Time-dependent internal forces in uncracked structures: analysis by the force method - Concrete Structures: Stresses and Deformations - page 127

Figure 4.8 Time versus reaction by slow settlement of support occurring in a period
of: 0, 10, 30, 365 days or 5 years (Example 4.5).

settlement at time in nity; t 0 is the time at which the settlement starts;

t 0.95 is the time at which 95 per cent of the ultimate settlement occurs.
Equation (4.19) closely approximates the standard-time consolidation
curve for clays given by Terzaghi and Peck (in the form of a table) 5 .
The results of the step-by-step analysis (employing Equation (4.31) )
are shown in Fig. 4.8 in which the period ( t 0.95

fi

t 0 ) - the time during
which 95 per cent of settlement occurs - is considered equal to 0, 10, 30,
90, 365 days or 5 years. The graphs show the variation of F with time;
the values of F are expressed in terms of F sudden which is the instant-
aneous reaction at B if the full settlement occurs suddenly at t 0

−

= 14

days. The broken curve represents the case when ( t 0.95 5 years,

with creep ignored. The curves in Fig. 4.8 show clearly the pronounced
e

− t 0 ) =

ect of creep on the forces induced by slow settlement of a support.
When the settlement is sudden, the curve for F versus time has the
same shape as the relaxation function r ( t , t 0 ), which represents the stress
variation with time due to a strain imposed at age t 0 and sustained
constant to age t (see Fig. A.3, Appendix A). The sudden drop, AB of
force at age t 0 (Fig. 4.8), is caused by the creep which develops in the
fi

ff

rst few days but is considered as if it occurs at time t 0 .