Instructional Objectives:
At the end of this lesson, the student should be able to:
•
identify the two types of problems – analysis and design types,
•
apply the formulations to design the flanged beams.
5.12.1
Introduction
Lesson 10 illustrates the governing equations of flanged beams and
Lesson 11 explains their applications for the solution of analysis type of
numerical problems. It is now necessary to apply them for the solution of design
type, the second type of the numerical problems. This lesson mentions the
different steps of the solution and solves several numerical examples to explain
their step-by-step solutions.
5.12.2 Design Type of Problems
We need to assume some preliminary dimensions of width and depth of
flanged beams, spacing of the beams and span for performing the structural
analysis before the design. Thus, the assumed data known for the design are:
D
f
,
b
w
,
D
,
effective span, effective depth, grades of concrete and steel and
imposed loads.
There are four equations: (i) expressions of compressive force
C
, (ii)
expression of the tension force
T
,
(iii)
C = T
and (iv) expression of
M
u
in terms
of
C
or
T
and the lever arm {
M
=
(
C
or
T
) (lever arm)}. However, the relative
dimensions of
D
f
,
D
and
x
u
and the amount of steel (under-reinforced, balanced
or over-reinforced) influence the expressions. Accordingly, the respective
equations are to be employed assuming a particular situation and, if necessary,
they need to be changed if the assumed parameters are found to be not
satisfactory. The steps of the design problems are as given below.
Step 1:
To determine the factored bending moment
M
u
Step 2:
To determine the
M
u
,
lim
of the given or the assumed section
The beam shall be designed as under-reinforced, balanced or doubly
reinforced if the value of
M
u
is less than, equal to or more than
M
u
,
lim
. The
design of over-reinforced beam is to be avoided as it does not increase the
bending moment carrying capacity beyond
M
u
,
lim
either by increasing the depth
or designing a doubly reinforced beam.
Version 2 CE IIT, Kharagpur