Lectures of Structure I 2017-2018[Department of architectural engineering]

University of Babylon

College of Engineering

Department of Architectural EngineeringLectures of

Structure I

Instructor: Dr. Majid Mohammed Ali E-mail :eng.majid.mohammed@uobabylon.edu.iq 2 hours per week Conduct

Quizzes, homework and project Mid-term exam Final exam10% 30% 60%

Content of the term

General introduction about forces, their kinds and affects 1 week

Resultant of forces 3 weeks

The couple 1 week

Equilibrium 4 weeks

Analysis of truss 3 weeks

Drawings of axial, shear forces ,and bending moments 3 weeks

References:

Higdon, and W. Stiles ," Engineering Mechanics", 3rd edition, prentice Hall of India, New Delhi ,1974

Hibbeler," Engineering Mechanics-Static", 12rd edition, Mc Grew Hill ,2008

Meriam, J. L., Kraige, L. G. " Engineering Mechanics-Static", 2008

Introduction1University of Babylon

Lectures of Structure I 2017-2018[Department of architectural engineering]

Mechanics - the physical science which describes or predicts the conditions of rest or motion of bodies under the action of forces.

Scalars and vectors

Scalar - A mathematical quantity possessing magnitude only (mass, volume, time … etc.)

Vector - A mathematical quantity possessing magnitude and direction (force, displacement, velocity … etc.)

Force

The action of a body on another body which changes or tempts to change the motion of the body acted on.

Elements of a Force

Given a single force, one is interested in knowing all of the

following:

1. Magnitude

2. Direction which defines by sign or slope

3. Line (point) of Action

Principle of Transmissibility

A 10 kN force is applied to the stone column in the diagram. The column will experience this force at every point along the line of action of the force. As a matter of fact, the force will also be transferred to the ground which is supporting the column. Thus, the earth below the column along the line of action of the force will also experience the 10 kN load. This illustrates the Principle of Transmissibility. The point of application of an external force acting on a body (structure) may be transmitted anywhere along the force's line of action without affecting the other external forces (reactions and loads) acting on that body. This means that there is NO NET CHANGE in the static effect upon anybody if the body is in equilibrium. This can be further illustrated with the following diagram. 

2University of Babylon

2 m

100 kN

10 kN

10 kN

Lectures of Structure I 2017-2018[Department of architectural engineering]

Composition and resolution of forces

I. Composition – the process of replacing a force system by its resultant.

For any two concurrent forces, the resultant can be determined by

1. Parallelogram law – the resultant of two concurrent forces is the diagonal of the parallelogram formed on the vectors of these forces.

2. Triangle law – the resultant of two concurrent forces is the third side of the triangle which begins from the tail of the first vector to the tip of the last vector.

R=√F12+F2

2−2F1F2 cos θ Cosine law

Rsin θ

=F1

sin β=F2

sinα Sine law

3University of Babylon

Force system

Coplanar (In plane)

Concurrent Parallel Non concurrent non parallel

Non coplanar (In space)

Concurrent Parallel Non concurrent non parallel

F1

F2θ

β

αF2

F1

R

F1

F2

θ

β

αF2

R

F1F1

F2

Lectures of Structure I 2017-2018[Department of architectural engineering]

For the case of θ=90o

R=√F12+F2

2Cosine law

R=F1

sin β=F2

sinα Sine law

II. Resolution – the process of replacing a single force by its components.

For the concurrent forces, the resolution can be conducted by:

Rectangular or perpendicular components

Fx=F . cosθ

Fy=F . sin θ

Or

F x=F . cos { θ ¿

F y=F .sin { θ ¿

HW1:

a.

b.

c. 4University of Babylon

y

θ x

Fy F

Fx

yF

xF

axisy

axisx

y

x

F

Lectures of Structure I 2017-2018[Department of architectural engineering]

d.

5University of Babylon

=34 kN

=34 kN