Chapter 2 Analysis of structures

Chapter 2 Analysis of structures زوشاخ ششح ذ اس ٠ ذ ح ا رذا اخ صاتمح عذ ٠ ذ ا اد أد ا رادح جا ا ع ا لع ١ ا زو س ٠ ال ذشض تأل ا ر ١ ز ا ط ك.

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 إرا ممم ذع ممم أ ٠ ممم ذمممز ة فى ا طشق ذف تا غشض.

examples of unstability partial constraints concurrent reactions parallel reactions ا أ ٠ ى ذ ٠ ه ا ذضر ١ مظ أج

examples of determinacy ال ر ١ جح تذ أ No gains without pains

2-3 Classify each of the beams in Fig. 2-18a through 2-18d 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. Compound beams, which are composed of pin-connected members are must be disassembled. Applying r =3n or r > 3n, the resulting classifications are indicated. إن الم نبت ال أرضا ق ط ع وال ظه ار أبقى

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. Applying r = 3n or r > 3n, the resulting classifications are indicated. الطيور عمي اشكالها تقع

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. Frame structures consist of members that are connected together by rigid joints. Sometimes the members form closed loop, In order to classify these structures, it s necessary to use the method of sections and cut the loop apart. عود لسانك عمي لين الكالم وبذل السالم يكثر محبيك ) االمام عمي (.

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. Solution The structures are classified as indicated. The member is stable since the reactions are non-concurrent and nonparallel. It s also statically determinate. (b) 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. استعينوا عمى قضاء حوائجكم بالكتمان

ذاتع د ا ثاي سل 2-6 (d) 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. المئ يم ت م ر د ا إذا أنت أ كر مت الكريم م م كت و *** ون ا أنت أكرمت

2-9 Classify each of the structures as statically determinate, statically indeterminate, stable, or unstable. If indeterminate, specify the degree of indeterminate. a) (partial constraints) b) (Statically determinate) c) Statically indeterminate to the first degree d) االماني رءوس مال المفمسين Statically indeterminate to the first degree

2-10 classify each of the structures as statically determinate, statically determinate, or unstable. If indeterminate, specify the degree of indeterminacy. (Fig. a, b,c,d) ( a) Statically determinate (b) Indeterminate to 3 (c) Statically determinate (d) parallel reactions on lower beam unstable. صاس ع ا ذسب ص.

2-11. Classify each of the structures as statically determinate, statically indeterminate, or unstable. If indeterminate, specify the degree of indeterminacy. n = number of parts r = number of reactions a) n = 1 r = 4 r > 3n statically indeterminate to 1 o. b) unstable since all reactions are parallel. c) n = 1 r = 6 r > 3n statically indeterminate to 3 o. d) unstable since all reactions are parallel. ك تاهلل أغ ا ذ و ع ١ و ف ا. ث

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) (a) Statically indeterminate to 3 (b) Statically indeterminate to 1 (c) Statically indeterminate to 1 (d) Parallel reactions unstable ا شى صالح ا ضعفاء.

2-13 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. a) The frame has no closed loops r = 15 Statically indeterminate to 6 o b) Cutting the loops as shown n = 4 r = 4 * 2 (pins) + 6 * 3 (reactions) = 8 + 18 = 26 Statically indeterminate to 14 o c) Cutting the loops as shown n = 4 r = 4 * 3 (supports) + 9 *3 (sections) r > 3 (n) Statically indeterminate to 27 o ا اض ال ٠ ضا ا ضرمث

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. a) 2 6 6 3 n = 6 r = 26 r > 3 n 3 3 3 statically indeterminate to (r 3 n) = 8 b) T n = 1 1 r = 2 + 1 = 3 r = 3 n 2 statically determinate 3 3 c) 3 6 3 n = 7 3 3 3 r = 27 statically indeterminate to (r 3 n) = 6 ٠ ى ا ذ ت ز ا طش ٠ مح أ دضة ا طش ٠ مح تا ضؤاي ا ضاتك ا اس ال ٠ ىش ه ع ١ ب ف ١ ه ى تضثة زا ٠ ان.

ذاتع د ا ثاي سل 2-14 June 2011 d) n = 9 3 6 3 r = 33 statically indeterminate to (r 3 n) = 6 3 e) 6 6 n = 5 r = 21 3 3 statically indeterminate to (r 3 n) = 6 f) 6 6 6 2 n = 9 r = 35 3 6 3 3 statically indeterminate to (r 3 n) = 8 ذخ ١ ا جاح ا ز ذشغث ذخ ١ أ ه ذضمرذم ذخ ١ أ ه لادس ع ذذم ١ م ارا تم

2-15 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. a) n = 2 r = 3+1+2 = 6 r = 3 n statically determinate 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 statically indeterminate to 3 o. ذخ ص االعرمماد ا فاصمذ تأ إ ىا ١ اذه ذذ دج.

2-17 Determine the reactions on the beam, the support at B can be assumed to be roller, Neglect the thickness of the beam. (Fig. 2-17). Fig (2-17) 7.5(3) = 22.5 kn 45 kn A x A y 1.5 m 4.5 m B y ا ج أ ذع فش األع اي تم فش ا طش ٠ مح ذر لع رائج خر فح. )أ شر ١ (

2-18 Determine the reactions at the supports A and B. Assume A is a roller, and B is a pin. (Fig. 2-18). June 2011 Fig (2-18) 7.5 kn/m 36 kn 36 kn A y By 2.4 m 2.1 m 2.1 m 2.1 m ٠ عمم ١ ا اس ضمما ا ١ مم فمم تمم لممشاساخ صمماتمح اذخز ا فأ ٠ ذذة أ ذى تعذ عشش ص اخ

2-19. Determine the reactions on the beam. - F 1 F 2 F 3 A y 0.9 0.9 1.35 0.45 0.9 B y ا عثذ ٠ م ش ع ت ا ع ص ا... ا ذ ش ذ ى ف ١ ا ال ح

2-20 Detremine the reactions on the beam. (Fig. 2-20) Fig (2-20) (30)(7.2) + (0.5)(15)(7.2) =272.25 kn A x A y 3.6 m 3.6 m 810 kn.m F B ص ١ ح ا م ا خشائظ غ ١ ش ا ح إرا ذى ذعشف ج ره.

2-21 Detremine the reactions on the beam. (Fig. 2-21) Fig (2-21) X F 2 2.6 F 1 1.3 3.9 X A x 7.8m F B A y y اتمممذأ ا ١ ممم درممم ال ذ مممذ غذا ع ف اخ األ ا.

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. (Fig. 2-22) Fig (2-22) 54 kn 45 kn 1.8 0.6 2.1 0.3 A y B y ا جذا ف صفش ا سو ب ا مطاس ا صذ ١ خ.

2-23 Determine the reactions at the supports A and B of the compound beam. There is a pin at C. (Fig. 2-23) Section AC Fig (2-23) C y 18 kn M o 24 kn C x B x B y C x A y C y Section CB ذ د أ ذع ١ ا ع ا ا ا ذ ١ اج و ا ٠ ع ١ ا أغ ة ا اس أ أ ذ ٠ ه إص ا اخ أل ره عا أج ع.

2-26 Determine the reactions at the smooth supports C and pinned support A. Assume the connection at B is fixed connected. (Fig. 2-26). Fig (2-26) 2.6 m F C 2.16 kn 1.5 m A x 30 o 3 m A y 0.9 m 0.9 m إرا ال ذعشف إ أ ٠ ذرجم فضم ١ ر تمه ا طاف ع األسجخ ف ىا ال ذش ٠ ذ.

2-27 Determine the reactions at the smooth support A and pin support B. The connection at C is fixed. (Fig. 2-27). Fig (2-27) 6 kn B x 1.5 m 1.5 m B y 1.5 m F A If you fail to plan, you plan to fail.

2-31 Detremine the reactions at supports A and B of frame. Assume that support at A is a roller. (Fig. 2-31). Fig (2-31) 25 kn 35 kn 50 kn 10 kn 4 m 3 m 3 m A y 4 m 2.5 kn 3 m B x B y ٠ ى ه ذ ف ١ ش صاعح ١ ٠ ا لد طعا ه وال ه أش ١ اء أخش... صرص ع ت ا ا عجزاخ.

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. B x (7 * 12) B x 84 kn (7 * 12 * 3.5) + (30 * 8) + (20 * 14) (A y * 8) 0 A y 101.75 kn 20 kn 30 kn 40 kn 6 m 8 m A y + B y 40 30 20 0 B y 11.75 kn A y 84 kn B x B y إرا ا ممممش ء مممم ٠ مممم ذ ش مممم ا مممم ع ش ض فى سداء ٠ شذذ ٠ ج ١

2-34. Determine the reactions at the supports A, B, and E. Assume the bearing support at B is a roller. 180 kn C A y B y 25 kn D E x E y خاطش اصرغ تشأ ٠. )ع ت أت طا ة(

2-35 Determine the reactions at the supports A, B, C, and E. 120 kn 40 kn 180 kn A y B y C y D y تذ ا عاد ر ١ ٠ رج أ : دلاخ ل ة ا شء لائ ح... إ ا ذ ١ اج دلائك ث ا

2-38 Determine the reactions at the supports A, C, and D. B is pinned. (30)(3)=150 kn 67.5 k A x A y C y D x 1.5 1.5 1.5 1.8 ما ذخماف م لمذ ٠ ذمذز ممه إرا ا دا د ع ا رفى ١ ش ف ١.

ال) ال) June 2011 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. (Fig. 2-39) Fig (2-39) 80 k A y 2 m 2 m 2.5 m 25 kn 2.5 m C x C y ) ماطعاخ ا اذف ١ ح داع ا. ذع ل ي: )ال( ٠ عط ه ) ط اسئ ا ر ال

2-40 Detremine the reactions at supports A and B. Assume that support at B is a roller, C is afixed- connected joint. (Fig. 2-40) Fig (2-20) 75 kn 350 kn 2 m 2.5 m 2.5 m 50 kn B y 2 m A x A y صأي ا ى ا ضرذ ١ : أ ٠ ذم ١ فأجات : ف أدال ا عاجز.

2-41. Determine the reactions at the supports A and B. Solution 27 kn 45 kn B x 67.5 kn A x B y M A A y ر ب خأ لم تمد ه أ م ك

2-44 Detremine the reactions at supports A and B. The joints C and D are fixed connected. (Fig. 2-44). Fig (2-44) 30 kn 4 m 3 m F B A x A y ذخ ١ ا جاح ا ز ذشغث ذخ ١ أ ه ذضرذم ذخ ١ أ ه لادس ع ذذم ١ م ارا تم

X X X X X June 2011 2-45 Detremine the horizontal and vertical coomponents of reaction at supports A and B. 100 kn X 2.5 m X 2.5 m X 48 3 m 3 m 4 m B x A x B y A y أ د أوثش أفض ا ذعرمذ ع فضه.

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. 30 kn 8 kn 6 kn 8 kn A x C x A y C y ىمم شمم ء آفممح مم ج ضمم... در ا ذذ ٠ ذ صطا ع ١ ا ثش د

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). Member AB: Fig (2-48) B y Member BC: B x 1.8 m 21.6 kn 1.8 m A x A y B y 18 kn 13.5 kn 1.8 m 1.2 m 0.9 m C x B x C y رى أ د أ ت ذ ف لائ ح ا ر ا اذه

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. A x A y Cy C x B y بفصل BE عند نقطة E y اخرالف ا شأ ال ٠ فضذ د ل ض ١ ح