PUC - DEPARTMENT OF BUILT ENVIRONMENT NANA BENYI ANSAH

PENTECOST UNIVERSITY COLLEGE

FACULTY OF ENGINEERING SCIENCES & COMPUTING

DEPARTMENT OF BUILT ENVIRONMENT

END OF SECOND SEMESTER EXAMINATIONS JUNE 2015

COURSE TITLE: STRUCTURAL ANALYSIS OF BEAMS & COLUMNS

LEVEL 200 - BRIDGING

BSc (Quantity Surveying & Construction Economics)BSc (Construction Technology & Engineering Management)ANSWER ALL QUESTIONS 3HRS

Time Allowed - 3 Hrs

INSTRUCTIONS TO STUDENTS

1. Do not write on the question paper

2. Do not leave your seat unless you are given permission by an invigilator3. All answers should be written in the answer booklet(s) provided4. All rough work should be written in the answer booklet and a line drawn through them to

indicate they are not part of the main answers.5. Write legibly in blue or black ink6. PDAs and mobile phones are not allowed in the examinations7. You may not leave the examination room until after the first hour

8. All announcements would be made when there are 30 minutes of the exam time left.9. At the end of examinations remain seated until your answer booklet(s) have been

collected and you have been asked to leave.

PUC - DEPARTMENT OF BUILT ENVIRONMENT NANA BENYI ANSAH

Question One

a) From the loaded beam shown below, draw the bending moment and shear forcediagrams.

b) Express the shear force V and the bending moment M as a function of the distance x,from the left end of the beam. Plot the shear force and the bending moment diagrams.

(25marks)

Question Twoa) In brittle materials failure occurs due to separation of atomic planes. In ductile materials

yielding occurs not due to separation of atoms but due to sliding of atoms. Discuss thefailure theory behind the outlined principle. (9 marks)

b) Using the Rankine Theory of structural instability show that the failure compressionstress (c) of a column of any length is given by c = = s/1+k (Le/r)2, where = k isthe material constant, Le/r = slenderness ratio. (7 marks)

c)

Question Threea) A solid circular shaft of diameter 225mm is to be replaced by a hollow shaft in which

the ratio of the diameters is 1 : 1. Determine the size of the hollow shaft required totransmit the same torque as the solid shaft at the same maximum shearing stress.Calculate the percentage economy in mass of material used that this change willproduce.

(11marks)

4m

3kN/m

4m

A B C D EF

2m 4m

3kN/m6kN

24kNm

4m

PUC - DEPARTMENT OF BUILT ENVIRONMENT NANA BENYI ANSAH

b) A simply supported beam is loaded as shown below. Determine the magnitude of thedeflection at mid span. EI = constant

(14 marks)

Question FourA statically determinate rigid jointed frame is shown below. For the loaded case shown,determine the following:

i) support reactionsii) sketch the axial loadiii) shear force andiv) bending moment diagrams (25 marks)

2m 4m 3m 1m

5kN 10kN 8kN

E

A B C D E

YEYA

PUC - DEPARTMENT OF BUILT ENVIRONMENT NANA BENYI ANSAH

15kN 2.5m

2.5m

24kN

6kN/m12kN

6.0m3.0m

A

B C D

E

FHA HF