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 : Part Slope Deflection Aims Determine the end moment for frame using Slope Deflection ethod. Expected Outcomes : Able to identify the frame with or without side sway. Able to determine end moment at critical points. References echanics of aterials, R.. Hibbeler, 7th Edition, Prentice Hall Structural Analysis, Hibbeler, 7th Edition, Prentice Hall Structural Analysis, SI Edition by Aslam Kassimali,engage earning Structural Analysis, oates, oatie and Kong Structural Analysis - A lassical and atrix Approach, Jack. cormac and James K. Nelson, Jr., 4th Edition, John Wiley
RAE WITH SIDE SWAY WITHOUT SIDE SWAY Displace to the side when the body or the loading acting on it is nonsymmetric Properly restrained Symmetric with respect both loading and geometry
EER SIZES DEPEND ON ONIGURATION OADING SYSTE SUPPORT SYSTE
RAE WITHOUT SIDESWAY RAE WITH SIDESWAY
EXAPE 1 ANAYSIS - RAE WITHOUT SIDESWAY. y using SD, determine the bending moment at critical points. Assume is constant.
SOUTION IXED END OENT PQ QP RS SR 0 QR RQ P 8 P 8 45(6) 8 45(6) 8.75 knm.75 knm
SOPE DEETION EQUATION P 0 S PQ 4 6 P Q PQ PQ Q QP QP Q P 4 Q 6 QP
.75 R Q QR.75 Q R RQ RQ Q R RQ 6 4 QR R Q QR 6 4
RS 4 6 R S RS RS R SR 4 6 S R SR SR R
EQUIIRIU AT JOINT Q 0 R 0 QP 4 RQ Q 4 R QR RS R Q 0 0.75.75 1
4 1 1 4 Q R.75.75 Y USING AUATOR Q R.75.75
SUSTITUTING INTO SDE PQ QP QR RQ RS SR 11.5kNm.5kNm.5kNm.5kNm.5kNm 11.5kNm
OOD O IND Determine end moment at critical point. 10kN/m 6m A D m m
SOUTION IXED END OENT A A D D 0 0kNm SOPE DEETION EQUATION A 0 D A ( ) A A A
A A A ) ( 4 A 0
D D D ) ( 4 D 0
D D D ) ( D EQUIIRIU AT JOINT 0 0 0 0 D A
1 1 0 0 Solving by using alculator 18 18
SUSTITUTING INTO SDE A A D D 1kNm 4kNm 4kNm 4kNm 4kNm 1kNm
ANAYSIS O RAE WITH SIDE SWAY. EER SIZES DEPEND ON ONIGURATION OADING SYSTE SUPPORT SYSTE
UNDAENTA ASSUPTIONS 1. That axial deformation is ignored. That transverse end displacement do not affect the member length A A
EXAPE DETERINE END OENT AT RITIA POINT. ASSUE IS ONSTANT. 00 kn 4m 6m A D 5m
00 kn 4m 6m A D 5m
SOUTION ixed End oment A A D D 0 SOPE DEETION EQUATION A 8 A 8
4 5 5 5 5 5 D 6 D 6
Equilibrium at joint 0 A 0 4 8 5 5 9 0 5 5 8 0 1
0 D 0 4 0 5 5 6 0 5 15 6
H 0 H A H D 00 0 onsider member A H A 0 A A H A (4) 0 H A A A H A A 4 A
onsider member D H D 0 D D H D (6) 0 H D D H D D 6 D
6 A A A 4 6 A D 6 4 D D 4 00 D 4800 Insert the value 1 5 9 4800 6
ATRIX OR 4800 0 0 6 5 1 9 6 1 15 5 8 5 5 9 Solving by using calculator 150.86 75.66 4.78
Substituting into SDE A A D D 4.78 (150.88) 47.16kNm 8 (150.88) 4.78 5.9kNm 8 4(4.78) (75.66) 5.9kNm 5 5 4(75.66) (4.78) 158.04kNm 5 5 (75.66) 150.88 158.04kNm 6 75.66 150.88 18.6kNm 6
THANKS
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