CEE-312Structural Analysis and Design Sessional-I

(1.0 credit)Lecture: 1

Bijit Kumar Banik

Assistant Professor, CEE, SUSTRoom No.: 115 (“C” building)

bijit_sustbd@yahoo.com

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

http://www.facebook.com/groups/cee15/