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Second Order Theory of Deflections for the Linear Elastic Isotropic Beams (Polish Version) Prof. Marcin Kami\303\261ski, Ph.D., D.Sc. Chair of Mechanics of Materials, Technical University of \302\243\303\263d\305\270, Al. Politechniki 6, 93-590 \302\243\303\263d\305\270, POLAND email: Marcin.Kaminski@p.lodz.pl, webpage: kmm.p.lodz.pl/pracownicy/Marcin_Kaminski/index.html Abstract: This script has been written to demonstrate a comparison between the first and the second order theories for the elastic isotropic beams deflection. As it is known, the second order theory enables to include directly the influence of the normal forces along the beam on its deflection function. From the mathematical point of view, the differential equation adequate to the deflection function is written on the deformed configuration of this beam, so that the normal forces can play significant role in the beam strength. This script consists of the three parts - the first one describes the classsical deflection determination procedure for the single bay structure clamped at both edges and loaded with the triangular force decreasing from the right to the left end. The extra loading is applied in the form of a concentrated bending moment at the right edge of the beam. The main aim of the second section is to present the procedure related to the second order theory with a compressive force, whereas the third section is devoted to the second order model with tension. Keywords: elastic beams, deflection analysis, internal forces diagrams
<Text-field style="Heading 1" layout="Heading 1"> <Font encoding="UTF-8" family="Arial">Classical solution with no normal force effect - Klasyczne rozwi\302\271zanie bez uwzglednienia wplywu sily normalnej</Font> </Text-field> restart: with(PDEtools): Zapisujemy w pierwszej kolejno\305\223ci funkcj\303\252 obci\302\271\302\277enia ci\302\271glego na belce z:=q-q*x/l; LCZJInFHNiIiIiIqKEYjRiVJInhHRiRGJUkibEdGJCEiIkYp i korzystaj\302\271c z niej, wielko\305\223\303\246 momentu w podporze oraz momentu zginaj\302\271cego w belce Ma:=Mo+Mb+Va*l-1/3*q*l^2; LCpJI01vRzYiIiIiSSNNYkdGJEYlKiZJI1ZhR0YkRiVJImxHRiRGJUYlKiZJInFHRiRGJUYpIiIjIyEiIiIiJA== M(x):=Va*x-Ma-z*x^2/2-1/2*(q-z)*x*2/3*x; LDAqJkkjVmFHNiIiIiJJInhHRiVGJkYmSSNNb0dGJSEiIkkjTWJHRiVGKSomRiRGJkkibEdGJUYmRikqJkkicUdGJUYmRiwiIiMjRiYiIiQqJiwmRi5GJiooRi5GJkYnRiZGLEYpRilGJkYnRi8jRilGLyooRi5GJkYnRjFGLEYpI0YpRjE= Do rozwi\302\271zania r\303\263wnania r\303\263\302\277niczkowego ugi\303\252cia belki potrzebne b\303\252d\302\271 nast\303\252puj\302\271ce warunki brzegowe bc1:=y(0)=0; Ly1JInlHNiI2IyIiIUYn bc2:=D(y)(0)=0; Ly0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInlHRik2IyIiIUYt a samo r\303\263wnanie ma tutaj posta\303\246 r1:=E*J*diff(y(x),x,x)=-M(x); LyooSSJFRzYiIiIiSSJKR0YlRiYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUYpNiQtSSJ5R0YlNiNJInhHRiVGMUYxRiYsMComSSNWYUdGJUYmRjFGJiEiIkkjTW9HRiVGJkkjTWJHRiVGJiomRjRGJkkibEdGJUYmRiYqJkkicUdGJUYmRjkiIiMjRjUiIiQqJiwmRjtGJiooRjtGJkYxRiZGOUY1RjVGJkYxRjwjRiZGPCooRjtGJkYxRj5GOUY1I0YmRj4= a jego rozwi\302\271zanie jest nast\303\252puj\302\271ce: dsolve({r1,bc1,bc2},y(x)); assign(%); Ly1JInlHNiI2I0kieEdGJSwkKipJIkVHRiUhIiJJIkpHRiVGK0kibEdGJUYrLDAqKEkjVmFHRiUiIiJGJyIiJEYtRjFGMSooSSNNb0dGJUYxRi1GMUYnIiIjISIkKihJI01iR0YlRjFGLUYxRidGNUY2KihGMEYxRi1GNUYnRjVGNiooSSJxR0YlRjFGLUYyRidGNUYxKihGO0YxRiciIiVGLUYxI0YrRj0qJkY7RjFGJyIiJiNGMSIjP0YxI0YrIiIn Dodatkowe warunki brzegowe slu\302\277\302\271 tutaj do znalezienia nadliczbowych reakcji bc3:=subs(x=l,y(x))=0; LywkKipJIkVHNiIhIiJJIkpHRiZGJ0kibEdGJkYnLCoqJkkjVmFHRiYiIiJGKSIiJSEiIyomSSNNb0dGJkYtRikiIiQhIiQqJkkjTWJHRiZGLUYpRjJGMyomSSJxR0YmRi1GKSIiJiNGLkY4Ri0jRiciIiciIiE= bc4:=subs(x=l,diff(y(x),x))=0; LywkKipJIkVHNiIhIiJJIkpHRiZGJ0kibEdGJkYnLCoqJkkjVmFHRiYiIiJGKSIiJCEiJComSSNNb0dGJkYtRikiIiMhIicqJkkjTWJHRiZGLUYpRjJGMyomSSJxR0YmRi1GKSIiJSMiIiZGOEYtI0YnIiInIiIh mamy wi\303\252c solve({bc3,bc4},{Va,Mb}); assign(%); PCQvSSNWYUc2IiwkKiZJInFHRiUiIiJJImxHRiVGKSMiIigiIz8vSSNNYkdGJSwmKiZGKEYpRioiIiMjRikiI0lJI01vR0YlISIi a funkcja opisuj\302\271ca lini\303\252 ugi\303\252cia ma posta\303\246 y(x):=simplify(eval(y(x))); LCQqLkkieEc2IiIiI0kicUdGJSIiIiwqKiZJImxHRiVGJkYkRigiIigqJEYrIiIkISIkKiZGJEYmRitGKCEiJiokRiRGLkYoRihJIkVHRiUhIiJJIkpHRiVGNEYrRjQjRjQiJD8i Przyjmujemy konkretne warto\305\223ci parametr\303\263w projektowych w zadaniu l:=10: q:=10: Mo:=20: E:=210*10^6: J:=2140/10^8: y(x):=simplify(eval(y(x))): evalf(y(x)); LCQqJkkieEc2IiIiIywqRiQkIiQrKCIiISQhJStJRioiIiIqJEYkRiYkISNdRioqJEYkIiIkRi1GLSQhKyVHQ1YmPSEjOg== sporz\302\271dzamy kolejno wykresy ugi\303\252cia, k\302\271ta ugi\303\252cia, momentu gn\302\271cego oraz siy tn\302\271cej deflection:=unapply(y(x)*E*J,x): moment:=unapply((diff(y(x),x,x),x)): shear:=unapply((diff(y(x),x,x,x),x)): plot(-y(x),x=0..l,color=black , thickness=2,title="Linia ugi\303\252cia belki", tickmarks=[10,10],axes=boxed,font=[TIMES, BOLD, 16]); 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 plot(diff(y(x),x),x=0..l,color=black,thickness=2,title="Wykres k\302\271ta ugi\303\252cia belki",tickmarks=[10,10],axes=boxed,font=[TIMES, BOLD, 16]); 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 plot(E*J*diff(y(x),x,x),x=0..l,color=black,thickness=2,title="Wykres moment\303\263w zginaj\302\271cych",tickmarks=[10,10],axes=boxed,font=[TIMES, BOLD, 16]); 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 plot(E*J*diff(y(x),x,x,x),x=0..l,color=black,thickness=2,title="Wykres sily tn\302\271cej",tickmarks=[10,10],axes=boxed,font=[TIMES, BOLD, 16]); NiwtJSdDVVJWRVNHNiM3UzckJCIiISEiIiQhJF0kISIiNyQkIjJtbW1tVDooekAhIzwkITFoQCl6Li9XRyQhIzk3JCQiMk5MTGU5dWkyJSEjPCQhMWhFKDNmIW8rSiEjOTckJCIxbm1tInpfIjRpISM7JCEyWFlHK15oJCkqRyEjOjckJCIxb21tVCZwaE4pISM7JCExc3lgSWVIKnAjISM5NyQkIjJMTCRlKj0pSFw1ISM7JCEyKDQpXFw5YGRdIyEjOjckJCIybm07ei8zdUMiISM7JCEybHAkKVJIJFJJQiEjOjckJCItREokUkRYIiEjNiQhMig0OT4lPmFIOiMhIzo3JCQiMm9tO3pSJ29rOyEjOyQhMjx4YEFrc1EoPiEjOjckJCItRDFKOnc9ISM2JCEya2Rhd1RXKSp6IiEjOjckJCIyUExMJDNFbiQ0IyEjOyQhMUo0QFQxXUQ7ISM5NyQkIjFubTsvUkUmRyMhIzokITJvbzw5bGRlWiIhIzo3JCQiMi4rK11LXTRdIyEjOyQhMCllUyx0eTY4ISM4NyQkIit2Ql88RiEiKiQhMj1HSnosQzw6IiEjOjckJCIrdidIaSNIISIqJCEyKUhEYUk4Ij4rIiEjOjckJCIxbm0ieipldjpKISM6JCExeVhgRyUza3ApISM6NyQkIjJOTEwkMzQ3VEwhIzskITFaeHJ5YExxciEjOjckJCIyUExMTGpNP2AkISM7JCExTSgqPiMqekc8ZiEjOjckJCItRCJvN1R2JCEjNiQhMUY1RSo+YWJdJSEjOjckJCIxTExMJFEqb11SISM6JCEyWC1lJW8lenFIJCEjOzckJCIxLCtEIj1sajslISM6JCEyKG9oRSpmWmMsIyEjOzckJCItdlYmUjxQJSEjNiQhMXRzJHAiKXlsUSkhIzs3JCQiMU1MJGU5RWdlJSEjOiQiMWsnKSo+YE5XVyQhIzs3JCQiMk5MJGVSIjNHeSUhIzskIjJPLyxlYWEvUiIhIzs3JCQiMW5tOy9UMSYqXCEjOiQiMjxcKkhSJDNgWiMhIzs3JCQiMW5tInpSUWJAJiEjOiQiMlk0JjQqZWpXYiQhIzs3JCQiLXY9PlkyYSEjNiQiMSlHTWgpcEhhVyEjOjckJCIydm1tInpYdTljISM7JCIxUWYtWnV3JVEmISM6NyQkIiomeSkpR2UhIikkIjA+aGdyNjRJJyEjOTckJCIsREUmUVFnISM1JCIxMDkiZUwvRzooISM6NyQkIjIwK103eSUzVGkhIzskIjFFWzcqPXlfJHohIzo3JCQiLHYuW2hZJyEjNSQiMVp1Y2BeJWZ2KSEjOjckJCIxTExMJFF4JG9tISM6JCIxeXYwcWA5XSUqISM6NyQkIjIwKytdUCtWKW8hIzskIjJNdVFCej9ZLCIhIzo3JCQiMW1tInpwZSp6cSEjOiQiMk5QMShSem10NSEjOjckJCIxLCsrRFwnUUgoISM6JCIydnQjelo7JVE4IiEjOjckJCIxTExlOVM4JlwoISM6JCIyKEhedj5CRyc9IiEjOjckJCIxLCtEMSM9YnEoISM6JCIyJCpbMlxtbm5CIiEjOjckJCIxTExMM3M/NnohIzokIjIob1NuTHMlPUciISM6NyQkIi1ESlhhRSIpISM2JCIyYWBJLkIzWEsiISM6NyQkIjFvbW1tKlJSTCkhIzokIjJzWW0jKT43N08iISM6NyQkIjFvbTthPC5ZJikhIzokIjJ2VDBxIikpSCVSIiEjOjckJCIxTkxlOXRPYygpISM6JCIxbiIpPSgpKW9FVSIhIzk3JCQiMSwrK11Ra1wqKSEjOiQiMiJmeSF6ZlBbVyIhIzo3JCQiMU5MJDNkZzY8KiEjOiQiMlkkSC5nN2xsOSEjOjckJCIxb21tbXhHcCQqISM6JCIxJT1PUjU1LFsiISM5NyQkIi1EIm9LMGUqISM2JCIyUS5EJWVCPyJcIiEjOjckJCIxLCt2PTVzI3kqISM6JCIyJltgQCNcUndcIiEjOjckJCIkKyIhIiIkIiRdIiEiIi0lJVZJRVdHNiQ7JCIiISEiIiQiJCsiISIiJShERUZBVUxURy0lKkFYRVNUSUNLU0c2JCIjNSIjNS0lJlRJVExFRzYkLSUpX1RZUEVTRVRHNiMtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliRzYiNjYtSSNtc0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjYjUThXeWtyZXN+c2lseX50biYjMTg1O2NlajYiLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuNiIvJSVzaXplR1EjMTY2Ii8lJWJvbGRHUSV0cnVlNiIvJSdpdGFsaWNHUSZmYWxzZTYiLyUqdW5kZXJsaW5lR1EmZmFsc2U2Ii8lKnN1YnNjcmlwdEdRJmZhbHNlNiIvJSxzdXBlcnNjcmlwdEdRJmZhbHNlNiIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXTYiLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV02Ii8lJ29wYXF1ZUdRJmZhbHNlNiIvJStleGVjdXRhYmxlR1EmZmFsc2U2Ii8lKXJlYWRvbmx5R1EmZmFsc2U2Ii8lKWNvbXBvc2VkR1EmZmFsc2U2Ii8lKmNvbnZlcnRlZEdRJmZhbHNlNiIvJStpbXNlbGVjdGVkR1EmZmFsc2U2Ii8lLHBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdRJmZhbHNlNiIvJSxtYXRodmFyaWFudEdRJWJvbGQ2Ii8lK2ZvbnR3ZWlnaHRHUSVib2xkNiItJS1UUkFOU1BBUkVOQ1lHNiMkIiIhISIiLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIiEhIiItJSpUSElDS05FU1NHNiMiIiMtJSVGT05URzYlJTBUaW1lc35OZXd+Um9tYW5HJSVCT0xERyIjOy0lKkFYRVNTVFlMRUc2IyUkQk9YRy0lKFNDQUxJTkdHNiMlLlVOQ09OU1RSQUlORURHLSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIkPyYhIiItJSlCT1VORFNfWUc2IyQiJCFSISIiLSUtQk9VTkRTX1dJRFRIRzYjJCIlIUglISIiLSUuQk9VTkRTX0hFSUdIVEc2IyQiJVNSISIiLSUpQ0hJTERSRU5HNiI= Znajdujemy kolejno miejsce zerowania sie sily tn\302\271cej x1:=fsolve(diff(y(x),x,x,x)=0,x); NiQkIitEV3hBWCEiKiQiK2VEc1o6ISIp w celu okreslenia miejsca wystepowania maksymalnego momentu gnacego Mmax:=evalf(moment(x1)*E*J); JCErVEEqUTkjISIp a w dalszej kolejno\305\223ci obliczamy wielko\305\223ci momentow w utwierdzeniu i tulei Ma:=evalf(moment(0.0)*E*J); JCIrLSsrK10hIik= Mb:=evalf(moment(l)*E*J); JCIrTExMTEwhIik= oraz odpowiadaj\302\271ce im reakcje pionowe Va:=evalf(shear(0.0)*E*J); JCErLCsrK04hIik= Vb:=evalf(shear(l)*E*J); JCIjOiIiIQ== Ostatecznie obliczamy miejsce zerowania si\303\252 k\302\271ta ugi\303\252cia x2:=fsolve(diff(y(x),x)=0,x=1..(l-1)); JCIrTSNcSXYlISIq dla okreslenia maksymalnego ugi\303\252cia rozpatrywanej belki ymax:=evalf(deflection(x2)/E/J); JCIrRVV1NkghIzY=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8" family="Arial"> Second order solution with the compressive force - Rozwi\302\271zanie drugiego rz\303\252du z uwzgl\303\252dnieniem sily \305\223ciskaj\302\271cej </Font></Text-field> restart: with(PDEtools): Zapisujemy w pierwszej kolejno\305\223ci funkcj\303\252 obci\302\271\302\277enia ci\302\271glego na belce z:=q-q*x/l; LCZJInFHNiIiIiIqKEYjRiVJInhHRiRGJUkibEdGJCEiIkYp i korzystaj\302\271c z niej, wielko\305\223\303\246 momentu w podporze oraz momentu zginaj\302\271cego w belce Ma:=Mo+Mb+Va*l-1/3*q*l^2; LCpJI01vRzYiIiIiSSNNYkdGJEYlKiZJI1ZhR0YkRiVJImxHRiRGJUYlKiZJInFHRiRGJUYpIiIjIyEiIiIiJA== M(x):=Va*x-Ma-z*x^2/2-1/2*(q-z)*x*2/3*x+N*y(x); LDIqJkkjVmFHNiIiIiJJInhHRiVGJkYmSSNNb0dGJSEiIkkjTWJHRiVGKSomRiRGJkkibEdGJUYmRikqJkkicUdGJUYmRiwiIiMjRiYiIiQqJiwmRi5GJiooRi5GJkYnRiZGLEYpRilGJkYnRi8jRilGLyooRi5GJkYnRjFGLEYpI0YpRjEqJkkiTkdGJUYmLUkieUdGJTYjRidGJkYm Do rozwi\302\271zania r\303\263wnania r\303\263\302\277niczkowego ugi\303\252cia belki potrzebne b\303\252d\302\271 nast\303\252puj\302\271ce warunki brzegowe bc1:=y(0)=0; Ly1JInlHNiI2IyIiIUYn bc2:=D(y)(0)=0; Ly0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInlHRik2IyIiIUYt a samo r\303\263wnanie ma tutaj posta\303\246 r1:=E*J*diff(y(x),x,x)=-M(x); LyooSSJFRzYiIiIiSSJKR0YlRiYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUYpNiQtSSJ5R0YlNiNJInhHRiVGMUYxRiYsMiomSSNWYUdGJUYmRjFGJiEiIkkjTW9HRiVGJkkjTWJHRiVGJiomRjRGJkkibEdGJUYmRiYqJkkicUdGJUYmRjkiIiMjRjUiIiQqJiwmRjtGJiooRjtGJkYxRiZGOUY1RjVGJkYxRjwjRiZGPCooRjtGJkYxRj5GOUY1I0YmRj4qJkkiTkdGJUYmRi5GJkY1 a jego rozwi\302\271zanie jest nast\303\252puj\302\271ce: dsolve({r1,bc1,bc2},y(x)); assign(%); 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 Dodatkowe warunki brzegowe slu\302\277\302\271 tutaj do znalezienia nadliczbowych reakcji bc3:=subs(x=l,y(x))=0; 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 bc4:=subs(x=l,diff(y(x),x))=0; LywoKiotSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyoqSSJFR0YqIyEiIiIiI0kiSkdGKkYuSSJOR0YqIyIiIkYwSSJsR0YqRjRGNEYyISIjLCYqKEYyRjRJI1ZhR0YqRjRGNUY0Ri8qKEYtRjRGMUY0SSJxR0YqRjRGNEY0RjVGL0YvKiwtSSRzaW5HRidGK0Y0Ri1GLkYxRi5GMiMhIiRGMCwsKihGMkY0RjtGNEY1RjBGNEY4RkAqJkYyRjRJI01vR0YqRjRGQComRjJGNEkjTWJHRipGNEZARjoiIiRGNCNGL0ZHKigsKCooLCZGOSEiJyomRjtGNEY1RjQiIidGNEYyRjRGNUY0RjRGQkZARjpGT0Y0RjJGNkY1Ri8jRjRGTyIiIQ== mamy wi\303\252c solve({bc3,bc4},{Va,Mb}); assign(%); 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 a funkcja opisuj\302\271ca lini\303\252 ugi\303\252cia ma posta\303\246 y(x):=simplify(eval(y(x))); 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 Przyjmujemy konkretne warto\305\223ci parametr\303\263w projektowych w zadaniu l:=10: q:=10: Mo:=20: E:=210*10^6: J:=2140/10^8: N:=100: y(x):=simplify(eval(y(x))): evalf(y(x)); LC4tSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkSSJ4R0YoJCIrKHkxPFwiISM1JCIrLEFLd1IhIiokISssQUt3UkYxIiIiKiRGKyIiIyQiKy8rKytdISM2LUkkc2luR0YlRikkISskWylIWG1GLiokRisiIiQkIStubW1tOyEjN0YrJCIrSXEkRyIqKkY5 sporz\302\271dzamy kolejno wykresy ugi\303\252cia, k\302\271ta ugi\303\252cia, momentu gn\302\271cego oraz siy tn\302\271cej deflection:=unapply(y(x)*E*J,x): moment:=unapply((diff(y(x),x,x),x)): shear:=unapply((diff(y(x),x,x,x),x)): plot(-y(x),x=0..l,color=green , thickness=2,title="Linia ugi\303\252cia belki", tickmarks=[10,10],axes=boxed,font=[TIMES, BOLD, 16]); 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 plot(diff(y(x),x),x=0..l,color=green,thickness=2,title="Wykres k\302\271ta ugi\303\252cia belki",tickmarks=[10,10],axes=boxed,font=[TIMES, BOLD, 16]); 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 plot(E*J*diff(y(x),x,x),x=0..l,color=green,thickness=2,title="Wykres moment\303\263w zginaj\302\271cych",tickmarks=[10,10],axes=boxed,font=[TIMES, BOLD, 16]); 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 plot(E*J*diff(y(x),x,x,x),x=0..l,color=green,thickness=2,title="Wykres sily tn\302\271cej",tickmarks=[10,10],axes=boxed,font=[TIMES, BOLD, 16]); 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 Znajdujemy kolejno miejsce zerowania sie sily tn\302\271cej x1:=fsolve(diff(y(x),x,x,x)=0,x); JCIrTnVrWlghIio= w celu okreslenia miejsca wystepowania maksymalnego momentu gnacego Mmax:=evalf(moment(x1)*E*J); JCErYCJ5akcjISIp a w dalszej kolejno\305\223ci obliczamy wielko\305\223ci momentow w utwierdzeniu i tulei Ma:=evalf(moment(0.0)*E*J); JCIrYiF5bjwmISIp Mb:=evalf(moment(l)*E*J); JCIrQCJbSFskISIp oraz odpowiadaj\302\271ce im reakcje pionowe Va:=evalf(shear(0.0)*E*J); JCErQGpyLU4hIik= Vb:=evalf(shear(l)*E*J); JCIrdU9HKFwiISIp Ostatecznie obliczamy miejsce zerowania si\303\252 k\302\271ta ugi\303\252cia x2:=fsolve(diff(y(x),x)=0,x=1..(l-1)); JCIrSyJcPXclISIq dla okreslenia maksymalnego ugi\303\252cia rozpatrywanej belki ymax:=evalf(deflection(x2)/E/J); JCIrXCxXIzMkISM2
<Text-field style="Heading 1" layout="Heading 1"> <Font encoding="UTF-8" family="Arial">Second order solution with tension - Rozwi\302\271zanie drugiego rz\303\252du z sil\302\271 rozci\302\271gaj\302\271c\302\271 </Font></Text-field> restart: with(PDEtools): Zapisujemy w pierwszej kolejno\305\223ci funkcj\303\252 obci\302\271\302\277enia ci\302\271glego na belce z:=q-q*x/l; LCZJInFHNiIiIiIqKEYjRiVJInhHRiRGJUkibEdGJCEiIkYp i korzystaj\302\271c z niej, wielko\305\223\303\246 momentu w podporze oraz momentu zginaj\302\271cego w belce Ma:=Mo+Mb+Va*l-1/3*q*l^2; LCpJI01vRzYiIiIiSSNNYkdGJEYlKiZJI1ZhR0YkRiVJImxHRiRGJUYlKiZJInFHRiRGJUYpIiIjIyEiIiIiJA== M(x):=Va*x-Ma-z*x^2/2-1/2*(q-z)*x*2/3*x-N*y(x); LDIqJkkjVmFHNiIiIiJJInhHRiVGJkYmSSNNb0dGJSEiIkkjTWJHRiVGKSomRiRGJkkibEdGJUYmRikqJkkicUdGJUYmRiwiIiMjRiYiIiQqJiwmRi5GJiooRi5GJkYnRiZGLEYpRilGJkYnRi8jRilGLyooRi5GJkYnRjFGLEYpI0YpRjEqJkkiTkdGJUYmLUkieUdGJTYjRidGJkYp Do rozwi\302\271zania r\303\263wnania r\303\263\302\277niczkowego ugi\303\252cia belki potrzebne b\303\252d\302\271 nast\303\252puj\302\271ce warunki brzegowe bc1:=y(0)=0; Ly1JInlHNiI2IyIiIUYn bc2:=D(y)(0)=0; Ly0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInlHRik2IyIiIUYt a samo r\303\263wnanie ma tutaj posta\303\246 r1:=E*J*diff(y(x),x,x)=-M(x); LyooSSJFRzYiIiIiSSJKR0YlRiYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUYpNiQtSSJ5R0YlNiNJInhHRiVGMUYxRiYsMiomSSNWYUdGJUYmRjFGJiEiIkkjTW9HRiVGJkkjTWJHRiVGJiomRjRGJkkibEdGJUYmRiYqJkkicUdGJUYmRjkiIiMjRjUiIiQqJiwmRjtGJiooRjtGJkYxRiZGOUY1RjVGJkYxRjwjRiZGPCooRjtGJkYxRj5GOUY1I0YmRj4qJkkiTkdGJUYmRi5GJkYm a jego rozwi\302\271zanie jest nast\303\252puj\302\271ce: dsolve({r1,bc1,bc2},y(x)); assign(%); 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 Dodatkowe warunki brzegowe slu\302\277\302\271 tutaj do znalezienia nadliczbowych reakcji bc3:=subs(x=l,y(x))=0; 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 bc4:=subs(x=l,diff(y(x),x))=0; 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 mamy wi\303\252c solve({bc3,bc4},{Va,Mb}); assign(%); 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 a funkcja opisuj\302\271ca lini\303\252 ugi\303\252cia ma posta\303\246 y(x):=simplify(eval(y(x))); 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 Przyjmujemy konkretne warto\305\223ci parametr\303\263w projektowych w zadaniu l:=10: q:=10: Mo:=20: E:=210*10^6: J:=2140/10^8: N:=100: y(x):=simplify(eval(y(x))): evalf(y(x)); LDJJInhHNiIkIitRWlQiKnohIzUqJEYjIiIjJCErKikqKioqKipcISM2KiRGIyIiJCQiK2ltbW07ISM3LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJkYjJCIrKHkxPFwiRickRjohIioiIiIkIStrK0hwUkYnLUYzNiMsJkYjJCErKHkxPFwiRidGO0Y9JCIrMnIwIz0iRjwtRjM2IywmRiNGQyQiK3ZOVCQpSEY8Rj0kISsnemJcTyVGMSQhK0UtLnlcRjxGPS1GMzYjLCRGI0Y5JCIrZTZpdTpGPA== sporz\302\271dzamy kolejno wykresy ugi\303\252cia, k\302\271ta ugi\303\252cia, momentu gn\302\271cego oraz siy tn\302\271cej deflection:=unapply(y(x)*E*J,x): moment:=unapply((diff(y(x),x,x),x)): shear:=unapply((diff(y(x),x,x,x),x)): plot(-y(x),x=0..l,color=blue , thickness=2,title="Linia ugi\303\252cia belki", tickmarks=[10,10],axes=boxed,font=[TIMES, BOLD, 16]); 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 plot(diff(y(x),x),x=0..l,color=blue,thickness=2,title="Wykres k\302\271ta ugi\303\252cia belki",tickmarks=[10,10],axes=boxed,font=[TIMES, BOLD, 16]); 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 plot(E*J*diff(y(x),x,x),x=0..l,color=blue,thickness=2,title="Wykres moment\303\263w zginaj\302\271cych",tickmarks=[10,10],axes=boxed,font=[TIMES, BOLD, 16]); 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 plot(E*J*diff(y(x),x,x,x),x=0..l,color=blue,thickness=2,title="Wykres sily tn\302\271cej",tickmarks=[10,10],axes=boxed,font=[TIMES, BOLD, 16]); 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 Znajdujemy kolejno miejsce zerowania sie sily tn\302\271cej x1:=fsolve(diff(y(x),x,x,x)=0,x); JCIrcSZbelwlISIq w celu okreslenia miejsca wystepowania maksymalnego momentu gnacego Mmax:=evalf(moment(x1)*E*J); JCErQihIcywjISIp a w dalszej kolejno\305\223ci obliczamy wielko\305\223ci momentow w utwierdzeniu i tulei Ma:=evalf(moment(0.0)*E*J); JCIrO0lJU1shIik= Mb:=evalf(moment(l)*E*J); JCIrbyMpWyo+JCEiKQ== oraz odpowiadaj\302\271ce im reakcje pionowe Va:=evalf(shear(0.0)*E*J); JCErdlpUKFwkISIp Vb:=evalf(shear(l)*E*J); JCIrIj4mZS06ISIp Ostatecznie obliczamy miejsce zerowania si\303\252 k\302\271ta ugi\303\252cia x2:=fsolve(diff(y(x),x)=0,x=1..(l-1)); JCIrPSkqZVdaISIq dla okreslenia maksymalnego ugi\303\252cia rozpatrywanej belki ymax:=evalf(deflection(x2)/E/J); JCIrQW5BZkYhIzY=
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