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PROBLEM 7.2

I: L

.~

2.';Omm

400N For the frame and loading of Prob. 6.78, detennine the internal forces at point J.

:

),

~

I

2.';Omm..j ~mm

L

--1-250 mn.-

SOLUTION

( IMA = 0:

FBD FRAME:

(0.95 m)(480 N) -(0.25 m)Dx = 0,

Dx = 1824N --.

II~

Ay + Dy + 480 N = 0

-f'FDN

(1)

F

P...

FBD ABC: Note: BE is a two-force member

(WB=O:

(0.75m)Ay=0

Then, from (1) above,

Ay=O

Dy = -480 N Dy==480N

F -1824 N = 0

F= 1.824kN--~

-480 N -V = 0 V = -480 N

V=480N t ~ M + (0.25m)(480 N) = 0

M=-120 N.m

M = 120.0N. m ) ..

PROPRIETARY MATERIAL. ~ 2007 The McGraw-Hill Companies, Inc.. All rights reserved.. No part of this Manual may be displayed, reproduced or distributed in anyform or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation If you are a student using this Manual, you are using it without permission. 1004

tD

PROBLEM7.5

lOin,

Detennine the internal forces at point J of the structure shown.

T 1.5 in ~~ 7.5 ill.

1

7.

"::J

ShearDiag: Vjwnps to Ay = 180N atA, thendecreases linearly (~

= -w = -360 N/m) to 180N -(360 N/m)(1 m) = -180 N atC.

FromC, V is piecewiseconstant(w = 0) withjwnps of -600 N at D, +1200N atE, -420N atE. MomentDiag:

M

(11/ -5'1

M starts at zero at A with slope ~ dx

= V = 180 N/m,

decreasing to zero

at x = 0.5m. There M = !(180 N)(0.5 m) = 45 N.m Mis zeroagain 2

at C, decreasing to -(180 N)(0.3 m) = -54 N.m atD. Mthen decreases by (780N)(O.2m) = 156N.m to -210N.m atE, andincreasesby (420N)(0.5 m) = 210 N.m to zeroatE. (b)

From the diagrams,

Ivlnmx= 780 N alongEB ~ lM1nm= 210N.m atE ~

PROPRIETARY MATERIAL. @ 2007 The McGraw-Hili Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any fonn or by any means, without the prior written pennission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, .YOUare using it ~'ithout permission. 1082