chapter 2 analysis of · pdf filestability: structure will be ... degree of indeterminacy = r...

Sept 2013

بالبريد اإللكترونيأو 9 4444 062 برسالة نصيةتراها ضرورية مالحظات أوأي خطأ باإلبالغ عن المساهمةالنوتات مجانية للنفع العام فيرجى

Physics I/II, English 123, Statics, Dynamics, Strength, Structure I/II, C++, Java, Data, Algorithms, Numerical, Economy

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Chapter 2

Analysis of

structures

،مذكرات شرح وتمارين محلولة

من المواد أدناه سابقة للعديد امتحانات

الموقعين المذكورين مجانا علىمتاحة

.قال ترض بأقل من التميز المطل

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Analysis of Structures

Considering:

n = number of parts in the structure.

r = number of reactions.

Stability:

Structure will be unstable in the following cases:

1) if r < 3 n

2) if r ≥ 3 n but all reactions are parallel.

3) if r ≥ 3 n but all reactions are concurrent.

Determinacy (provided of stability):

r = 3 n statically determinate.

r > 3 n statically indeterminate.

Degree of indeterminacy = r - 3 n

،إذا لمممع تعلمممع أيمممن تمممذه

.فكل الطرق تفي بالغرض


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Examples of Unstability

partial constraints

concurrent reactions

parallel reactions

من المهع أن يكون لديك

.ما تستيقظ من أجله


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Examples of Determinacy

ـعـدون ألــــة بـــال نتيج

No gains without pains


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Compound beams, which are composed of pin-connected members

could be disassembled.

Applying r = 3n or r > 3n, the resulting classifications are indicated.

.المنبت ال أرضا قطع وال ظهرا أبقى إن

Example 2-3 Classify each of the following beams as statically determinate or

statically indeterminate. If statically indeterminate, report the number of

degrees of indeterminacy. The beams are subjected to external loadings that

are assumed to be known and can act anywhere on the beams.


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Applying r = 3n or r > 3n, the resulting classifications are indicated.

.على أشكالها تقعر الطيو

Example 2-4 Classify each of the pin-connected structures shown in Fig. 2-19a

through 2-19d as statically determinate or statically indeterminate. If statically

indeterminate, report the number of degrees of indeterminacy. The structures

are subjected to arbitrary external loadings that are assumed to be known and

can act anywhere on the structures.

r = 7, n = 2, 7 > 6

statically indeterminate to

the first degree.

r = 9, n = 3, 9 = 9

statically determinate

r = 10, n = 2, 10 > 6

statically indeterminate to

the fourth degree.

r = 9, n = 3, 9 = 9

statically determinate


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If the members form closed loop, it’s necessary to use the method of

sections and "cut" the loop apart.

Example 2-5 Classify each of the following frames as statically determinate or

statically indeterminate. If statically indeterminate, report the number of degrees

of indeterminacy. The frames are subjected to external loadings that are assumed

to be known and can act anywhere on the frames.

.عود لسانك علي لين الكالم وبذل السالم يكثر محبوك

r = 9, n = 2

9 > 6

Statically

indeterminate to the

third degree

r = 9, n = 1

9 > 3

Statically

indeterminate to

the sixth degree

This frame has no closed loops.


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The member is stable since the reactions are non-concurrent and non-

parallel. It’s also statically determinate.

The compound beam is stable. It’s also indeterminate to the second

degree.

The member is unstable since the three reactions are concurrent at B.

(b)

.استعينوا على قضاء حوائجكع بالكتمان

Example 2-6 Classify each of the following structures as stable or unstable. The

structures are subjected to arbitrary external loads that are assumed to be known.


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The beam is unstable since the three reactions are all parallel.

The structure is unstable since r = 7, n = 3, so that r < 3n, 7 < 9.

Also, this can be seen by inspection, since AB can move horizontally

without restraint.

6-2تابع حل المثال رقع

(d)

♣هـإذا أنت أكرمت الكريع ملكت

دا ♣ وإن أنت أكرمت اللئيع تمر

A

A


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Solution:

a)

b)

Statically determinate.

c)

Statically indeterminate to the first degree.

d)

Statically indeterminate to the first degree.

2-9 Classify each of the structures as statically determinate, statically

indeterminate, stable, or unstable. If indeterminate, specify the degree of

indeterminacy.

.األماني رءوس مال المفلسين


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Solution:

( a)


(b)

Indeterminate to 3˚.

(c)


(d) Lower beam is unstable.

.من سار على الدرب وصل


indeterminate, or unstable. If indeterminate, specify the degree of indeterminacy.

(Fig. a, b ,c ,d)


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Solution:

a)

n = 1

r = 4

r > 3n

Statically indeterminate to 1o.

b)

Unstable since all reactions are parallel.

c)

n = 1

r = 6

r > 3n


d)

Unstable since all reactions are parallel.

2-11. Classify each of the structures as statically determinate, statically indeterminate,

or unstable. If indeterminate, specify the degree of indeterminacy.

.من وثق باهلل أغناه ومن توكل عليه كفاه


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Solution:

(a)

Statically indeterminate to 3˚.

(b)


(c)


(d) Unstable since all reactions are parallel.

.الشكوى سالح الضعفاء

2-12 Classify each of the structures as statically determinate, statically indeterminate,

or unstable. If indeterminate, specify the degree of indeterminacy. The supports or

connections are to be assumed as stated. (Fig. a, b ,c ,d)


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Solution:

a)

The frame has no closed loops.

r = 9


b)

Cutting the loops as shown.

n = 4

r = 4 * 2 (pins) + 6 * 3 (reactions)

= 8 + 18 = 26


c)

Cutting the loops as shown.

n = 4

r = 4 * 3 (supports) + 9 * 3 (sections)

r > 3 (n)


Classify each of the frames as statically determinate, statically indeterminate, or

unstable. If indeterminate, specify the degree of indeterminacy. All internal

joints are fixed connected.

.الماضي ال يساوي المستقبل

(a)

(b)

(c)


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Solution:

a)

The frame has no loops.

n = 1

r = 11

r > 3 n

Statically indeterminate to (r – 3 n) = 8.

b)

n = 1

r = 2 + 1 = 3

r = 3 n


c)

n = 1

r = 9


2-14 Classify each of the frames as statically determinate, statically

indeterminate, or unstable. If indeterminate, specify the degree of

indeterminacy. All internal joints are fixed connected.

2

3 3 3

1

T

3 3 3

2

. ولكن بسب مزاياك ،الناس ال يكرهونك لعيوب فيك


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d)

n = 3

r =15


e)

n = 2

r = 12


f)

n = 2

r = 14


3

3

3 3

2

3

3

تخيمممل النجممماح المممذي ترغبمممه،

تخيل أنك تسمتحقه، تخيمل أنمك

قادر على تحقيقه، ماذا بقي؟

14-2تابع حل المثال رقع

3

3

2 3 3 1

3

3

3


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Solution:

a)

n = 2

r = 3 + 1 + 2 = 6

r = 3 n


b)

Improper constraints.

n = 1

r = 3

r = 3 n

But all reactions are parallel (unstable).

c)

n = 1

r = 2 + 1 + 1 + 2 = 6

r > 3 n



indeterminate, or unstable. If indeterminate, specify the degree of

indeterminacy. The supports or connections are to be assumed as stated.

االعتقاد الفاسد تخلص من

.بأن إمكانياتك محدودة


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Sept 2013




Ay

Ax

45 kN

Solution:

30o

الجنون هو أن تعمل نفس األعمال بمنفس

(ينتأنش) .الطريقة وتتوقع نتائج مختلفة

2-17 Determine the reactions on the beam, the support at B can be assumed to

be roller, Neglect the thickness of the beam.

By

7.5(3) = 22.5 kN

4.5 m 1.5 m


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Solution:

يعمميا اإلنسممان اليمموم فممي ظممل قممرارات سممابقة

اتخذها فأين تح أن تكون بعد عشر سنوات؟

2-18 Determine the reactions at the supports A and B. Assume A is a roller, and

B is a pin.

By Ay

18 kN 36 kN 36 kN

1.2m 2.1 m 2.1 m 2.1 m 1.2m


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Solution:

– – –

– – –

2-19. Determine the reactions on the beam.

.والحر تكفيه المالمة... العبد يق رع بالعصا

0.9 0.45 1.35 0.9 0.9

Ay

F1

By

F2 F3

Ax


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Ax

Ay FB

(30)(7.2) + (0.5)(15)(7.2) =270 kN

3.6 m 3.6 m 810 kN.m

Solution:

60o

وسممميلة النقمممل والخمممرائ غيمممر

.هامة إذا لع تكن تعرف وجهتك

2-20 Detremine the reactions on the beam.


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Solution:

y

2-21 Detremine the reactions on the beam.

X

X

اليوم حتى ال تندم ابدأ

.غدا على فوات األوان

F2 F1

1.3 3.9

2.6

A y

FB A x 7.8m

7.2m


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By Ay

33.75 kN 27 kN

1.2 1.2

Bx

1.2

27 kN

1.2

11.25 kN

Solution:

من المهع جدا في سفرنا

.الصحيحركوب القطار

2-22 Determine the reactions at the supports A and B. the floor deck CD, DE,

EF and FG transmit their loads to the girder on smooth support, assume A is a

roller and B is a pin.


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By

18 kN Cy

Cx

Cx

24 kN

Ay

Bx

MB

Cy

2 m 2 m

3 m 3 m

Solution:

Member AC:

Member CB:

هل تود أن تعيا على هاما الحياة

كما يعيا أغل الناس أم أن لديك

.إسهامات ألمتك وللعالع أجمع

2-23 Determine the reactions at the supports A and B of the compound beam.

There is a pin at C.

4 kN/m

2-23 Determine the reactions at the supports A and B of the compound beam.

There is a pin at C.

4 kN/m 18 kN

6 m 2 m 2 m


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Sept 2013




Ay

Ax

FC

2.16 kN

0.9 m 0.9 m

3 m 30o

1.5 m

2.6 m

30o

Solution:

فسينتهي بك ،تتجه نتعرف إلى أيإذا ال

.ال تريدهالمطاف على األرجح في مكان

2-26 Determine the reactions at the smooth supports C and pinned support A.

Assume the connection at B is fixed connected.


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Bx

By

FA

6 kN

1.5 m 1.5 m

1.5 m

60o

Solution:

If you fail to plan,

you plan to fail.

2-27 Determine the reactions at the smooth support A and pin support B. The

connection at C is fixed.

3 m


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Bx

By

Ay

25 kN 35 kN 50 kN 10 kN

2.5 kN

4 m 3 m 3 m

4 m

3 m

Solution:

من وقت طعامك وكالمك يمكنك توفير ساعة يوميا

.وستصنع بها المعجزات. . . وأشياء أخرى

2-31 Detremine the reactions at supports A and B of frame. Assume that support

at A is a roller.


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Bx

By

Ay

20 kN 30 kN 40 kN

84 kN

8 m 6 m 3.5 m

3.5

Solution:

Bx – (7 * 12)

Bx 84 kN

(7 * 12 * 3.5) + (30 * 8) + (20 * 14) – (Ay * 8) 0

Ay 101.75 kN

Ay 102 kN

Ay + By – 40 – 30 – 20 0

By 11.75 kN

2-33. Determine the horizontal and vertical components of reaction at the supports

A and B. the joints at C and D are fixed connections.

م عرضه وس من الل ن د إذا المرء لع ي

.فكل رداء يرتديه جميل


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Ey

Ex

Ay By 25 kN

180 kN

C

D

Ax

Solution:

2-34. Determine the reactions at the supports A, B, and E. Assume the bearing

support at B is a roller.

.خاطر من استغنى برأيه

(علي بن أبي طال )


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Ay By Cy Dy

180 kN 120 kN 40 kN

Solution:

– –

– –

:بحل المعادلتين ينتج أن

– – –

– – –

2-35 Determine the reactions at the supports A, B, C, and D.

♣دقات قل المرء قائلة له

♣ وان ـق وث ـاة دقائـإن الحي


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Cy Ay

Ax

Dx

67.5 k (30)(3) = 90 kN

1.8 1.5 1.5 1.5

B

Solution:

2-38 Determine the reactions at the supports A, C, and D. B is pinned.

ما تخاف منه قد يحدث لك إذا

.ما داومت على التفكير فيه


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Sept 2013




Cy

25 kN

Ay

80 k

2 m 2 m 2 .5 m

2 .5 m

Solution:

للمقاطعات ( ال)لمن يعطلك، ( ال: )تعلع قول

.اـداعي له تي الـللطوارئ ال( ال) ة،ـالهاتفي

2-39 Detremine the reactions at supports A and C. Assume that support at A is

a roller, B is a fixed-connected joint, and C is a pin.

Cx


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Ay

Ax

50 kN By

350 kN

2 .5 m 2 .5 m 2 m

2 m

75 kN

Solution:

أيمممن : سمممأل الممكمممن المسمممتحيل

.في أحالم العاجز: تقيع؟ فأجابه

2-40 Detremine the reactions at supports A and B. Assume that support at B is a

roller, C is a fixed-connected joint.


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By

Bx

Ay

Ax

MA

45 kN 27 kN

67.5 kN

Solution:

.رب أخ لع تلده أم ـك

2-41 Determine the reactions at the supports A and B.


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Sept 2013




FB

Ay Ax

30 kN

4 m

1.5 m 2 m 1.5 m 4

3

5

Solution:

تستحقه، تخيل النجاح الذي ترغبه، تخيل أنك

تخيل أنك قادر على تحقيقه، ماذا بقي؟

2-44 Detremine the reactions at supports A and B. The joints C and D are fixed

connected.


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Solution:

2-45 Detremine the horizontal and vertical coomponents of reaction at supports

A and B.

.أنت أكبر وأفضل مما تعتقده عن نفسك

X X

100 kN

2.5 m 2.5 m

3 m

3 m

X X

X X

4 m

B y

B x

A y

A x

48kN X

X


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Sept 2013




Cy

Cx

30 kN 8 kN 6 kN

8 kN

Ay

Ax

1 m 3.5 m 1.5 m 2 m

2 m

Solution:

–

– – –

–

–

2-47 Determine the reactions at the supports A and C. The frame is pin

connected at A, B, and C and the two joints are fixed connected.

... آفة من جنسه شيءولكل

.سطا عليه المبرد حتى الحديد


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Sept 2013




1.8 m

Bx

By

Cx

B

Ac

Ax

Ay

C

Solution: Member AB:

Member BC:

.لتكن أنت أهع بند في قائمة اهتماماتك

2-48 Detremine the horizontal and vertical components of force at the connections

A, B and C. Assume each of these connections is a pin. (Fig. 2-48).

Cy

18 kN

By

Bx B

1.2 m 0.9 m 1.8 m

13.5 kN

1.8 m

21.6 kN


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Sept 2013




Ax

Ay Cy

Cx

By

MC

Solution:

y

– –

اختالف الرأي ال

.ضي ةفسد للود ق ي

2-50. Determine the horizontal and vertical components of reaction at the

supports A, B, and C. Assume that the frame is pin connected at A, B, D, E, and

F, and there is a fixed connected joint at C.


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chapter 2 analysis of · pdf filestability: structure will be ... degree of indeterminacy = r...

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