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CEE-312Structural Analysis and Design Sessional-I
(1.0 credit)Lecture: 1
Bijit Kumar Banik
Assistant Professor, CEE, SUSTRoom No.: 115 (“C” building)
Department of Civil and Environmental Engineering
Industrial Roof Truss Analysis
Syllabus
Attendance 10%
Evaluation process
Mini project 30%
Final Exam 40%
Total 100%
Class performance 20%
2. Design of steel structures – Elias G. Abu-Saba
References
3. Simplified Design of steel structures
– Harry Parker and James Ambrose
4. Strength of materials
– Andrew Pytel and Ferdinand L. Singer
1. Supplied sheet
Better quality control
Why steel structures?
Faster to erect
Reduced site time- Fast track construction
Large column free space and amendable for alteration
Lighter
Less material handling at site
Less % of floor area occupied by structural elements
Better lateral and earthquake load resistance
Skilled labor is required
Why not?
Higher maintenance cost
Poor fireproofing, as at 10000F (5380C) 65% & at 16000F (8710C) 15% of strength remains
Higher cost of construction
Electricity may be required
Stress-strain diagram
Strain
Str
ess
AA = Proportional limit
C
C = Yield Strength
B
B = Elastic limit
D
D = Ultimate Strength
E
E = Rapture Strength
F
F = Actual Rapture Strength
Plastic design
Elastic design
Centriod
The centroid of a body is the center of its mass (or masses), the point at which it would be stable, or balance, under the influence of gravity.
Centriod of a composite structure
51
5
1
A1
A2
X
Y
......2211 +×+×=× YAYAYA
YY1=5.5
Y2=2.5
10X = (5X1)X5.5+(5X1)X2.5YY = 4
A = 5X1+5X1=10
Double Moment of Area (So called Moment of Inertia)
The Double Moment of Area (I) is a term used to describe the capacity of a cross-section to resist bending. It is a mathematical property of a section concerned with a surface area and how that area is distributed about the reference axis.
dA
X
Y
y
∫= dAyI x2
x
∫= dAxI y2
Moment of Inertia
For rectangular section
X
Y
h
b
X’
d
A
Transfer formula
2' AdII xx +=
12
3bhI x =
= Moment of inertial about centroidal X-axisxI
Moment of Inertia
P
4
1
2
8 CA
CA
P
A = 8X2
A = 2X8
1
2
(2) Is 16 times stiffer than (1) !!!
Moment of Inertia
d2
d1
12”X1”
I1 = 2850 in4
A1 = 24.8 in2
1
2
26.75”
CA
CA2
CA1
36.8X = 24.8X(26.75/2)+(12X1)X27.25YY = 17.9
Y
A = 24.8+12X1=36.8
={ 2850+24.8*(4.52)2}+{1+12*(9.35)2}
d1= 17.9-26.75/2=4.52
d2= 26.75-17.9+0.5=9.35
I2= (1/12)*12*13=1
= 4407 in4
I = (I1+A1d12) + (I2+A2d2
2)
Moment of Inertia
Divers reducing their momentsof inertia to increase their rates of
rotation
The deflection of a beam under load depends not only on the load, but alsoon the geometry of the beam's cross-section. This is why beams with higherarea moments of inertia, such as I-beams (properly denoted as: wide-flangebeams), are so often seen in building construction as opposed to other
beams with the same cross sectional area.
Radius of gyration (r)
Describes the way in which the area of a cross-section is distributed aroundits centroidal axis. If the area is concentrated far from the centroidal axis it
will have a greater value of ‘r’ and a greater resistance to buckling.
A
Ir =
wherer = radius of gyrationI = moment of inertiaA = area of the cross section
Folding paper example
8 ft
2”Solid
round rod
4 “Standard
pipe
Tube4”X2”X5/16”
Tube3”X3”X5/16”
Radius of gyration (r)
12.7 k 54 k 28k 44 k
r = 0.5 r = 1.51 r = 0.74 r=1.07
All members has X-sectional area = 3-1/8 in2
Section Modulus (Z)
The section modulus of the cross-sectional shape is of significant importancein designing beams. It is a direct measure of the strength of the beam.
Section modulus Load taking capacity
c
IZ =
Mathematically can be expressed as
Where, Z = Section modulusI = Moment of Inertia of areac = distance from the neutral axis to the remotest element
c
Sections
Sections
Tension members
1. Chord Members in trussesVertical Top chord
Diagonal
Bottom chord
Tension members
2. Diagonal bracing in bracing systems
Tension members
3. Cable elements in suspension roofs, main cablesof suspension bridges and suspenders
The Verrazano-Narrows in USA was the largest from 1964 until 1981.It serves a main span of 1298 meters. Now 7th.
Compression member
Compression member
;–
1. Columns in buildings
Compression member
;–
2. Chord Members in trusses
3. Diagonal members in end panels of trusses
Beam member
Open web joist
Wide flange section
Designation W 10X30
W is the short for Wide-flange10 is the height (h)30 is weight per linear length
Channel section
Designation C 3X4.1
C is the short for channel3 is the height (h)4.1 is weight per linear length
Angle section
Designation L 1.5X2X1/8
L denotes angle1.5 is the height (d)2 is base length (bw)1/8 is the thickness(t)
AISC chart sample (Wide-flange)
pp- 571-578; Strength of materials-By Singer (4th edition)
AISC chart sample (Channel)
pp- 581-582; Strength of materials-By Singer (4th edition)
AISC chart sample (Angles)
pp- 583-588; Strength of materials-By Singer (4th edition)
Group Formation
Four groups
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