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Catégorie :Category: mViewer GX Creator App HP-Prime
Auteur Author: jeanpaul2809
Type : Application
Page(s) : 22
Taille Size: 1.20 Mo MB
Mis en ligne Uploaded: 10/10/2019 - 00:09:36
Uploadeur Uploader: jeanpaul2809 (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a2362689

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© 2012 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.



8–10. Determine the slope at B and the maximum 15 k
displacement of the beam. Use the moment-area theorems.
Take E = 29(103) ksi, I = 500 in4. A
C

B

6 ft 6 ft



M
Using the diagram and the elastic curve shown in Fig. a and b, respectively,
EI
Theorem 1 and 2 give

1 90 k # ft
uB = ƒ uB>A ƒ = a b (6 ft)
2 EI

270 k # ft2 270 (144) k # in2
= = = 0.00268 rad Ans.
c 29(10 ) 2 d (500 in4)
EI k
3
in
1 90 k # ft
¢ max = ¢ C = ƒ tB>A ƒ = c a b (6 ft) d c 6 ft + (6 ft) d
2
2 EI 3
2700 k # ft3
=
EI
2700 (1728) k # in3
=
c 29(103) d (500 in4)
k
in2
= 0.322 in T Ans.




278
© 2012 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.



8–11. Solve Prob. 8–10 using the conjugate-beam method. 15 k

A
C

B

6 ft 6 ft




The real beam and conjugate beam are shown in Fig. b and c, respectively.
Referring to Fig. c,
1 90 k # ft
+ c a Fy = 0; - V¿B - a b (6 ft) = 0
2 EI
270 k # ft2
uB = V¿B = –
EI
270 (122) k # in2
= = 0.00268 rad Ans.
c 29(103) d (500 in4)
k
in2
Referring to Fig. d,
1 90 k # ft
M¿C + c a b (6 ft) d c6 ft + (6 ft) d = 0
2
a+ a MC = 0;
2 EI 3
2700 k # ft3
¢ max = ¢ C = MC¿ = -
EI
2700 (123) k # in3
= = 0.322 in T Ans.
c 29(10 ) 2 d (500 in )
3 k 4
in




279
© 2012 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.



*8–12. Determine the slope and displacement at C. EI is 15 k
constant. Use the moment-area theorems.

A C
B
30 ft 15 ft

M
Using the diagram and the elastic curve shown in Fig. a and b, respectively,
EI
Theorem 1 and 2 give

225 k # ft 5062.5 k # ft2 5062.5 k # ft2
a- b (45 ft) = -
1
uC>A = =
2 EI EI EI

1 225 k # ft 33750 k # ft3
ƒ tB>A ƒ = c a b (30 ft) d c (30 ft) d =
1
2 EI 3 EI
1 225 k # ft 1 225 k # ft
ƒ tC>A ƒ = c a b (30 ft) d c 15 ft + (30 ft) d + c a b(15 ft) d c (15 ft) d
1 2
2 EI 3 2 EI 3

101250 k # ft3
=
EI
Then,

45 33750 k # ft3 50625 k # ft3
a b =
45
¢¿ = (tB>A) =
30 30 EI EI

ƒ tB>A ƒ 33750 k # ft3>EI 1125 k # ft2
uA = = =
LAB 30 ft EI
+b uC = uA + uC>A

–1125 k # ft2 5062.5 k # ft2 3937.5 k # ft2
uC = + = Ans.
EI EI EI

101250 k # ft3 50625 k # ft3
¢ C = ` tC>A ` – ¢ ¿ = -
EI EI
50625 k # ft3
= T Ans.
EI




280
© 2012 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.



8–13. Solve Prob. 8–12 using the conjugate-beam method. 15 k



A C
B
30 ft 15 ft


The real beam and conjugate beam are shown in Fig. a and b, respectively.
Referring to Fig. c,

1 225 k # ft
a+ a MA = 0; B¿y(30 ft) - c a b (30 ft) d (20 ft)
2 EI
2250 k # ft2
B¿y =
EI
Referring to Fig. d,

1 225 k # ft 2250 k # ft
+ c a Fy = 0; - V¿C - a b (15 ft) -
2 EI EI
3937.5 k # ft2 3937.5 k # ft2
uC = V¿C = - = Ans.
EI EI

1 225 k # ft 2250 k # ft2
a+ a MC = 0; M¿C + c a b (15 ft) d (10 ft) + a b(15 ft)
2 EI EI

50625 k # ft3 50625 k # ft3
¢ C = M¿C = = T Ans.
EI EI




281
© 2012 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.



8–14. Determine the value of a so that the slope at A is P ...

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3.06 Ko KB readme.txt
3.65 Ko KB lisezmoi.txt
1.09 Ko KB RESISTEN.hpprgm
1.09 Mo MB RESISTEN 01_20.hpappdir.zip
110.12 Ko KB RESISTEN 21_22.hpappdir.zip
167 octets bytes appslist.txt

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