THEORY OF STRUCTURES CHAPTER 3 : SLOPE DEFLECTION (FOR BEAM) PART 1

Size: px

Start display at page:

Download "THEORY OF STRUCTURES CHAPTER 3 : SLOPE DEFLECTION (FOR BEAM) PART 1"

Godfrey Green
5 years ago
Views:

1 or updated version, please click on THEORY O STRUCTURES CHAPTER : SOPE DEECTION (OR EA) PART 1 by Saffuan Wan Ahmad aculty of Civil Engineering & Earth Resources saffuan@ump.edu.my

2 Chapter : Part 1 Slope Deflection Aims Determine the end moment for beam using Slope Deflection ethod. Expected Outcomes : Able to indicate the degree of freedom. Able to indicate the moment due to angular displacement. Able to determine the moment due to linear displacement Able to determine the fixed end moment Able to write the slope deflection equation. References echanics of aterials, R.C. Hibbeler, 7th Edition, Prentice Hall Structural Analysis, Hibbeler, 7th Edition, Prentice Hall Structural Analysis, SI Edition by Aslam Kassimali,Cengage earning Structural Analysis, Coates, Coatie and Kong Structural Analysis - A Classical and atrix Approach, Jack C. ccormac and James K. Nelson, Jr., 4th Edition, John Wiley

3 INTRODUCTION Introduced for analyzing statically indeterminate structure reactions and internal forces. The method required the solution of simultaneous equations representing the overall system of equilibrium equation.

DEGREE O REEDO When a structure is loaded, specified point on it call nodes, will undergo displacements. These displacement are referred to as the degree of freedom for the structure.

4 DEGREE O REEDO When a structure is loaded, specified point on it call nodes, will undergo displacements. These displacement are referred to as the degree of freedom for the structure. To determined the number of degrees of freedom, we can imagine the structure to consist of a series member connected to nodes, which is usually located at JOINT, SUPPORT, and at the END O EER or where the member have SUDDEN CHANGE IN CROSS SECTION.

6 EXAPE A P When load P is applied to the beam, will cause node A to rotate, while node is completely restricted from moving. A P Onedegreeof freedom, A C our degreeof freedom, P C,,, A C C Three degreeof freedom, A D, C,

7 Conclusion 0 Real beam

8 OOD O IND ind the number of degree of freedom P w P P A C D Ans : 4

9 SOPE DEECTION EQUATION A - INTERNA END OENT Angular displacement at A (Near) Angular displacement at (ar) inear displacement ixed end moment

10 1. ANGUAR DISPACEENT AT A A A A A 4 EI A A EI A

11 . ANGUAR DISPACEENT AT A A 4 A EI A EI

12 EXAPE. A 4EI A A EI 4EI EI A

13 C 4EI C EI C 4EI EI C

14 CD 4EI C DC EI D 4EI EI D C

15 DE 4EI D ED EI E 4EI EI E D

16 . REATIVE INEAR DISPACEENT A 6EI A

17 EXAPE 1 Determine the moment due to linear displacement for each members. Assume mm settlement occur at support. 7kN 10kN/m A 4 m 4 m C

18 A A 6EI 6EI( 0.00) EI C C 6EI 6EI( 0.00) EI

19 OOD O IND Determine the moment due to linear displacement for each members. Assume mm and 1mm settlement occur at support and C respectively. 7kN 10kN/m A 4 m 4 m C

20 4. IXED END OENT A A oment cause by external load whilst the both support are fixed. - REER TAE

21 EXAPE Determine the ixed End oment for each members. 7kN 10kN/m A m m 4 m C

22 A P 8 7(4) 8.5kNm A P 8 7(4) 8.5kNm

23 C C w 1 10(4) 1 1.kNm w 1 10(4) 1 1.kNm

24 SOPE DEECTION EQUATION A 4EI EI 6EI A A Angular displacement at A Angular displacement at ixed end moment inear displacement

25 A 4EI EI 6 A EI A Angular displacement at Angular displacement at A ixed end moment inear displacement

26 Write down the slope deflection equation TU 4EI EI 6 T U EI TU UT 4EI EI 6 U T EI UT

27 EXAPE Analyse the two span continuous beam as shown below for the bending moment at the support point or member end using SD. The relative flexural rigidity for both span are identical ie EI is constant and the beam is subjected to a point moment of 100kNm at

28 Solution. ixed End oment A A C C 0 Slope Deflection Equation A C 0 0 A 4EI EI 6EI A A EI A 4EI EI 6EI A A EI

29 C 4EI EI 6EI C C EI C 4EI EI 6EI C C EI EQUIIRIU AT JOINT 100 A C 100 EI EI EI

30 SUSTITUTING INTO SDE A A C C 5kNm 50kNm 50kNm 5kNm

31 In figure below, the two span continuous beam shown earlier is now subjected two in span loads of UD having an intensity of 10 kn/m over span A and a point load of 5kN at the mid span of C. EI is constant. Determine the support moment at A, and C. Draw the bending moment diagram. 10 kn/m EXAPE 4 5 kn A EI EI C 6m 6m

32 SOUTION Step # 1 IXED END OENT A A C C W 1 0kNm P 5(6) kNm 0kNm 18.75kNm

33 Step # SOPE DEECTION EQUATION A C 0 A A A A 4EI EI EI 0 6 6EI A 4EI EI 6EI A EI 0 A A

34 C 4EI EI 6EI C C C EI C 4EI EI 6EI C C C EI 18.75

35 Step # Equilibrium Equation 0 A C 0 EI 0 EI EI 8.8

36 Step # 4 SUSTITUTING INTO SDE A A C C.81kNm 4.7kNm 4.8kNm 15.9kNm

37 OENT PROIE

38 Span A kn R kn R R A A (6) 10(6) m x x knm oment ax knm Area (.14)(1.4) 1

39 Span C R C R 11.09kN () 1.91kN R C (6) 0 Area ()(1.91) 41.7kNm ax oment kNm

40 D

41 EXAPE 5 Continuous beam with settlement at support and C. Determine the end moment in the figure if there is 1mm downward movement at support and C. Take EI is 75E knm for all span

42 SOUTION IXED END OENT A A C C CD DC.5kNm.5kNm 4kNm 6kNm 0 0

43 OENT DUE TO SHRINKAGE EI 6 A 50kNm EI 6 A 50kNm C 0 6EI

44 C 6EI EI 6 CD 18kNm EI 6 DC 18kNm 5

45 Slope Deflection Equation. A 4EI EI 6EI A A A A

46 A 4EI EI 6EI A A A A 10, C 4EI EI 6EI C C C C C 4 60,000 0,000 C 4

47 C 60,000 0,000 C 6 CD 60, C DC 0, C EQUIIRIU AT JOINT 0 A C 0 160,000 0, C

48 C 0 C CD 0 0,000 10, C 160,000 0,000 0,000 10,000 C

49 Solving by using calculator C SUSTITUTING INTO SDE A A C C CD DC 51.19kNm 15.1kNm 15.1kNm 15.9kNm 15.40kNm 1.0kNm

50 THANKS

51 Author Information ohd Arif in Sulaiman ohd aizal in d. Jaafar ohammad Amirulkhairi in Zubir Rokiah inti Othman Norhaiza inti Ghazali Shariza inti at Aris

THEORY OF STRUCTURES CHAPTER 3 : SLOPE DEFLECTION (FOR FRAME) PART 2

THEORY OF STRUCTURES CHAPTER 3 : SLOPE DEFLECTION (FOR FRAME) PART 2 or updated version, please click on http://ocw.ump.edu.my THEORY O STRUTURES HAPTER : SOPE DEETION (OR RAE) PART by Saffuan Wan Ahmad aculty of ivil Engineering & Earth Resources saffuan@ump.edu.my hapter