EAS253

Sem 1 / 2009-2010 /

Assgn 2 (SFD and BMD of statically determinate beams and frames)

1. Fig.1 shows a simply supported beam with two equal overhangs. Two loading conditions as shown in Fig.2(a) and 2(b) have to be considered for analysis. Draw the shear force and bending moment diagrams for the beam corresponding to the two loading conditions. Sketch also the qualitative deflected shape. Which loading condition will cause (a) the highest sagging moment and (b) the highest hogging moment? Indicate also the magnitude of the maximum sagging and hogging moments.

Fig.1 Fig.2

Note : Meaning of sagging and hogging moments are shown in the following illustrations

2. It is later found that the span length between B and C has increased by 2% as shown in Fig.3. Reanalyse the beam as shown in Fig.3 for the two loading conditions as shown previously in Fig.2(a) and 2(b). Draw the shear force and bending moment diagrams. What are the percentage change in (a) maximum sagging moment and (b) maximum hogging moment, compared with the values obtained in Question 1, due to the change in span length BC?

Fig.3

3. For the beam shown in Fig.4, draw the shear force and bending moment diagrams. Sketch also the qualitative deflected shape. Use (a) method of section and (b) method of direct integration, in the drawing of shear force and bending moment diagrams.

Fig.4

4. If the location of hinge C in the beam shown in Fig.4 above is shifted to the new location as indicated in Fig.5 below, redraw the shear force and bending moment diagrams. Use method of direct integration. Assume that the loading condition remains the same.

What is the effect of such change in the location on hinge C on the magnitude of : (a) maximum sagging moment, (b) maximum hogging moment and (c) internal force at hinge C ? Does the change in the location of hinge C also affect the location of section where maximum sagging and hogging moments occur?

Fig.5

5. Draw shear force and bending moments diagrams for the frame shown in Fig.6. Draw the bending moment diagram on compression and tension sides. Use method of section. Sketch also the qualitative deflected shape.

Fig.6

INSTRUCTION TO STUDENTS : Please read carefully

  1. Submit Questions 1, 2, 3 and 4 as group work. The number of students in a group must not be more than 3.
  1. Submit Question 5 as individual work
  1. Your work will be judged not only in terms of your answers but also in terms of

tidiness of your submitted assignment report. You are required to start your

answer toeach question on a new page.

  1. Consultation/discussion among yourselves is permitted. However, the work

submitted must be your own work. Any act of copying will be penalized.

  1. Deadline of submission: September 28 before 5pm
  1. Place of submission : PPKA office. Group and individual works must be submitted as separate reports with separate cover page.

7. Penalty will be imposed on late submission without any valid reason.