Slope deflection method

a)Slope-deflection method of analysis: Slope-deflection equations, equilibrium equation of
slope-deflection method, application to beams with and without joint translation and rotation,
yielding of support, application to non-sway rigid jointed rectangular portal frames, shear force and bending moment diagram.
b) Sway analysis of rigid jointed rectangular portal frames using slope-deflection method
(Involving not more than three unknowns)

1. Mr. S. R. Suryawanshi 1 JSPM’s Imperial College of Engg . & Research, Civil Engineering Department Structural Analysis-II TE Civil (2015c) Date:-08/07/2020 Mr. S. R. Suryawanshi Assistant Professor in Civil Engineering JSPM’s ICOER, Wagholi, Pune Email: [email protected] Mobile : [phone]

2. Unit-I- Slope-deflection method of analysis Mr. S. R. Suryawanshi 2 JSPM’s Imperial College of Engg . & Research, Civil Engineering Department A. APPLICATION TO BEAMS WITH AND WITHOUT JOINT TRANSLATION AND ROTATION, YIELDING OF SUPPORT. B. Non-sway & Sway analysis of rigid jointed rectangular portal frames (Involving not more than three unknowns)

3. Mr. S. R. Suryawanshi 3 JSPM’s Imperial College of Engg . & Research, Civil Engineering Department Slope Deflection Equation

4. Mr. S. R. Suryawanshi 4 JSPM’s Imperial College of Engg . & Research, Civil Engineering Department Steps to follow :- 1. Find D ki (degree of kinematic indeterminacy/Degree of freedom) 2. Find fixed end moment 3. Write Slope deflection equations for each span 4. Apply the equilibrium condition at joints

5. Mr. S. R. Suryawanshi 5 JSPM’s Imperial College of Engg . & Research, Civil Engineering Department 5. Find the unknown displacements 6 .Find final end moments 7. Find reactions and draw SFD 8. Draw Superimposed BMD Steps to follow :-

6. Mr. S. R. Suryawanshi 6 JSPM’s Imperial College of Engg . & Research, Civil Engineering Department Types of Numerical to Study:- Analysis of Indeterminate Beams Continuous beam with both ends fixed 2 . Continuous beam with one end or both ends simple 3 . Continuous beam with overhanging span 4 . Continuous beam with sinking of support

7. Mr. S. R. Suryawanshi 7 JSPM’s Imperial College of Engg . & Research, Civil Engineering Department B. Analysis of Indeterminate Rigid jointed rectangular portal frames Non-sway frames 2. Sway frames. Types of Numerical to Study:-

8. Mr. S. R. Suryawanshi 8 JSPM’s Imperial College of Engg . & Research, Civil Engineering Department Structural Analysis-II TE Civil (2015c) Date:- 13 /07/2020 Mr. S. R. Suryawanshi Assistant Professor in Civil Engineering JSPM’s ICOER, Wagholi, Pune Email: [email protected] Mobile : [phone]

9. Mr. S. R. Suryawanshi 9 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Q. Analyse the beam shown in fig. using Slope Deflection Method , Draw superimposed BMD take EI=Constant (10Marks)

10. Mr. S. R. Suryawanshi 10 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Solution :- Step 1] find degree of freedom (D ki ) D ki =01( ) Step 2] Find fixed end moments For span AB M ab = = = -15 kN.m   M ba = = = +15 kN.m  

11. Mr. S. R. Suryawanshi 11 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department For span BC M bc = = = -25kN.m   M cb = = = +25kN.m  

12. Mr. S. R. Suryawanshi 12 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 3] write slope deflection equations For span AB ) a s No support settlement so, =  

13. Mr. S. R. Suryawanshi 13 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department As Support A is fixed   ……… (1 )  

14. Mr. S. R. Suryawanshi 14 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department = ………… (2)  

15. Mr. S. R. Suryawanshi 15 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Now considering span BC =   As Support C is fixed   ……… (3)  

16. Mr. S. R. Suryawanshi 16 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department   …………….( 4 )  

17. Mr. S. R. Suryawanshi 17 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 4] Apply joint equilibrium condition at Joint B At Joint B i.e. Equation No (2) + Equation No. (3) =  

18. Mr. S. R. Suryawanshi 18 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department By solving above we get ..unknown displacement  

19. Mr. S. R. Suryawanshi 19 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 5] Find Final End moments Put the value of in Equation (1), (2), (3) & (4) to get final End Moments  

20. Mr. S. R. Suryawanshi 20 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department  

21. (In kN.m) 21 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 6] S uperimposed BMD 3m 2 m 2 m WL 2 /8=20 x 3 2 /8 = 22.50 WL/4=50x4/4 = 50 12.125 20.709 27.145 A B C

22. Mr. S. R. Suryawanshi 22 JSPM’s Imperial College of Engg . & Research, Civil Engineering Department Structural Analysis-II TE Civil (2015c) Date:- 14 /07/2020 Mr. S. R. Suryawanshi Assistant Professor in Civil Engineering JSPM’s ICOER, Wagholi, Pune Email: [email protected] Mobile : [phone]

23. Mr. S. R. Suryawanshi 23 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Quick Revision of L ast Session Discussed Type-I numerical i.e. Continuous beam with both ends fixed

24. Mr. S. R. Suryawanshi 24 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Unit-I:- Slope Deflection Method of Analysis A] Analysis of statically Indeterminate Beams Type II] Continuous beam with end support simple

25. Mr. S. R. Suryawanshi 25 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department

26. Mr. S. R. Suryawanshi 26 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department SPPU Insem Exam Aug.2017

27. Mr. S. R. Suryawanshi 27 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Solution:- Step 1] find degree of freedom (D ki ) D ki =02( , ) Step 2] Find fixed end moments For span AB M ab = = = -15 kN.m   M ba = = = +15 kN.m  

28. Mr. S. R. Suryawanshi 28 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department For span BC M bc = = = -25kN.m   M cb = = = +25kN.m  

29. Mr. S. R. Suryawanshi 29 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 3] write slope deflection equations For span AB ) a s No support settlement so, =  

30. Mr. S. R. Suryawanshi 30 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department As Support A is fixed   ……… (1 )  

31. Mr. S. R. Suryawanshi 31 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department = ………… (2)  

32. Mr. S. R. Suryawanshi 32 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Now considering span BC =   As Support C is s   ……… (3)  

33. Mr. S. R. Suryawanshi 33 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department …….( 4 )  

34. Mr. S. R. Suryawanshi 34 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 4] Apply joint equilibrium condition at Joint B At Joint B i.e . Equation No (2) + Equation No. (3) =  

35. Mr. S. R. Suryawanshi 35 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department By solving above we get At Joint C i.e. Equation No.(4)=0 =0 = -25 ……….(6)  

36. Mr. S. R. Suryawanshi 36 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department By solving Equation No.(5) and (6) we get = -25 ……….(6)  

37. Mr. S. R. Suryawanshi 37 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 5] Find Final End moments Put the value of in Equation (1), (2), (3) & (4) to get final End Moments,  

38. 38 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department  

39. (In kN.m) 39 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 6] S uperimposed BMD 3m 2 m 2 m WL 2 /8=20 x 3 2 /8 = 22.50 WL/4=50x4/4 = 50 7.752 29.387 A B C

40. Mr. S. R. Suryawanshi 40 JSPM’s Imperial College of Engg . & Research, Civil Engineering Department Structural Analysis-II TE Civil (2015c) Date:- 15 /07/2020 Mr. S. R. Suryawanshi Assistant Professor in Civil Engineering JSPM’s ICOER, Wagholi, Pune Email: [email protected] Mobile : [phone]

41. Mr. S. R. Suryawanshi 41 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Quick Revision of L ast Session Discussed Numerical on Continuous beam with End simple

42. Mr. S. R. Suryawanshi 42 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Unit-I:- Slope Deflection Method of Analysis A] Analysis of statically Indeterminate Beams MCQs from Competitive examination & Type II] Continuous beam with end support simple

43. Mr. S. R. Suryawanshi 43 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department

44. Mr. S. R. Suryawanshi 44 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department

45. Mr. S. R. Suryawanshi 45 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department

46. Mr. S. R. Suryawanshi 46 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department

47. 47 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department

48. Mr. S. R. Suryawanshi 48 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Q. Analyse the beam shown in fig. using Slope Deflection Method , Draw superimposed BMD take EI=Constant (10Marks)

49. 49 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Solution:- Step 1] find degree of freedom (D ki ) D ki =03( , ) Step 2] Find fixed end moments For span AB M ab = = = -56.25kN.m   M ba = = = + 56.25 kN.m  

50. 50 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department For span BC M bc = = = -255 kN.m   M cb = = = +255 kN.m For span CD M cd = = = -44.44 kN.m   M dC = = == +22.22 kN.m  

51. Mr. S. R. Suryawanshi 51 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 3] write slope deflection equations For span AB ) =  

52. Mr. S. R. Suryawanshi 52 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department As Support A is fixed   ……… (1 )  

53. Mr. S. R. Suryawanshi 53 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department = …… (2)  

54. Mr. S. R. Suryawanshi 54 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Now considering span BC =    …( 3)  

55. Mr. S. R. Suryawanshi 55 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department ...( 4 )  

56. Mr. S. R. Suryawanshi 56 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Now considering span CD =    …( 5 )  

57. Mr. S. R. Suryawanshi 57 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department ...(6)  

58. Mr. S. R. Suryawanshi 58 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 4] Apply joint equilibrium condition at Joint B At Joint B i.e . Equation No (2) + Equation No. (3) =  

59. 59 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department By solving above we get At Joint C i.e. Equation No.(4 ) + Equation No .(5) =0 +[ ]=0 + = -210.56 ……….(8)  

60. Mr. S. R. Suryawanshi 60 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department At Joint D i.e. Equation No.(6) =0 =0 = -22.22 ……….(9)  

61. Mr. S. R. Suryawanshi 61 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department By solving Equation No.(7) , (8) & (9) we get + = - 210.56 = -22.22  

62. Mr. S. R. Suryawanshi 62 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 5] Find Final End moments Put the value of in Equation (1), (2), (3) , (4 ),(5)& (6) to get final End Moments,  

63. 63 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department = = -170.451 =0  

64. Mr. S. R. Suryawanshi 64 JSPM’s Imperial College of Engg . & Research, Civil Engineering Department Structural Analysis-II TE Civil (2015c) Date:-20/07/2020 Mr. S. R. Suryawanshi Assistant Professor in Civil Engineering JSPM’s ICOER, Wagholi, Pune Email: [email protected] Mobile : [phone]

65. Mr. S. R. Suryawanshi 65 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Quick Revision of L ast Session Discussed Numerical on Continuous beam with End simple

66. Mr. S. R. Suryawanshi 66 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Unit-I:- Slope Deflection Method of Analysis A] Analysis of statically Indeterminate Beams Type I II] Continuous beam with overhanging span

67. Mr. S. R. Suryawanshi 67 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department At Simple end support C M cb +M cd =0 M cd =Moment due to overhanging span =40×2=80kN.m

68. Mr. S. R. Suryawanshi 68 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Q. Analyse the beam shown in fig. using Slope Deflection Method , Draw superimposed BMD take EI=Constant (10Marks)

69. 69 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Solution:- Step 1] find degree of freedom (D ki ) D ki =02( , ) Step 2] Find fixed end moments For span AB M ab = = = -60 kN.m  M ba = = = +60 kN.m  

70. 70 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department For span BC M bc = = = -30 kN.m   M cb = = = +30 kN.m   For span CD M cd =Moment due to overhanging span =40×2=80kN.m

71. Mr. S. R. Suryawanshi 71 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 3] write slope deflection equations For span AB ) =  

72. Mr. S. R. Suryawanshi 72 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department As Support A is fixed   ……… (1 )  

73. Mr. S. R. Suryawanshi 73 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department = …… (2)  

74. Mr. S. R. Suryawanshi 74 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Now considering span BC =    …( 3)  

75. Mr. S. R. Suryawanshi 75 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department ...( 4 )  

76. Mr. S. R. Suryawanshi 76 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 4] Apply joint equilibrium condition at Joint B At Joint B i.e . Equation No (2) + Equation No. (3) =  

77. 77 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department By solving above we get At Joint C i.e. Equation No.(4 ) + M cd =0 +[ ]=0 = -110 ……..…….( 6 )  

78. Mr. S. R. Suryawanshi 78 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department By solving Equation No.(5 ) & (6) ,we get = -110  

79. Mr. S. R. Suryawanshi 79 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 5] Find Final End moments Put the value of in Equation (1), (2), (3) & ( 4) to get final End Moments,  

80. 80 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department = 80 kN.m =40×2 = 80kN.m  

81. (In kN.m) 81 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 6] S uperimposed BMD 6 m 2 m 2 m WL 2 /8=20 x 6 2 /8 = 90 WL/4=60x4/4 = 60 54.190 71.795 A B C D 2 m 80

82. Mr. S. R. Suryawanshi 82 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department

83. Mr. S. R. Suryawanshi 83 JSPM’s Imperial College of Engg . & Research, Civil Engineering Department Structural Analysis-II TE Civil (2015c) Date:-21/07/2020 Mr. S. R. Suryawanshi Assistant Professor in Civil Engineering JSPM’s ICOER, Wagholi, Pune Email: [email protected] Mobile : [phone]

84. Mr. S. R. Suryawanshi 84 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Unit-I:- Slope Deflection Method of Analysis A] Analysis of statically Indeterminate Beams Type IV] Continuous beam with sinking of Support / Settlement of support

85. Mr. S. R. Suryawanshi 85 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department

86. Mr. S. R. Suryawanshi 86 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department

87. Mr. S. R. Suryawanshi 87 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department

88. 88 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Solution:- Step 1] find degree of freedom (D ki ) D ki =02( , ) Step 2] Find fixed end moments For span AB M ab = = -28.8kN.m M ba = = +43.20kN.m  

89. 89 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department For span BC M bc = = = -40 kN.m   M cb = = = +40 kN.m  

90. Mr. S. R. Suryawanshi 90 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 3] write slope deflection equations For span AB ) =  

91. Mr. S. R. Suryawanshi 91 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department As Support A is fixed   =-28.80+8000 -24 ……… (1 )  

92. Mr. S. R. Suryawanshi 92 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department = 16000 -24 …… (2 )  

93. Mr. S. R. Suryawanshi 93 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Now considering span BC =    20000 10000 37.5 …( 3)  

94. Mr. S. R. Suryawanshi 94 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department = 000 0000 37.5 ...( 4 )  

95. Mr. S. R. Suryawanshi 95 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 4] Apply joint equilibrium condition at Joint B At Joint B i.e . Equation No (2) + Equation No. (3) =  

96. 96 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department By solving above we get At Joint C i.e. Equation No.(4 ) =0 as Support C is simple end support =0 = -77.5……..…….( 6 )  

97. Mr. S. R. Suryawanshi 97 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department By solving Equation No.(5 ) & (6) ,we get = -77.5  

98. Mr. S. R. Suryawanshi 98 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 5] Find Final End moments Put the value of in Equation (1), (2), (3) & ( 4) to get final End Moments,  

99. 99 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department =  

100. Mr. S. R. Suryawanshi 100 JSPM’s Imperial College of Engg . & Research, Civil Engineering Department Structural Analysis-II TE Civil (2015c) Date:-22/07/2020 Mr. S. R. Suryawanshi Assistant Professor in Civil Engineering JSPM’s ICOER, Wagholi, Pune Email: [email protected] Mobile : [phone]

101. Mr. S. R. Suryawanshi 101 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Quick Revision on Analysis of beam

102. Mr. S. R. Suryawanshi 102 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department I II

103. Mr. S. R. Suryawanshi 103 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department III IV

104. Mr. S. R. Suryawanshi 104 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Unit-I:- Slope Deflection Method of Analysis A] Analysis of statically Indeterminate Rigid jointed frame Sway and Non sway Frame

105. Mr. S. R. Suryawanshi 105 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department What is Sway and Non-sway Frame? Sway- Sway Frame- displacement due to horizontal force move or cause to move slowly or backwards and forwards or from side to side.

106. Sway and Non sway frame Mr. S. R. Suryawanshi 106 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department

107. Mr. S. R. Suryawanshi 107 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Frame said to be Non-sway if :- 1.Loading on frame is symmetrical. 2. Support conditions of frames are same. 3. Coumns are idnetical i.e. Same E,I,A.

108. 108 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Frame said to be Non-sway if :- *Constraints(support) at beam level Non-Sway Frames

109. 109 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Non-Sway Frames

110. Mr. S. R. Suryawanshi 110 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department

111. 111 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Sway Frames Sway Frames

112. Mr. S. R. Suryawanshi 112 JSPM’s Imperial College of Engg . & Research, Civil Engineering Department Structural Analysis-II TE Civil (2015c) Date:- 07 /08/2020 Mr. S. R. Suryawanshi Assistant Professor in Civil Engineering JSPM’s ICOER, Wagholi, Pune Email: [email protected] Mobile : [phone]

113. Mr. S. R. Suryawanshi 113 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Unit-I:- Slope Deflection Method of Analysis B] Analysis of statically Indeterminate Rigid jointed frame Sway and Non sway Frame

114. Non-Sway Frame 114 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Q. Analyse the frame shown in Fig. Using Slope deflection Method Take EI=Const.

115. Mr. S. R. Suryawanshi 115 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 1] find degree of freedom (D ki ) D ki =02( , ) Step 2] Find fixed end moments For span AB M ab = = = -26.67 kN.m   M ba = = = +26.67 kN.m  

116. Mr. S. R. Suryawanshi 116 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department M bc = = - 28.8kN.m M cb = = = +19.20kN.m M bd = = = -10 kN.m   M db = = = +10 kN.m  

117. Mr. S. R. Suryawanshi 117 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 3] write slope deflection equations For span AB ) As support A is fixed so =0 = =-26.67+0.5 ………..(1)  

118. Mr. S. R. Suryawanshi 118 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department ) = ) =+26.67+ ………………….(2)   ) = ) =-28.20+0.8 +0.4 …………(3)  

119. 119 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department ) = ) = +19.20 + 0. + 0 . …………(4) ) = ) , =0 due to fixity =-10+ …………(5)  

120. Mr. S. R. Suryawanshi 120 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department ) = ) , =0 due to fixity =10 + …………(6)  

121. Mr. S. R. Suryawanshi 121 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 4] Apply joint equilibrium condition at Joint B & Joint C Joint B M ba +M bc +M bd =0 Joint C M cb =0

122. JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Joint B M ba +M bc +M bd = i.e. Eq n (2)+ Eq n (3)+ Eq n (5)=0 26.67 + +[ - 28.20+0.8 +0.4 2.8 +0.4 =11.53……………(7) Joint C M cb =0 i.e. Eq n (4)=0 19.20 + 0. + 0. =0 0. + 0. =-19.20………..( 8)  

123. Mr. S. R. Suryawanshi 123 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department 2.8 +0.4 =11.53……………(7 ) . + 0. =-19.20………..(8 ) By solving Eq n (7) & (8) We get, =8.126 =-28.063  

124. Mr. S. R. Suryawanshi 124 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 5] Find Final End moments Put the value of in Equation (1), (2), (3) , (4 ),(5) &(6) to get final End Moments,  

125. Mr. S. R. Suryawanshi 125 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department M ab =- 26.67+0.5 = -22.607kN.m M ba = =+26.67+ = 34.796kN.m M bc =- 28.20+0.8 +0.4 = -32.924kN.m M cb = +19.20 + 0. + 0. =0 M bd = =-10+ = -1.874kN.m M db = 10+ = 14.063kN.m  

126. Mr. S. R. Suryawanshi 126 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department

127. Mr. S. R. Suryawanshi 127 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 5] Draw Superimposed BMD   40     34.796 22.607 32.924 1.874 14.063 A B C D 4m 4m 3m 2 m

128. Mr. S. R. Suryawanshi 128 JSPM’s Imperial College of Engg . & Research, Civil Engineering Department Structural Analysis-II TE Civil (2015c) Date:- 07 /08/2020 Mr. S. R. Suryawanshi Assistant Professor in Civil Engineering JSPM’s ICOER, Wagholi, Pune Email: [email protected] Mobile : [phone]

129. Mr. S. R. Suryawanshi 129 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department

130. Sway Frame 130 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Q. Analyse the frame shown in Fig. Using Slope deflection Method Take EI=Const.

131. Mr. S. R. Suryawanshi 131 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 1] find degree of freedom (D ki ) Step 2] Find fixed end moments

132. Mr. S. R. Suryawanshi 132 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 3] write slope deflection equations For span AB ) = = ……………….( 1)  

133. Mr. S. R. Suryawanshi 133 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department ) = = ……………….(2)  

134. Mr. S. R. Suryawanshi 134 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department For span BC ) = = ……………….(3)   Don’t consider sway effect in Beam

135. Mr. S. R. Suryawanshi 135 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department ) = = ……………….(4)  

136. Mr. S. R. Suryawanshi 136 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department For span CD ) = = ……………….(5)  

137. Mr. S. R. Suryawanshi 137 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department ) = = ……………….(6)  

138. Mr. S. R. Suryawanshi 138 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 4] Apply joint equilibrium condition at Joint B , Joint C & Horizontal shear Eqll m . At Joint B M ba +M bc =0 At joint C M cb + M cd =0 Horizontal Shear Equilibrium i.e. H a + H d = 10kN  

139. Mr. S. R. Suryawanshi 139 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department At Joint B M ba +M bc =0 i.e. Equation (2)+ Equation(3)=0 + =0 =0…………..(7)  

140. Mr. S. R. Suryawanshi 140 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department At joint C M cb + M cd =0 i.e . Equation (4)+ Equation(5)= + = + - = 0…………..(8)  

141. Mr. S. R. Suryawanshi 141 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Horizontal Shear Equilibrium i.e. H a + H d = 10kN H a = & H d = ( +( )=10  

142. Mr. S. R. Suryawanshi 142 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department H a= = = H d = = =  

143. Mr. S. R. Suryawanshi 143 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department H a + H d = 10kN i.e. - + - =10 1.5 + - 13.5 =10……(9) Solving Eq n (7),(8) & (9) we get  

144. Mr. S. R. Suryawanshi 144 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department = 0 ……..( 7) + - = 0 ……..( 8) 1.5 + - 13.5 = 10 ……( 9 ) = -0.833 = -1.25  

145. Mr. S. R. Suryawanshi 145 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department Step 5] Find Final End moments Put the value of & in Equation (1), (2), (3) , (4 ),(5) &(6) to get final End Moments,  

146. Mr. S. R. Suryawanshi 146 JSPM’s Imperial College of Engg. & Research, Civil Engineering Department 1.237kN.m 0.404 kN.m M bc = = -0.404 kN.m M cb = = -3.33 kN.m = 3.33 kN.m M dc = = 5.78 kN.m