Structural Concrete - Hassoun

578 Chapter 16 Continuous Beams and Frames
Choose three no. 8 bars (A s = 2.35 in. 2 ).
A s2
=
R 2 27
= = 0.82 in.2
0.55 × f y 0.55 × 60
Choose two no. 7 bars (A s = 1.2 in. 2 ). Arrange the crossing bars by placing one no. 8 bar and
then one no. 7 bar, as shown in Fig. 16.19 (or use five no. 8 bars.)
b. Lateral ties should be placed along a distance a = 8d b = 8.0 in. within the column and footing.
The bursting force is
F = P u Ha
tan θ +
2 0.85d
For θ = 30 ∘ , d = 17.5 in., and a = 8.0 in.,
F = 85
2 tan 30∘ + 22.5 × 8
0.85 × 17.5 = 36.6K
Area of ties =
36.6
= 0.72 in.2
0.85 × 60
If no. 3 closed ties (two branches) are chosen, then the area of one tie is 2 × 0.11 = 0.22 in. 2 The
number of ties is 0.72/0.22 = 3.27, say, four ties spaced at 8 = 2.7 in., as shown in Fig. 16.19.
3
8. Design the footing: If the height of the footing is assumed to be h ′ , then the forces acting on the
footing are the axial load P and a moment M = H/h ′ . The soil pressure is calculated from Eq. 13.14
of Chapter 13:
q =+ P A ± Mc ≤ allowable soil pressure
I
The design procedure of the footing is similar to that of Example 13.7.
16.7 INTRODUCTION TO LIMIT DESIGN
16.7.1 General
Limit state design of a structure falls into three distinct steps:
1. Determination of the factored design load, obtained by multiplying the dead and live loads
by load factors. The ACI Code adopted the load factors given in Chapter 3.
2. Analysis of the structure under factored loads to determine the factored moments and forces
at failure or collapse of the structure. This method of analysis has proved satisfactory for steel
design; in reinforced concrete design, this type of analysis has not been fully adopted by the
ACI Code because of the lack of ductility of reinforced concrete members. The Code allows
only partial redistribution of moments in the structure based on an empirical percentage, as
will be explained later in this chapter.
3. Design of each member of the structure to fail at the factored moments and forces determined
from structural analysis. This method is fully established now for reinforced concrete design
and the ACI Code permits the use of the strength design method, as was explained in earlier
chapters.
16.7.2 Limit Design Concept
Limit design in reinforced concrete refers to the redistribution of moments that occurs throughout
a structure as the steel reinforcement at a critical section reaches its yield strength. The ultimate