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. Span AB Span BC
SOLUTION 2 Compute the relative stiffness of the beam. Relative stiffness, k of a member is given by
SOLUTION 3 Compute the distribution factors. Distribution factors, DF for each member at each node based on relative stiffness of the members using equation below,
SOLUTION 4 Calculate the final moments for the beam.
SOLUTION 4 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 portal frame is loaded as shown in figure below, i. Calculate fixed end moments for each span of the frame. 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 portal frame is loaded as shown in figure below, i. Calculate fixed end moments for each span of the frame. 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 4 Calculate the truss members forces using method of joints and method of section. CHAPTER 5 Identify types of trusses, tension members and compression members Discuss between determinate and indeterminate trusses. ANALYSIS OF STATICALLY DETERMINATE 2D PIN-JOINTED TRUSSES At the end of this chapter , student should be able to : 3 Identify zero-force members.
A simply supported truss is subjected to a load at joint C respectively as shown in figure below. i. Identify the truss as statically determinate structure. ii. Compute the reactions at support A and B. iii. Calculate the forces at joint B, E and C by the method of joint. iv. Based the answer on the example (iii), produced a diagram of truss by showing forces including sign of force direction. EXAMPLE
1 2 SOLUTION Identify the truss as statically determinate structure Compute reaction at support A and B
3 SOLUTION Calculate the internal forces at joint B, E and C
3 SOLUTION Calculate the internal forces at joint B, E and C
3 4 SOLUTION Calculate the internal forces at joint B, E and C Produced a diagram of truss by showing forces including sign of force direction.
Figure below shows a frame structure subjected to a horizontal load of 30kN at joint D and a vertical load of 10kN at joint C. i. Calculate the reaction at support A and B. ii. Calculate the internal forces at joint B, C and A by using the method of joint. iii. Calculate the force in members AB, AD and CD by using the method of sections. iv. Based on the answers in Question (i) and (ii), produced a diagram of the truss by showing its forces including its sign of direction. Name: Program: Metric Number: TUTORIAL 1 50
A simply supported truss is subjected to a load at joint B as shown in figure below, i. Identify the truss as statically determinate structure ii. Calculate the reaction force for the truss. iii. Determine the internal forces at joint D and joint C by using the joint method. Name: Program: TUTORIAL 2 50 Metric Number:
1 2 4 Calculate the vertical, horizontal and resultant displacement of the truss joint due to external loads CHAPTER 6 Describe the displacement causes of external load. Explain the principle of virtual work method or unit load method. THE JOINT DISPLACEMENT OF STATICALLY DETERMINATE 2D PIN-JOINTED TRUSSES At the end of this chapter , student should be able to : 3 Write the joint displacement formula for a truss derived from the method of virtual work or unit load method due to external load
EXAMPLE 6.1
1 b. 36 d. 111 SOLUTION Reactions By using equilibrium equations, ANIZA BINTI TAHIR Compute reaction at support A and B Real system the real system consists of the loading given in the problem, as shown in Figure 6.1(b). The member axial forces due to the real loads (F) obtained by using the method of joints. The results are shown in Figure 6.1(b). Positive answers indicate that the member is in tension and negative answers indicate that the member is in compression 2 Calculate the internal force in each member of the truss due to the real loads.
3 b. 36 d. 111 SOLUTION ANIZA BINTI TAHIR Compute the internal force in each member of the truss due to a vertical virtual unit load at joint C.
4 b. 36 d. 111 SOLUTION ANIZA BINTI TAHIR Based on the answers in Example 6.1 (ii) and 6.1(iii), calculate the vertical displacement of joint C.
Name: Program: Metric Number: TUTORIAL 1 50
Name: Program: TUTORIAL 2 50 Metric Number:
1 2 CHAPTER 7 Explain indeterminate trusses. Discuss between internal statically indeterminate and external indeterminate trusses. ANALYSIS OF STATICALLY INDETERMINATE 2D PIN-JOINTED TRUSSES At the end of this chapter, student should be able to : 3 Calculate the internal forces in truss members using the unit load method.
EXAMPLE 7.1
1 b. 36 ANIZA BINTI TAHIR 2 Select AC as a redundant member. Then, compute the internal forces in all truss members. 3 d. 111 SOLUTION Identify the truss as statically indeterminate structure. I. IDENTIFY THE TRUSS AS STATICALLY INDETERMINATE STRUCTURE. Calculate the forces in all members due to the virtual unit load.
ANIZA BINTI TAHIR b. 36 d. 111 SOLUTION
4 ANIZA BINTI TAHIR b. 36 d. 111 SOLUTION Determine the magnitude of redundant, R.
4 ANIZA BINTI TAHIR b. 36 d. 111 SOLUTION Produced the actual force in all members of the truss by using the magnitude of redundant, R
Name: Program: Metric Number: TUTORIAL 1 50
Name: Program: TUTORIAL 2 50 Metric Number:
1 2 CHAPTER 8 Sketch the influence line diagram for reaction, shear force and bending moment for simply supported beam, simply supported beam with one hanging and simply supported beam with two end hanging. Calculate the maximum shear force and bending moment at a certain section of beam using the influence lines diagram for a beam subjected to a set of moving loads. INFLUENCE LINES FOR STATICALLY DETERMINATE BEAMS At the end of this chapter, student should be able to : 3 Measure the absolute maximum moment in a simply supported beam subjected to a series of moving point loads.
EXAMPLE 8.1
ANIZA BINTI TAHIR 1 b. 36 SOLUTION Shear Created at Point B.
ANIZA BINTI TAHIR 2 b. 36 d. 111 SOLUTION Moment Created at Point B.
EXAMPLE 8.2
ANIZA BINTI TAHIR 1 b. 36 SOLUTION The Maximum Positive Shear Created At Point C.
ANIZA BINTI TAHIR b. 36 SOLUTION
ANIZA BINTI TAHIR 2 b. 36 SOLUTION The Maximum Moment Created At Point C
ANIZA BINTI TAHIR b. 36 SOLUTION
Name: Program: Metric Number: TUTORIAL 1 50 Figure below shows a beam carry a series of three moving concentrated loads which is 5kN leading move over the beam. Compute, i. the maximum positive shear created at point C. ii. the maximum moment created at point C.
A 15m long simply supported beam carry a series of four moving concentrated loads as shown in figure below, i. calculate the resultant force of the load series. ii. calculate the location of the resultant force from point X. iii. calculate the absolute maximum moment due to the moving concentrated load series. Name: Program: TUTORIAL 2 50 Metric Number:
REFERENCES
DCC 40163 THEORY OF STRUCTURE EXAMPLE & REVISION QUESTION This Book Is Published For Convenience To Students Polytechnic . The Information Contained In This Book Meets The Needs Of Engineering Students At Polytechnics For Revision Guide On Examination