Final 022615
370/407
8/18/2019 Cantilever-si Units Final 022615
371/407
8/18/2019 Cantilever-si Units Final 022615
372/407
8/18/2019 Cantilever-si Units Final 022615
373/407
8/18/2019 Cantilever-si Units Final 022615
374/407
8/18/2019 Cantilever-si Units Final 022615
375/407
8/18/2019 Cantilever-si Units Final 022615
376/407
8/18/2019 Cantilever-si Units Final 022615
377/407
8/18/2019 Cantilever-si Units Final 022615
378/407
8/18/2019 Cantilever-si Units Final 022615
379/407
8/18/2019 Cantilever-si Units Final 022615
380/407
8/18/2019 Cantilever-si Units Final 022615
381/407
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*
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
8/18/2019 Cantilever-si Units Final 022615
382/407
arly from superposition.
8/18/2019 Cantilever-si Units Final 022615
383/407
8/18/2019 Cantilever-si Units Final 022615
384/407
8/18/2019 Cantilever-si Units Final 022615
385/407
8/18/2019 Cantilever-si Units Final 022615
386/407
8/18/2019 Cantilever-si Units Final 022615
387/407
Work 8re
8/18/2019 Cantilever-si Units Final 022615
388/407
8/18/2019 Cantilever-si Units Final 022615
389/407
8/18/2019 Cantilever-si Units Final 022615
390/407
8/18/2019 Cantilever-si Units Final 022615
391/407
8/18/2019 Cantilever-si Units Final 022615
392/407
8/18/2019 Cantilever-si Units Final 022615
393/407
8/18/2019 Cantilever-si Units Final 022615
394/407
8/18/2019 Cantilever-si Units Final 022615
395/407
8/18/2019 Cantilever-si Units Final 022615
396/407
8/18/2019 Cantilever-si Units Final 022615
397/407
8/18/2019 Cantilever-si Units Final 022615
398/407
8/18/2019 Cantilever-si Units Final 022615
399/407
8/18/2019 Cantilever-si Units Final 022615
400/407
8/18/2019 Cantilever-si Units Final 022615
401/407
8/18/2019 Cantilever-si Units Final 022615
402/407
8/18/2019 Cantilever-si Units Final 022615
403/407
8/18/2019 Cantilever-si Units Final 022615
404/407
8/18/2019 Cantilever-si Units Final 022615
405/407
;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 $
8/18/2019 Cantilever-si Units Final 022615
406/407
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
8/18/2019 Cantilever-si Units Final 022615
407/407
orkbook,
procedure by
the following:
re the steps:
eam for 'oad0.
a blank worksheet.
have three tables of results:
Top Related