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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 13 "Question 4.8:" }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 289 "A simply sup
ported nonmetallic beam of 0.25 m height, 0.1 m width and 1.5 m span i
s subjected to a uniform loading of 6 KN/m.Determine the factor of saf
ety for this loading according  to (a)the maximum distortion energy th
eory and (b) the maximum shearing stress theory.Use sigmayp= 28MPa." }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 8 "Solution" }
{TEXT -1 1 ":" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "sigmayp:=28*10^6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%(sigmaypG\")+++G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "This beam i
s being subjected to two different types of stresses: bending and shea
r" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "sig
mab:=-(M*y)/i;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'sigmabG,$*(%\"M
G\"\"\"%\"yGF(%\"iG!\"\"F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "Her
e,\"y\"is the distance of the fiber from the neutral axis." }{MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "tau:=sf/area;\n
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$tauG*&%#sfG\"\"\"%%areaG!\"\"" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "area:=b*h;\n" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%%areaG*&%\"bG\"\"\"%\"hGF'" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 74 "The bending moment at any cross-section distanc
e \"x\" from the left end is:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 21 "M:=-w*l/2*x+w*x*x/2;\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"MG,&*&#\"\"\"\"\"#F(*(%\"wGF(%\"lGF(%\"xGF(F(!\"\"*
&#F(F)F(*&F+F()F-F)F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "i:=(b*h^3)/12;\n" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG,$*(\"#7!\"\"%\"bG\"\"\"%\"hG\"
\"$F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "sigma1:=(sigmab/2)
+((sigmab/2)^2+tau^2)^(1/2);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'s
igma1G,&*,\"\"'\"\"\",&*&#F(\"\"#F(*(%\"wGF(%\"lGF(%\"xGF(F(!\"\"*&#F(
F,F(*&F.F()F0F,F(F(F(F(%\"yGF(%\"bGF1%\"hG!\"$F1*&F,F1,&*,\"#sF(F)F,F6
F,F7!\"#F8!\"'F(**\"\"%F(%#sfGF,F7F>F8F>F(F3F(" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 47 "sigma2:=(sigmab/2)-((sigmab/2)^2+tau^2)^(1/2);
\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'sigma2G,&*,\"\"'\"\"\",&*&#F(
\"\"#F(*(%\"wGF(%\"lGF(%\"xGF(F(!\"\"*&#F(F,F(*&F.F()F0F,F(F(F(F(%\"yG
F(%\"bGF1%\"hG!\"$F1*&F,F1,&*,\"#sF(F)F,F6F,F7!\"#F8!\"'F(**\"\"%F(%#s
fGF,F7F>F8F>F(F3F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "b:=0.1
;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG$\"\"\"!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "h:=0.25;\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"hG$\"#D!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 8 "l:=1.5;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG$\"#:!\"\"" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 104 "Combine the pricipal stress in
to von-mises stress so that we can apply maximum distortion energy the
ory." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "
sigmav:=((sigma1^2)+(sigma2^2)-(sigma1*sigma2))^(1/2);\n" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#>%'sigmavG*$,(*$),&*($\"++++SQ!\"'\"\"\",&*($\"+
++++v!#5F.%\"wGF.%\"xGF.!\"\"*&#F.\"\"#F.*&F4F.)F5F9F.F.F.F.%\"yGF.F6*
&F9F6,&*($\"+++7\\H!\"#F.)F/F9F.)F<F9F.F.*&$\"+++++kF-F.)%#sfGF9F.F.F8
F.F9F.F.*$),&*($\"++++SQF-F.F/F.F<F.F6*&F9F6F>F8F6F9F.F.*&F)F.FLF.F6F8
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 10 "x:=1.5/2;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%\"xG$\"+++++v!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "sf:=
0;\ntau:=0;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#sfG\"\"!" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$tauG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "w:=6000;
\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"%+g" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 
"y:=h/2;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG$\"++++]7!#5" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "sigma1/10^6;\n" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#$\"+$\\cFQ\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "sigma2/10^6;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"
+q]VsB!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "sigmav/10^6;\n
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+`Cs!G\"!\"*" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 22 "fos1:=sigmayp/sigmav;\n" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%%fos1G$\"+OgE'=#!\")" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "taumax:=(sigma1+sigma2)/2;\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%'taumaxG$\"+++++\")!\"%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "fos2:=sigmayp/(2*taumax);\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%fos2G$\"+i]RG<!\")" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 1 "\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "x:=0;
\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG\"\"!" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 13 "sf:=(w*l)/2;\n" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#sfG$\"+++++X!\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
14 "tau:=sf/area;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$tauG$\"+++++
=!\"%" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "y
:=h/2;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG$\"++++]7!#5" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sigmab;\n" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#$\"\"!F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 
"sigma1;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+++++=!\"%" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sigma2;\n" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#$!+++++=!\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 8 "sigmav;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+a9p<J!\"%" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 163 "Note that this taumax is differen
t from the tau existing at that cross-section.Since, we note that the \+
principal stressea are opposite in sign, we write taumax as:" }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "taumax:
=sigma1-sigma2;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'taumaxG$\"++++
+O!\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "fos3:=sigmayp/sig
mav;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%fos3G$\"+'=/5)*)!\")" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "fos4:=sigmayp/(2*taumax);\n
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%fos4G$\"+*)))))))Q!\")" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "\n\n" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 1 " " }{TEXT 256 12 "Final answer" }{TEXT -1 13 " :  FOS= \+
17.3" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0 0" 10 }{VIEWOPTS 1 1 
0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }