10 solved structural FE exam problems

Professional Engineer Exam đ?š°

Study Guide For Structural Engineering Exam

Professional Engineer Exam Ι - Study Guide for Structural Engineering Exam

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COPYRIGHT NOTICE Copyrights © 2014 National Center for Assessment in Higher Education (QIYAS) Unless stated otherwise, copyright in this report (including content and design) is owned by the National Center for Assessment in Higher Education (QIYAS) - Riyadh – Saudi Arabia. EXCEPT with the expressed written permission from QIYAS, you may not reproduce, use (in particular for academic or commercial purposes), store in a retrieval system, adapt, modify, communicate to the public or photocopy any part of this report.

Professional Engineer Exam Ι - Study Guide for Structural Engineering Exam

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1. Objectives The aim of this manual is to provide guidelines for the examinees about the exam structure, timing, percentage of question coverage and distribution among various topic areas. In essence, the manual represents the bridge between the developed Structural Engineering Standards and the actual phrased questions, which constitute the tests to be administered. It is designed to familiarize the examinees with the test questions formats and contents.

2. Contents This study guide contains essential information for the examinees. Specifically, the following topics are presented in this manual: 

Exam structure, exam schedule and organization, exam type, eligibility for exam, and exam rules



Organization of the exam framework



Table of Specifications which includes an overview of the table, its structure and contents



Sample of questions and solutions for the Structural Engineering discipline

3. Exam Structure The exam is conducted in two sessions and the duration of each session is 3 hours.

3.1 General Engineering Exam The first session covers the General Engineering topics. These include the following fourteen topics: 1. Mathematics 2. Probability and Statistics 3. Computer Literacy 4. Statics and Dynamics 5. Chemistry Professional Engineer Exam Ι - Study Guide for Structural Engineering Exam

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6. Thermodynamics 7. Fluid Mechanics 8. Materials Science and Engineering 9. Electricity and Magnetism 10. Engineering Drawing 11. Engineering Economics 12. Project Management 13. Ethics 14. General Skills a. Use analytical thinking (logical deductions, statements and assumptions, cause and effect, verbal reasoning, analyzing arguments, statements and conclusions, break a complex problem into smaller problems and solve them) b. Use effective communication in writing, orally, and graphically c. Work cooperatively with other team members to deliver the required outcomes d. Set goals and ways for personal development e. Strive for ways to resolve conflicts while being sensitive to others opinions f. Be able to use time and available resources in an efficient way g. Recognize and interpret environmental, social, cultural, political and safety considerations in engineering solutions. h. Recognize decision making process i. Recognize major engineering concepts outside the discipline. j. Interpret uncertainties in measurements and calculations k. Analyze and interpret data l. Apply evaluation criteria and contemporary knowledge to select the optimum design from alternative solutions

3.2 Engineering Discipline Exam The second session covers the Engineering Standards and is based on topics associated with one of the following engineering disciplines:

Code CE CHE

Discipline Civil Engineering Chemical Engineering

Professional Engineer Exam Ι - Study Guide for Structural Engineering Exam

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EE

Electrical Engineering

IE

Industrial Engineering

ME

Mechanical Engineering

SE

Structural Engineering

4. Exam Implementation The exam consists of two sessions: 

The first session consists of General Engineering Exam. The total duration of this session is 3 hours with a total number of 90 questions.



The second session consists of Engineering Discipline Exam. This session consists of 50 questions with a total time of 3 hours.

5. Exam Type The exam is initially paper-based and will become computer based in a later stage. The exam, in both sessions, is of a multiple choice type where each question has four choices for the answer. There is no negative marking for wrong answers.

6. Eligibility for the Exam Bachelor degree holders in an Engineering discipline i.e., Chemical Engineering, Civil Engineering, Electrical Engineering, Industrial Engineering, Mechanical Engineering, and Structural Engineering.

7. Exam Rules  Books, lecture notes, or any type of materials are not allowed in the exam. Necessary reference sheets, monographs, equations, relevant data from codes will be provided in the exam.

 Calculators approved by Exam authorities are allowed.  Admission in the examination center will be only through authorized admission card

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 Examinees are subjected to all the rules and procedures applied by National Center for Assessment in Higher Education (Qiyas)

8. Organization of the Exam Framework The core topics constitute the basis of this Engineering Exam. Indicators are used to describe the knowledge to be tested in each topic. Each of these indicators is further subdivided into three major levels following the recent Bloom’s taxonomy of learning levels (Remembering and Understanding; Applying and Analyzing; and Evaluating and Creating).

Example Topic:

T2: Structural Analysis

Indicator:

SE-T2-03: Analyze statically determinate structures using equations of equilibrium

Learning Level:

Applying and Analyzing (AA)

9. Table of Specifications 9.1 Overview The Table of Specifications is a map which facilitates the transformation of the Engineering Standards for each Topic Area into balanced and coherent question sheets to be used in the proposed Exam The Table of Specifications is essentially a tableau structure which distributes, vertically, the exam Questions among various Topic Areas in accordance with the applicable Engineering Standards and, horizontally, over various Learning Levels (Remembering and Understanding, Applying and Analyzing, Evaluating and Creating).

9.2 Structure and Contents The table below constitutes the Table of Specifications for the Structural Engineering Discipline. The Table of Specifications contains the following columns:

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9.2.1 Topic Area These are the widely recognized Topic areas, which are covered in the Structural Engineering Discipline, namely: 1.

2.

3.

4.

5.

Mechanics Structural Analysis Design of Reinforced Concrete (RC) Structures Design of Steel Structures Materials

9.2.2 % of Test This column summarizes the total percentage (of the total test) allocated for each Topic Area.

9.2.3 Suggested Number of Questions This column indicates the number of questions to be allocated for each Engineering Standard.

The total number of questions per test conforms to the general guidelines which govern the total duration of the test. In the present case, 50 questions are included in each Discipline.

9.2.4 Engineering Standards This column lists the Engineering Standards to be addressed under each Topic Area.

Standards are coded SE-TJ (where SE denotes the Structural Engineering Discipline, TJ denotes the Topic Number J), whereas the Indicators are coded SE-TJ-K (where K denotes the Indicator number).

For example: SE-T2-5 is for the question in Structural Engineering (SE) that represents Topic 2 (Structural Analysis) and Indicator 5.

9.2.5 Assigned Allocations among Learning Levels The three sub-columns (Remembering and Understanding (RU), Applying and Analyzing (AA), and Evaluating and Creating (EC)) under this main column specify the question distribution among the three Learning Levels. For example, for the Design of RC Structures Principles (SE-T3), there are three questions assigned to Learning Level RU, six questions for AA, and six questions for EC. It is to be noted that the Learning Levels used in the Table of Specifications represent the so-called cognitive levels/processes (levels of thinking) in the revised Bloom's taxonomy.

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It is also important to note that the distribution of questions among various Topic Areas follows a careful and rigorous question allocation process, which ensures that appropriate relative levels of coverage are maintained for the various Learning Levels. For Structural Engineering, the distribution of questions (for all Topic Areas) among the three Learning Levels is 13 questions (26%) for Remembering and Understanding, 24 questions (48%) for Applying and Analyzing, and 13 questions (26%) for Evaluating and Creating.

Professional Engineer Exam Ι - Study Guide for Structural Engineering Exam

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Table of Specifications for Structural Engineering Exam

% of Test

#Q

T1- Mechanics

10

5

T2- Structural Analysis

30

T3- Design of RC Structures

Topic Area

Assigned Allocations of Questions among Learning Levels

Engineering Standard

Remembering and Understanding

Applying and Analyzing

Evaluating and Creating

SE-T1

2

2

1

15

SE-T2

4

8

3

30

15

SE-T3

3

6

6

T4- Design of Steel Structures

10

5

SE-T4

1

2

2

T5- Materials

20

10

SE-T5

3

6

1

100

50

13 (26%)

24 (48%)

13 (26%)

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10.

Sample Questions

A sample of questions is shown in the following tabular format in accordance with the following instructions.

1.

For Learning Levels  RU for Remembering and Understanding  AA for Applying and Analyzing  EC for Evaluating and Creating

2.

References sheets are denoted in the last column of the Table

Professional Engineer Exam Ι - Study Guide for Structural Engineering Exam

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Table of Questions Sample Q. No.

Topic Area

Indicator Learning Code Level

1

Mechanics

SE-T1-01

RU

Question Statement (Answer’s Choices)

Answer

The shown rectangular section is for a reinforced

B

Expected Supplied Time Reference (min)

3–4

None

concrete column, which supports an eccentric compressive load

P

acting at point B. The

combined normal and bending stresses at point A is: A)

6 Pex P  hb 2 bh

C) 

6 Pex P  hb 2 hb

B)

6 Pex P  bh 2 bh

D)

6 Pex P  bh 2 hb

Professional Engineer Exam Ι - Study Guide for Structural Engineering Exam

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All the three members of the frame shown below are of equal length and of the same flexural rigidity EI. If a moment of 11 kN.m is applied at joint B, the rotation of the joint is: 2m

D

Structural 2

Analysis

SE-T2-09

EC

2m

2m

B

C

B

11 kN.m

3–4

Reference #2

A

A)

1 EI

B)

2 EI

C)

3 EI

D)

4 EI

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For the shown loaded truss, the internal forces (kN) in the members CD, CE, DE and EF are, respectively:

G

B

C

4m

A Structural 3

Analysis

SE-T2-04

AA

E

F 2m

10 kN 4m

D 15 kN 4m

A

3–4

None

A) 0, 15, 0, 0 B) 0, -15, 0, 0 C) 15, 0, 0, 0 D) -15, 0, 0, 0

Note: Negative sign indicates compressive internal force in a member

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A rectangular reinforced concrete beam section is shown below. If the shear carried by the concrete and stirrups are 180 kN and 120 kN, respectively, then the design shear strength of the section (in kN) is: b

Design of 4

RC

SE-T3-02

AA

h

C

2 – 2.5

None

Structures

A)

120

B)

180

C)

225

D)

300

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For

the

beam

section

shown,

the

28-day

compressive strength of concrete (fc’) is 30 MPa and the yielding strength of steel (fy) is 420 MPa. According to the Saudi Building Code “SBC 304” (Structural – Concrete Structures) section 10.2.7, the nominal moment capacity (kN.m) of the beam is: (All dimensions are in mm) Design of 5

RC

SE-T3-08

EC

A 375

Structures

3–4

Reference #5

450

300

A) 138.2 B) 178.2 C) 195.8 D) 210.6

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A 24 kg of aggregate is sieved through 9.5 mm, 4.75 mm, 2.36 mm, 1.18 mm, 600 µm, 300 µm and 150 µm standard sieves and the masses retained in each sieve are 0 kg, 0.6 kg, 3 kg, 4.8 kg, 5.6 kg, 5 kg, and 4 kg, respectively. The fineness modulus of this aggregate is:

6

Materials

SE-T5-05

AA

A) 2.75 B) 2.80

C

3–4

None

C) 2.85 D) 2.90

Hint: According to ASTM C125, the fineness modulus of aggregates is calculated by adding the cumulative percentage of mass retained on each of specified series of sieves.

Professional Engineer Exam Ι - Study Guide for Structural Engineering Exam

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Reference #2 The stiffness of a joint (k) in a member of length L is equal to: 4đ??¸đ??ź đ?‘˜={ đ??ż 3đ??¸đ??ź đ??ż

opposite and fixed opposite and pinned

Reference #5

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11. Solution of the Sample Questions Question #1: Topic Area: Mechanics

Learning Level:

Remembering and Understanding

Indicator: SE-T1-01

Evaluate axial, normal, shear and bending stresses in prismatic bars of rectangular and circular cross sections

Question Statement:

The shown rectangular section is for a reinforced concrete column, which supports an eccentric compressive load P acting at point B. The combined normal and bending stresses at point A is: A)

6 Pex P  hb 2 bh

C) 

6 Pex P  hb 2 hb

B)

6 Pex P  bh 2 bh

D)

6 Pex P  bh 2 hb

Answer: B

Supplied Reference: None Estimated Solution Time by Examinee: 3.0 – 4.0 minutes Professional Engineer Exam Ι - Study Guide for Structural Engineering Exam

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Remarks:

The objective of this question is to ensure that the examinee can formulate and determine stresses

Solution:

At point A, M x is causing tensile stresses and P is causing compressive stress.

Thus, the stress at point A is given by:

A 

Mx P  Zx A

where

Zx & A

=

the section modulus about x and the area of the section, respectively

bh 2 Zx  6 A  bh The bending moments resulted from the load P is:

M x  P  ex

A 

6 Pex P  bh 2 bh

(Ans.)

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Question #2: Topic Area: Structural Analysis Learning Level:

Evaluating and Creating

Indicator: SE-T2-09

Analyze indeterminate beams and frames using different methods including both classic and numerical methods

Question Statement:

All the three members of the frame shown below are of equal length and of the same flexural rigidity EI. If a moment of 11 kN.m is applied at joint B, the rotation of the joint is: 2m

2m

D 2m

B

C

11 kN.m

A

A)

1 EI

B)

2 EI

C)

3 EI

D)

4 EI

Answer: B

Supplied Reference: Reference #2

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Estimated Solution Time by Examinee: 3.0 – 4.0 minutes

Remarks:

The objective of this question is to ensure that the examinee can determine rotation of indeterminate frame

Solution:

 4 EI   4 EI   3EI  11EI 11EI Total stiffness of the joint K T  K BA  K BD  K BC       L 2  L   L   L  11EI 2M 2  11 2 we know, M  K T        Ans. 2 11EI 11EI EI

Professional Engineer Exam Ι - Study Guide for Structural Engineering Exam

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Question #3: Topic Area: Structural Analysis

Learning Level:

Applying and Analyzing

Indicator: SE-T2-04

Evaluate the internal forces in determinate beams, frames and trusses

Question Statement:

For the shown loaded truss, the internal forces (kN) in the members CD, CE, DE and EF are, respectively:

G

B

C

4m A

E

F 2m

10 kN 4m

D 15 kN 4m

Note: Negative sign indicates compressive internal force in a member

A) 0, 15, 0, 0 B) 0, -15, 0, 0 C) 15, 0, 0, 0 D) -15, 0, 0, 0

Answer: A Reference Sheet: None Professional Engineer Exam Ι - Study Guide for Structural Engineering Exam

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Estimated Solution Time by Examinee: 3.0 – 4.0 minutes

Remarks:

The objective of this question is to ensure that the examinee can determine internal force in a truss

Solution:

From equilibrium of joint D, FCD  0

Ans.

FDE  0

Ans.

From equilibrium of joint E,

E



 Fx  0  FEF  0

Ans.



 Fy  0  FCE  15 kN (T)

Ans.

15 kN

Professional Engineer Exam Ι - Study Guide for Structural Engineering Exam

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Question #4: Topic Area: Design of RC Structures Learning Level:

Applying and Analyzing

Indicator: SE-T3-02

Analyze and design reinforced concrete beams for flexure and shear according to code provisions

Question Statement:

A rectangular reinforced concrete beam section is shown below. If the shear carried by the concrete and stirrups are 180 kN and 120 kN, respectively, then the design shear strength of the section (in kN) is: b

h

(A)

120

(B)

180

(C)

225

(D)

300

Answer: C

Reference Sheet: None Estimated Solution Time by Examinee: 2.0 – 2.5 minutes Professional Engineer Exam Ι - Study Guide for Structural Engineering Exam

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Remarks:

The objective of this question is to ensure that the examinee can evaluate shear strength of beam

Solution:

The design shear strength : Vn   Vc  Vs   0.75  (180  120)  225 kN

Ans.

Professional Engineer Exam Ι - Study Guide for Structural Engineering Exam

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Question #5: Topic Area: Design of RC Structures Learning Level:

Evaluating and Creating

Indicator: SE-T3-08

Recognize the importance of building codes, especially SBC and ACI Codes, in the RC design process

Question Statement:

For the shown beam section, the 28-day compressive strength of concrete (fc’) is 30 MPa and the yielding strength of steel (fy) is 420 MPa. According to the Saudi Building Code “SBC 304” (Structural – Concrete Structures) section 10.2.7, the nominal moment capacity (kN.m) of the beam is: (All dimensions are in mm)

375

450

300

A) 138.2 B) 178.2 C) 195.8 D) 210.6 Answer: A Supplied Reference: Reference #5 Estimated Solution Time by Examinee: 3.0 – 4.0 minutes

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Remarks:

The objective of this question is to ensure that the examinee can evaluate ultimate moment of a beam and apply SBC

Solution:

0.85 f c'

1c  a 375

C  0.85 f c'ab d

a 2

3-

T  As f y

300    T  As f y   3   20 2   420  10  3  395 .8 kN 4   C  0.85 f c' ab  0.85  30  a  300  10  3  7.65a Equating T and C for equilibriu m and solving for a : 775454 .4 C  T  7.65a  395 .8  a   51.7 mm 5950 Compute M n : a 51.7    3 M n  T  d    395 .8   375    138 .2  10 kNmm  138.2 kN.m 2 2   

Professional Engineer Exam Ι - Study Guide for Structural Engineering Exam

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Question #6: Topic Area: Materials Learning Level:

Applying and Analyzing

Indicator: SE-T5-05

Analyze testing results of concrete and other construction materials

Question Statement:

A 24 kg of aggregate is sieved through 9.5 mm, 4.75 mm, 2.36 mm, 1.18 mm, 600 µm, 300 µm and 150 µm standard sieves and the masses retained in each sieve are 0 kg, 0.6 kg, 3 kg, 4.8 kg, 5.6 kg, 5 kg, and 4 kg, respectively. The fineness modulus of this aggregate is:

A) 2.75 B) 2.80 C) 2.85 D) 2.90

Hint: According to ASTM C125, the fineness modulus of aggregates is calculated by adding the cumulative percentage of mass retained on each of specified series of sieves

Answer: C

Reference Sheet: None Estimated Solution Time by Examinee: 3.0 – 4.0 minutes

Remarks:

The objective of this question is to ensure that the examinee can analysis engineering properties of constituent materials of concrete

Solution: Professional Engineer Exam Ι - Study Guide for Structural Engineering Exam

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Sieve size 9.5 mm 4.75 mm 2.36 mm 1.18 mm 600 µm 300 µm 150 µm Pan Total

Retained mass (kg) 0.00 0.60 3.00 4.80 5.60 5.00 4.00 1.00 24.00

% retained 0.00 2.50 12.50 20.00 23.33 20.83 16.67 4.17 100.00

Fineness modulus = 285/100 = 2.85

Cumulative % retained 0.00 2.50 15.00 35.00 58.33 79.17 95.83 285.83 (Ans.)

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