Before the load P was applied, a gap, ?0 existed between the cantilever beam AC andthe support at B. Knowing that E=200 GPa, determine the magnitude of P for which thedeflection at C is δ and the reaction at B(Hint: Use the method of superposition and beam deflections in Appendix A)?0 (mm)=2.75 δ (mm)=5.5 PAВ60 mmog.60 mm0.5 m-0.2 m→ Appendix ABeam Deflections and Slopesgbx(3L + 3a – 2x)12EI(0sxsa)qbx2EI +a - x)(0sxsa)* - 4Lr + 6L?r²– 4a'x + a*)(a SxS L)24EI=- – 3Lr² + 3Ł?x – a')6EI(aSrS L)qa*b12E 3L + a)qabL2EIAt x= a: v=-8g =24EI24E7 (3L* - 4a'L +a)Og =6EIP(3L - x)6EIPx(2L – x)2EIPLPL?Og =2EI3EIPr«За — х)6EIPx(2a – x)2EI(0Sxsa)Pa3х — а)6EIPa2EI(a sxs L)PaPaAt x= a: v =3EI2EIPa(3L – a)6EIPa2EIMoxEI2EIMoMOL?8g =2EIMoLOz =EI

Answered: Image /qna-images/answer/771bdad7-cad2-453b-9e5a-470d1e5a0e22.jpg

Answered: B |A C 60 mm do 60 mm .0.2 m→ 0.5 m

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

Before the load P was applied, a gap, ?0 existed between the cantilever beam AC and
the support at B. Knowing that E=200 GPa, determine the magnitude of P for which the
deflection at C is δ and the reaction at B

(Hint: Use the method of superposition and beam deflections in Appendix A)

?0 (mm)=2.75 δ (mm)=5.5

Appendix A
Beam Deflections and Slopes
gbx
(3L + 3a – 2x)
12EI
(0sxsa)
qbx
2EI +a - x)
(0sxsa)
* - 4Lr + 6L?r²– 4a'x + a*)
(a SxS L)
24EI
=- – 3Lr² + 3Ł?x – a')
6EI
(aSrS L)
qa*b
12E 3L + a)
qabL
2EI
At x= a: v=-
8g =
24EI
24E7 (3L* - 4a'L +a)
Og =
6EI
P
(3L - x)
6EI
Px
(2L – x)
2EI
PL
PL?
Og =
2EI
3EI
Pr
«За — х)
6EI
Px
(2a – x)
2EI
(0Sxsa)
Pa
3х — а)
6EI
Pa
2EI
(a sxs L)
Pa
Pa
At x= a: v =
3EI
2EI
Pa
(3L – a)
6EI
Pa
2EI
Mox
EI
2EI
Mo
MOL?
8g =
2EI
MoL
Oz =
EI

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