Exercise
A simply supported beam shown below is subjected
to a concentrated load, Q applied at the mid-span.
Based on Euler-Bernoulli beam theory, prove that
deflection and moment at the mid-span are given by
these expressions:
3
QL
y
48 EI
QL
M
4
Exerci

EQUATIONS OF MOTION
(SDOF)
CHAPTER 1
Introduction
The displaced configuration of many
mechanical system & structures subject to
dynamic loads can be described by timevarying displacement along one coordinate
direction.
Systems are designated as single-d

RESPONSE TO HARMONIC
LOADING (SDOF)
CHAPTER 3
Introduction
Free vibration response
(transient)
Particular solution
(steady state)
Introduction
When the applied force are of a short duration,
the response also of a comparatively short
duration.
Response

FREE VIBRATION
(SDOF)
CHAPTER 2
Introduction
What is free vibration?
A structure is said to be undergoing free
vibration when it is disturbed from its static
equilibrium position & allowed to vibrate
without any external excitation.
Occurs when the mot

EQUATIONS OF MOTION
(MDOF)
CHAPTER 4
Introduction
Generally,
dynamic
response
of
structures
cannot
be
described
adequately by SDOF model; usually the
response includes time variations of the
displacement shape as well as its
amplitude.
may
require
specif

FREE VIBRATIONS
(MDOF)
CHAPTER 5
Introduction
As in the case of SDOF, MDOF will also
vibrate even without the presence of an
external force whenever it is subjected
to disturbances in the form of initial
displacements or initial velocities.
The governin

EQUATIONS OF MOTION
(MDOF)
CHAPTER 4
Introduction
Generally,
dynamic
response
of
structures
cannot
be
described
adequately by SDOF model; usually the
response includes time variations of the
displacement shape as well as its
amplitude.
may
require
specif

FREE VIBRATIONS
(MDOF)
CHAPTER 5
Introduction
As in the case of SDOF, MDOF will also
vibrate even without the presence of an
external force whenever it is subjected
to disturbances in the form of initial
displacements or initial velocities.
The governin

TUTORIAL 1
QUESTION 1
Write the equation of motion for the one-story, onebay frame shown in figure. The flexural rigidity of
the beam and columns is as noted. The mass
lumped at the beam is m, otherwise, assume the
frame to be massless and neglect damping

RESPONSE TO HARMONIC
LOADING (SDOF)
CHAPTER 3
Introduction
Free vibration response
(transient)
Particular solution
(steady state)
Introduction
When the applied force are of a short duration,
the response also of a comparatively short
duration.
Response

TUTORIAL 4
QUESTION 1
Consider a two story shear frame with lumped mass subjected to lateral forces
shown in figure. The beams are rigid and flexural rigidity of the column is EI.
a)Determine the natural vibration frequencies and modes. Express the
freque

TUTORIAL 3
QUESTION 1
Using the definition of stiffness & mass
influence coefficients, formulate the equations
of motion for the 2 and 3-story shear frames
with lumped masses shown in figure. The
beams are rigid & the flexural rigidity of the
columns is E

TUTORIAL 2
QUESTION 1
A heavy table is supported by flat steel legs as
shown in figure. Its natural period in lateral
vibration is 0.5 sec. When a 50-lb plate is clamped
to its surface, the natural period in lateral vibration
is lengthened to 0.75 sec. Wh

Exercise
Derive expressions for deflection, moment and slope
for the beam-column below. If c = L/2, show that:
3
ymax
QL
48EI
M max
3 tan u u
3
u
QL tan u
4 u
Exercise
Q
c
x
P
P
L

One end fixed and one end guided column
One end fixed and one end guided column
Equilibrium of the free body requires that,
P
M Py
2
(1)
The critical buckling load is found to be,
Pcr
EI
2
2
L
Pe
(2)
One end fixed and one end guided column
Exercise

Introduction to
Structural Steelwork
Why Steel.?
High strength-to-depth ratio
High tensile & compressive strength
High impact resistance
Uniformity in properties
Ductile
Durable
Good dimension control
Low self-weight
Economical (materials usage,

5/29/2014
Overview
Introduction
Bolted joints
Welded joints
JOINTS
DR. SHAHRIZAN BIN BAHAROM
EN-1993-1-8
Part 1.8 of Eurocode 3 is some 50%
longer than the
general Part 1.1.
It provides a much more extensive
treatment of the
whole subject area of conne

5/14/2014
Overview
DESIGN OF COMPRESSION
MEMBER
Background
Cross-section resistance Nc,Rd
Member buckling resistance Nb,Rd
DR. SHAHRIZAN BIN BAHAROM
ELASTIC BUCKLING THEORY
Elastic Buckling Theory
From stability theory, the elastic buckling load
of a perf

Beams & Stability of
Beam-Columns
What is BEAM ?
An element that is structural in nature and one that resist
lateral load primarily by bending.
Beams tackle loads by allowing themselves to bend. The
bending force that is generated on a beam is due to th

Stability of Columns
Classical column theory
Ideal column elastic, initially
perfectly straight and compressed by
a centrally applied axial load.
Imagine that we have a straight
column loaded concentrically by an
axial force, P.
The column is assumed t

Structural Stability
General Principles for
Structural Stability
1940 Tacoma Narrows Bridge, Washington
torsional vibration under 40 mph (64 km/h)
winds
1970 Milford Haven Bridge, Wales errors in
the box girder design
1968 Ronan Point, Newham, East Londo

KKKH4574
Structural Stability & Dynamics
UNIVERSITI KEBANGSAAN MALAYSIA
Department of Civil & Structural Engineering
An Elective Course for
Bachelor of Engineering (Hons) (Civil & Structural)
Academic Session : Semester 1, 2015/2016
Structural Stability

INTRODUCTION TO
EUROCODE 3 (EN 1993: 2005)
The EUROCODES.
The Eurocodes are a set of structural design
standards, developed by CEN (European
Committee for Standardisation) over the last 30
years, to cover the design of all types of structures
in steel, c

DESIGN OF UNRESTRAINED
OR PARTIALLY RESTRAINED
BEAMS TO EUROCODE 3
(EN 1993: 2005)
Lateral & Rotational Restraints.
Lateral restraint
prevents sideways
movement of
compressive
flange.
Torsional
restraint prevents
movement of one
flange relative to
the o

DESIGN OF RESTRAINED
BEAMS TO EUROCODE 3
(EN 1993: 2005)
Restrained Beams.
Beams that are unable to move
laterally & unaffected by out-of-plane
buckling (lateral torsional instability).
Examples:
attachment of floor system to the top
flange of beam
pr

DESIGN OF BEAM-COLUMNS
TO EUROCODE 3
(EN 1993: 2005)
Beam-Columns.
Beam-column is a structural member subjected
simultaneously to axial load (compression) and
bending moments produced by lateral forces or
eccentricity of the longitudinal load.
A beam co

JOINTS 2
DR. SHAHRIZAN BIN BAHAROM
Overview
Bolted joints
Welded joints
Bolted Joints
Combined tension and shear
In some situations, bolts may experience tension and shear
in combination. In general, bolt capacities would be
expected to reduce when high

5/29/2014
Overview
Introduction
Bolted joints
Welded joints
JOINTS
DR. SHAHRIZAN BIN BAHAROM
EN-1993-1-8
EN-1993-1-8
Part 1.8 of Eurocode 3 is some 50% longer than the
general Part 1.1.
It provides a much more extensive treatment of the
whole subject a

DESIGN OF TENSION
MEMBER
DR. SHAHRIZAN BIN BAHAROM
Overview
Example of Tension members
Design of tension members
Examples
Example of Tension Members
Example of Tension Members
Plate and Angle in Tension with Bolts
Typical Truss and Frame Connections
Ru