THEORY OF STRUCTURE DCC40163 E X A M P L E & R E V I S I O N G U I D E F O R P O L Y T E C H N I C S T U D E N T S ANIZA TAHIR MOHMAD NAZRI MAHBOB
Published by : Politeknik Sultan Azlan Shah Behrang Stesen, Behrang 35950 Perak. Tel :05-4544431 Faks:05-4544993 Email : http://www.psas.edu.my First published 2021 All rights reserved. No part of this publication may be reproduced stored in a retrievel system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without premission of Sultan Azlan Shah Polytechnics. PERPUSTAKAAN NEGARA MALAYSIA Theory of Structure DCC40163 Example and Revision Guide e ISBN 978-967-2409-43-4
covers basic knowledge of facts and principles in calculate the reactions, bending moments and shear forces for statically indeterminate beams and portal frame using the slope deflection method and moment distribution method. It also includes basic principles in analyse the forces in truss members using the equilibrium joint method for the statically determinate and using unit load method for the statically indeterminate trusses. Influence lines have important application for the design of structures that resist large live loads. Evaluation in influence lines include determination of shear force, bending moment and the absolute maximum moment. THEORY OF STRUCTURES SYNOPSIS
1 2 3 Evaluate the influence lines for statically determinate beams correctly. (C5, PLO2). Calculate statically indeterminate beams and portal frame using appropriate method (C3, PLO1). Analyze joint displacement in statically determinate trusses and internal forces for statically indeterminate trusses correctly (C4, PLO2). COURSE LEARNING OUTCOMES (CLO) Upon completion of this course , student should be able to :
PLO 1 apply knowledge of applied mathematics, applied science, engineering fundamentals and an engineering specialization as specified in DK1 to DK4 respectively to wide practical procedures and practices identify and analyse welldefined engineering problems reaching substantiated conclusions using codified method of analysis specific to their field of activity (DK1 to DK4) PROGRAMME LEARNING OUTCOMES (PLO) Upon completion of this course , student should be able to : PLO 2 DK1 : A descriptive, formula-based understanding of the natural sciences applicable in a sub-discipline DK2 : Procedural mathematics, numerical analysis, statistics applicable in a subdiscipline DK3 : A coherent procedural formulation of engineering fundamentals required in an accepted sub-discipline DK4 : Engineering specialist knowledge that provides the body of knowledge for an accepted sub-discipline
C O N T E N T S T A B L E O F 7 20 34 47 61 69 76 84 SLOPE DEFLECTION FOR STATICALLY INDETERMINATE BEAMS SLOPE DEFLECTION FOR STATICALLY INDETERMINATE PORTAL FRAMES MOMENT DISTRIBUTION METHOD FOR STATICALLY INDETERMINATE BEAMS MOMENT DISTRIBUTION METHOD FOR STATICALLY INDETERMINATE PORTAL FRAMES ANALYSIS OF STATICALLY DETERMINATE 2D-PIN JOINTED TRUSSES THE JOINT DISPLACEMENT OF STATICALLY DETERMINATE 2D-PIN JOINTED TRUSSES ANALYSIS OF STATICALLY INDETERMINATE 2D-PIN JOINTED TRUSSES INFLUENCE LINES FOR STATICALLY DETERMINATE BEAMS
1 2 3 Draw shear force and bending moment diagram CHAPTER 1 State the slope deflection equation Calculate the internal moments at support for continuous beams subjected to point loads and distributed loads up to three unknowns using slope deflection method SLOPE DEFLECTION METHOD FOR STATICALLY INDETERMINATE BEAMS At the end of this chapter , student should be able to : PLO 1: Apply knowledge of applied mathematics, applied science, engineering fundamentals and engineering specialization as specified in DK 1 to DK4 respectively to wide practical procedures and practices
A continuous beam is loaded as shown in figure below i. Calculate fixed end moments for each member. ii. Write down the slope deflection equations. iii. Compute the value of joint rotation at joint B, ƟB. iv. Calculate the final moments for support A, B and C. v. Calculate the reactions at support A, B and C. vi. Draw shear force and bending moment diagram. EXAMPLE
1 Fixed end moments By using the fixed-end moment expression, evaluate the fixed-end moments due to the external loads for each member. SOLUTION Calculate fixed end moments for each member.
1 SOLUTION Calculate fixed end moments for each member. Span AB Span BC
2 Slope deflection equations express the final end moments of each member in terms of the joint rotations and displacements. Note that since the support A and C are fixed and no support settlement occur, it follow that SOLUTION Write down the slope deflection equations.
2 SOLUTION Write down the slope deflection equations. ....(1) ....(2) ....(3) ....(4)
3 SOLUTION Compute the value of joint rotation at joint B, ƟB. Joint rotation at joint B, ƟB. Write down joint equilibrium equations except fixed supports. Then, solve the equilibrium equations.
4 Final moments can now be computed by substituting the value of joint rotation in slope deflection equations. SOLUTION Calculate the final moments for support A, B and C.
5 Reactions are obtaining by apply the equations of equilibrium to the free body of the entire structure. SOLUTION Calculate the reactions at support A, B and C.
6 SOLUTION Draw shear force and bending moment diagram. shear force diagram bending moment diagram
STEP OF SOLUTION Remember: Help is always available. 1 2 3 4 5 6
Name: Program: TUTORIAL 1 50 Metric Number:
Name: Program: TUTORIAL 2 50 Metric Number:
1 2 3 Draw shear force and bending moment diagram CHAPTER 2 State the slope deflection equation Calculate the internal moment at portal frame support and joint subjected to point loads and distributed loads up to three (3) unknowns using the slope deflection method. SLOPE DEFLECTION METHOD FOR STATICALLY INDETERMINATE PORTAL FRAMES At the end of this chapter , student should be able to : PLO 1: Apply knowledge of applied mathematics, applied science, engineering fundamentals and engineering specialization as specified in DK 1 to DK4 respectively to wide practical procedures and practices PLO 1: Apply knowledge of applied mathematics, applied science, engineering fundamentals and engineering specialization as specified in DK 1 to DK4 respectively to wide practical procedures and practices
A portal frame are subjected to distributed load, 10kN/m and point load 10kN as shown in figure below i. Calculate fixed end moments for each member. ii. Write down the slope deflection equations. iii. Compute the joint rotation at joint B. iv. Calculate the final moments for support A, B and C. v. Calculate the reactions at support A, B and C. vi. Draw shear force and bending moment diagram. EXAMPLE
1 b. 36 d. 111 SOLUTION Calculate fixed end moments for each member. Fixed end moments By using the fixed-end moment expression, evaluate the fixed-end moments due to the external loads for each member.
1 b. 36 d. 111 SOLUTION Calculate fixed end moments for each member. Span AB Span BC
2 SOLUTION Slope deflection equations express the final end moments of each member in terms of the joint rotations and displacements. Note that since the support A and C are fixed and no support settlement occur, it follow that b. 36 d. 111 Write down the slope deflection equations.
2 b. 36 SOLUTION Write down the slope deflection equations. ....(1) ....(2) ....(3) ....(4)
3 b. 36 SOLUTION Compute the value of joint rotation at joint B, ƟB. Joint rotation at joint B, ƟB. Write down joint equilibrium equations except fixed supports. Then, solve the equilibrium equations.
4 Final moments can now be computed by substituting the value of joint rotation in slope deflection equations. b. 36 d. 111 SOLUTION Calculate the final moments for support A, B and C.
5 b. 36 d. 111 SOLUTION Calculate the reactions at support A, B and C. Reactions are obtaining by apply the equations of equilibrium to the free body of the entire structure.
5 b. 36 d. 111 SOLUTION Calculate the reactions at support A, B and C.
Calculate the reactions at support A, B and C. 6 b. 36 d. 111 SOLUTION Draw shear force and bending moment diagram.
STEP OF SOLUTION Remember: Help is always available. 1 2 3 4 5 6
Name: Program: Metric Number: TUTORIAL 1 50 A portal frame are subjected to distributed load, 10kN/m and point load 40kN as shown in figure below, i. Calculate fixed end moments for each member. ii. Write down the slope deflection equations. iii. Compute the joint rotation at joint A and B. iv. Calculate the final moments for support A, B and C. v. Calculate the reactions at support A, B and C. vi. Draw shear force and bending moment diagram.
A portal frame is loaded as shown in figure below, i. Calculate fixed end moments for each member. ii. Write down the slope deflection equations. iii. Compute the joint rotation at joint A and B. iv. Calculate the final moments for support A, B and C. v. Calculate the reactions at support A, B and C. Name: Program: TUTORIAL 2 50 Metric Number:
1 2 3 Draw shear force and bending moment diagram. CHAPTER 3 Describe the basic concept of moment distribution method for statically indeterminate beams. Calculate the internal moment at supports for continuous beams subjected to point loads and distributed loads using moment distribution method. MOMENT DISTRIBUTION METHOD FOR STATICALLY INDETERMINATE BEAMS At the end of this chapter , student should be able to : PLO 1: Apply knowledge of applied mathematics, applied science, engineering fundamentals and engineering specialization as specified in DK 1 to DK4 respectively to wide practical procedures and practices
Figure below shows 40kN of point load acting on span AB and 60kN/m uniformly distributed load acting along span BC. By using moment distribution method, i. Calculate fixed end moments for each member. ii. Compute the relative stiffness of the beam. iii. Compute the distribution factors. iv. Calculate the final moments for the beam. v. Calculate the reactions at support A, B and C. vi. Draw shear force and bending moment diagram. EXAMPLE
SOLUTION 1 Calculate fixed end moments for each member. Fixed end moments By using the fixed-end moment expression, evaluate the fixed-end moments due to the external loads for each member.
1 SOLUTION Calculate fixed end moments for each member. Span AB Span BC
2 SOLUTION Compute the relative stiffness of the beam. Relative stiffness, k of a member is given by
3 SOLUTION Compute the distribution factors. Distribution factors, DF for each member at each node based on relative stiffness of the members using equation below,
4 SOLUTION Calculate the final moments for the beam.
4 SOLUTION Calculate the final moments for the beam.
5 SOLUTION Calculate the reactions at support A, B and C. Reactions are obtained by apply the equations of equilibrium to the free body of the entire structure.
6 SOLUTION Draw shear force and bending moment diagram. shear force diagram bending moment diagram
STEP OF SOLUTION Remember: Help is always available. 1 2 3 4 5 6
A continuous beam is loaded as shown in figure below, i. Calculate fixed end moments for each member. ii. Compute the relative stiffness of the beam. iii. Compute the distribution factors. iv. Calculate the final moments for the beam. v. Calculate the reactions at support A, B and C. vi. Draw shear force and bending moment diagram. Name: Program: Metric Number: TUTORIAL 1 50
A continuous beam is loaded as shown in figure below, i. Calculate fixed end moments for each member. ii. Compute the relative stiffness of the beam. iii. Compute the distribution factors. iv. Calculate the final moments for the beam. v. Calculate the reactions at support A, B and C. vi. Draw shear force and bending moment diagram. Name: Program: TUTORIAL 2 50 Metric Number:
1 2 3 Draw shear force and bending moment diagram. CHAPTER 4 Describe the basic concept of moment distribution method for portal frame. Calculate the internal moment at supports and joint subjected to point loads, distributed loads for the frame using moment distribution method. MOMENT DISTRIBUTION METHOD FOR STATICALLY PORTAL FRAMES At the end of this chapter , student should be able to : PLO 1: Apply knowledge of applied mathematics, applied science, engineering fundamentals and engineering specialization as specified in DK 1 to DK4 respectively to wide practical procedures and practices
A portal frame is subjected with a uniformly distributed load and point loads as shown below. By using moment distribution method, i. Calculate fixed end moments for each member. ii. Compute the relative stiffness of the beam. iii. Compute the distribution factors. iv. Calculate the final moments for the beam. v. Calculate the reactions at support A, B and C. vi. Draw shear force and bending moment diagram. EXAMPLE
SOLUTION 1 Calculate fixed end moments for each member. Fixed end moments By using the fixed-end moment expression, evaluate the fixed-end moments due to the external loads for each member.
SOLUTION 1 Calculate fixed end moments for each member. Fixed end moments By using the fixed-end moment expression, evaluate the fixed-end moments due to the external loads for each member.