1. Review : Beam Theory • • • • •
I. Basics : BEAM : structural member subjected to lateral loads, i.e. forces or moments having their vectors perpendicular to the axis of the bar
nomenclature :
L=length or span, b=width, h=height
NA=neutral axis (y=0) passes through centroid of cross-section=yiAi/AT
I=moment of inertia of cross section about NA
Irectangular=bh3/12, Icircular=pr4/ EI=flexural modulus
rectangular
cross-section y z h x b L
flange
web
web
I-beam
cross-section NA NA
flange
T-beam
cross-section
flange
II. Types of Supports and
Boundary Conditions
III. Types of Loading
concentrated
moment or
couple
1. simply supported
2. overhanging
3. cantilever a P • Mo L A B a Po
concentrated load
yA=0
yB=0 • L P A B
yA=0
yB=0 Po
distributed, uniform load a • L
linearly varying load Po
slope=k P A B
yA=0, qA=0 a • L
parabolically varying load Po
slope=k a • L