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Catégorie :Category: mViewer GX Creator App HP-Prime
Auteur Author: mathijsbaks
Type : Application
Page(s) : 16
Taille Size: 614.31 Ko KB
Mis en ligne Uploaded: 14/01/2021 - 14:40:17
Uploadeur Uploader: mathijsbaks (Profil)
Téléchargements Downloads: 3
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a2680293
Type : Application
Page(s) : 16
Taille Size: 614.31 Ko KB
Mis en ligne Uploaded: 14/01/2021 - 14:40:17
Uploadeur Uploader: mathijsbaks (Profil)
Téléchargements Downloads: 3
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a2680293
Description
MEMECH2.2, Jaar 2020-2021: week 5 Dr. ir. A.J.M. Sipers
????
Vervorming t.g.v. torsiemoment
???????? ????
???? ????
Δ???? ????????
???????? ????
???? ???? ????
???? ???? ????
????????
Hoekverandering:
????
Δ???? = ???????? − ???????? =
????
Stijfheid (veerconstante):
???? ∙ ????????
????=
????
Van de buis ???????? is gegeven de inwendige straal ???????? = 5 mm, de uitwendige straal ???????? = 15 mm en
???? = 60 kN/mm2 . ????
????
10 mm
400 Nm 450 Nm 150 Nm ???? 5 mm
???? ????
5 mm
???? ???? ???? ????
300 mm 400 mm 300 mm
10 mm
Het polair traagheidsmoment van de dwarsdoorsnede is:
???? ????
???????? = ∙ (????????4 − ????????4 ) = ∙ ( 154 − 54 ) = 25000 ∙ ???? mm4
2 2
De stijfheden van de delen ???????? , ???????? en ???????? zijn:
????∙???????? (60)∙(25000∙????)
???????????? = = = 5000 ∙ ???? Nm/rad
???????????? 300
????∙???????? (60)∙(25000∙????)
???????????? = = = 3750 ∙ ???? Nm/rad
???????????? 400
????∙???????? (60)∙(25000∙????)
???????????? = = = 5000 ∙ ???? Nm/rad
???????????? 300
a) Bepaal de rotatie ???????? [rad] van de dwarsdoorsnede bij punt ????.
b) Bepaal de rotatie ???????? [rad] van de dwarsdoorsnede bij punt ???? .
c) Bepaal de rotatie ???????? [rad] van de dwarsdoorsnede bij punt ????.
Oplossing:
???????? 400 Nm 450 Nm 150 Nm
???? ???? ???? ????
300 mm 400 mm 300 mm
MEMECH2.2, Jaar 2020-2021: week 5 Dr. ir. A.J.M. Sipers
Evenwicht van buis ???????? .
∑ ???????? = 0:
+???????? − 400 + 450 − 150 = 0
???????? − 100 = 0
???????? = 100 Nm
100 Nm 400 Nm 450 Nm 150 Nm
???? ???? ???? ????
300 mm 400 mm 300 mm
Snede bij ????, 0 < ???? < 300 mm
????(????) ????(????) 400 Nm 450 Nm 150 Nm
100 Nm
???? ???? ???? ???? 400 mm ???? 300 mm ????
???? mm 1000 − ???? mm
Evenwicht van deel ????????.
∑ ???????? = 0:
+????(????) + 100 = 0
????(????) + 100 = 0
????(????) = −100 Nm
Evenwicht van deel ???????? .
∑ ???????? = 0:
−????(????) − 400 + 450 − 150 = 0
−100 = ????(????)
????(????) = −100 Nm
Snede bij ????, 300 < ???? < 700 mm
400 Nm ????(????) ????(????) 450 Nm 150 Nm
100 Nm
???? 300 mm ???? ???? ???? ???? 300 mm ????
???? mm 1000 − ???? mm
Evenwicht van deel ????????.
∑ ???????? = 0:
+????(????) + 100 − 400 = 0
????(????) − 300 = 0
????(????) = +300 Nm
Evenwicht van deel ???????? .
∑ ???????? = 0:
−????(????) + 450 − 150 = 0
300 = ????(????)
????(????) = +300 Nm
MEMECH2.2, Jaar 2020-2021: week 5 Dr. ir. A.J.M. Sipers
Snede bij ????, 700 < ???? < 1000 mm
400 Nm 450 Nm ????(????) 150 Nm
100 Nm ????(????)
???? 300 mm ???? 400 mm ???? ???? ???? ????
1000 − ???? mm
???? mm
Evenwicht van deel ????????.
∑ ???????? = 0:
+????(????) + 100 − 400 + 450 = 0
????(????) + 150 = 0
????(????) = −150 Nm
Evenwicht van deel ???????? .
∑ ???????? = 0:
−????(????) − 150 = 0
−150 = ????(????)
????(????) = −150 Nm
Torsiemomentfunctie ????(????)
−100, 0 < ???? < 300 mm
????(????) = { +300, 300 < ???? < 700 mm Nm
−150, 700 < ???? < 1000 mm
400
300
200
100 400 Nm
450 Nm
0
100 200 300 400 500 600 700 800 900 1000
100 Nm
100
150 Nm
200
300
400
MEMECH2.2, Jaar 2020-2021: week 5 Dr. ir. A.J.M. Sipers
Vervormingen:
400 Nm 450 Nm 150 Nm
100 Nm
???? ???? ???? ????
???????? ???????? ???????? ????????
???????? = 0
???? −100
???????? − ???????? = ???????? =
???????????? ????????????
???? +300
???????? − ???????? = ???????? =
???????????? ????????????
???? −150
???????? − ???????? = ???????? =
???????????? ????????????
+
100 100 −20
???????? = − =− = rad
???????????? 5000 ∙ ???? 1000 ∙ ????
100 300 100 300 +60
???????? = − + =− + = rad
???????????? ???????????? 5000 ∙ ???? 3750 ∙ ???? 1000 ∙ ????
100 300 150 100 300 150 +30
???????? = − + − =− + − = rad
???????????? ???????????? ???????????? 5000 ∙ ???? 3750 ∙ ???? 5000 ∙ ???? 1000 ∙ ????
−20 ????
???????? = < 0 rad
1000 ∙ ????
????
+60
???????? = 1000∙???? > 0 rad
????
????
+30
???????? = 1000∙???? > 0 rad ????
????
MEMECH2.2, Jaar 2020-2021: week 5 Dr. ir. A.J.M. Sipers
De waarden van de schuifspanning ???? = ???? ∙ ????/???????? in een dwarsdoorsnede van deel ???????? voldoen aan:
???????????????? ≤ ???? ≤ ????????????????
a) Bepaal de ondergrens ???????????????? [N/mm2 ].
b) Bepaal de bovengrens ???????????????? [N/mm2 ].
???????????? ∙???? −100∙103 4
????(????) = = ...
????
Vervorming t.g.v. torsiemoment
???????? ????
???? ????
Δ???? ????????
???????? ????
???? ???? ????
???? ???? ????
????????
Hoekverandering:
????
Δ???? = ???????? − ???????? =
????
Stijfheid (veerconstante):
???? ∙ ????????
????=
????
Van de buis ???????? is gegeven de inwendige straal ???????? = 5 mm, de uitwendige straal ???????? = 15 mm en
???? = 60 kN/mm2 . ????
????
10 mm
400 Nm 450 Nm 150 Nm ???? 5 mm
???? ????
5 mm
???? ???? ???? ????
300 mm 400 mm 300 mm
10 mm
Het polair traagheidsmoment van de dwarsdoorsnede is:
???? ????
???????? = ∙ (????????4 − ????????4 ) = ∙ ( 154 − 54 ) = 25000 ∙ ???? mm4
2 2
De stijfheden van de delen ???????? , ???????? en ???????? zijn:
????∙???????? (60)∙(25000∙????)
???????????? = = = 5000 ∙ ???? Nm/rad
???????????? 300
????∙???????? (60)∙(25000∙????)
???????????? = = = 3750 ∙ ???? Nm/rad
???????????? 400
????∙???????? (60)∙(25000∙????)
???????????? = = = 5000 ∙ ???? Nm/rad
???????????? 300
a) Bepaal de rotatie ???????? [rad] van de dwarsdoorsnede bij punt ????.
b) Bepaal de rotatie ???????? [rad] van de dwarsdoorsnede bij punt ???? .
c) Bepaal de rotatie ???????? [rad] van de dwarsdoorsnede bij punt ????.
Oplossing:
???????? 400 Nm 450 Nm 150 Nm
???? ???? ???? ????
300 mm 400 mm 300 mm
MEMECH2.2, Jaar 2020-2021: week 5 Dr. ir. A.J.M. Sipers
Evenwicht van buis ???????? .
∑ ???????? = 0:
+???????? − 400 + 450 − 150 = 0
???????? − 100 = 0
???????? = 100 Nm
100 Nm 400 Nm 450 Nm 150 Nm
???? ???? ???? ????
300 mm 400 mm 300 mm
Snede bij ????, 0 < ???? < 300 mm
????(????) ????(????) 400 Nm 450 Nm 150 Nm
100 Nm
???? ???? ???? ???? 400 mm ???? 300 mm ????
???? mm 1000 − ???? mm
Evenwicht van deel ????????.
∑ ???????? = 0:
+????(????) + 100 = 0
????(????) + 100 = 0
????(????) = −100 Nm
Evenwicht van deel ???????? .
∑ ???????? = 0:
−????(????) − 400 + 450 − 150 = 0
−100 = ????(????)
????(????) = −100 Nm
Snede bij ????, 300 < ???? < 700 mm
400 Nm ????(????) ????(????) 450 Nm 150 Nm
100 Nm
???? 300 mm ???? ???? ???? ???? 300 mm ????
???? mm 1000 − ???? mm
Evenwicht van deel ????????.
∑ ???????? = 0:
+????(????) + 100 − 400 = 0
????(????) − 300 = 0
????(????) = +300 Nm
Evenwicht van deel ???????? .
∑ ???????? = 0:
−????(????) + 450 − 150 = 0
300 = ????(????)
????(????) = +300 Nm
MEMECH2.2, Jaar 2020-2021: week 5 Dr. ir. A.J.M. Sipers
Snede bij ????, 700 < ???? < 1000 mm
400 Nm 450 Nm ????(????) 150 Nm
100 Nm ????(????)
???? 300 mm ???? 400 mm ???? ???? ???? ????
1000 − ???? mm
???? mm
Evenwicht van deel ????????.
∑ ???????? = 0:
+????(????) + 100 − 400 + 450 = 0
????(????) + 150 = 0
????(????) = −150 Nm
Evenwicht van deel ???????? .
∑ ???????? = 0:
−????(????) − 150 = 0
−150 = ????(????)
????(????) = −150 Nm
Torsiemomentfunctie ????(????)
−100, 0 < ???? < 300 mm
????(????) = { +300, 300 < ???? < 700 mm Nm
−150, 700 < ???? < 1000 mm
400
300
200
100 400 Nm
450 Nm
0
100 200 300 400 500 600 700 800 900 1000
100 Nm
100
150 Nm
200
300
400
MEMECH2.2, Jaar 2020-2021: week 5 Dr. ir. A.J.M. Sipers
Vervormingen:
400 Nm 450 Nm 150 Nm
100 Nm
???? ???? ???? ????
???????? ???????? ???????? ????????
???????? = 0
???? −100
???????? − ???????? = ???????? =
???????????? ????????????
???? +300
???????? − ???????? = ???????? =
???????????? ????????????
???? −150
???????? − ???????? = ???????? =
???????????? ????????????
+
100 100 −20
???????? = − =− = rad
???????????? 5000 ∙ ???? 1000 ∙ ????
100 300 100 300 +60
???????? = − + =− + = rad
???????????? ???????????? 5000 ∙ ???? 3750 ∙ ???? 1000 ∙ ????
100 300 150 100 300 150 +30
???????? = − + − =− + − = rad
???????????? ???????????? ???????????? 5000 ∙ ???? 3750 ∙ ???? 5000 ∙ ???? 1000 ∙ ????
−20 ????
???????? = < 0 rad
1000 ∙ ????
????
+60
???????? = 1000∙???? > 0 rad
????
????
+30
???????? = 1000∙???? > 0 rad ????
????
MEMECH2.2, Jaar 2020-2021: week 5 Dr. ir. A.J.M. Sipers
De waarden van de schuifspanning ???? = ???? ∙ ????/???????? in een dwarsdoorsnede van deel ???????? voldoen aan:
???????????????? ≤ ???? ≤ ????????????????
a) Bepaal de ondergrens ???????????????? [N/mm2 ].
b) Bepaal de bovengrens ???????????????? [N/mm2 ].
???????????? ∙???? −100∙103 4
????(????) = = ...
