REI NFORCED CONCRETE DES IGN
20
Similarly , failure by crushing of the concrete in the compression zone has a factor of 1.5 x 1.6"" 2.40 due to live loads only , which re n ects the fact that such failure is generally without warning and may be very serious. Thus the basic values of part ial factors chosen afe such that under normal circumstances the global factor of safety is similar to that used in earlier design methods.
(b) Permissible Stress Method Design load = 3.0 + 2.0 • S.O kN Permissible stress
Example 2.1 Determine the cross-sectional area of a mild steel cable which supports a total dead load of 3 .0 kN and a live load of 2 .0 kN as shown in figure 2.2. The characteristic yield stress of the mild steel is 250 N/mml .
=
y ield stress safety fac to r
250 2 == 139 N/mm 1. 8 design load = -=~= permissible stress
Required cross·sectional area
Carry out the calculations using )
= 5 .0xl 0
(1) The load factor method with a load fact or "" 1.8. (2) A pennissible stress design with a facto r of safety of 1.8 on the yield stress. (3) A limit state design with the following factors of safety. 'YG = 1.4 for the dead load, 'YQ '" 1.6 for the live load, 'Y m = 1. 15 for the steel strength.
21
LI MIT ST ATE DESIGN
3
=36mm 2
139
(c) Limit State Method Design load = 'Yo x dead load + 'YQ x live load "" 1.4 x 3.0 + 1.6 x 2.0 "" 7.4kN
. s, ress DeSlgn
=
· ld=,=,=,,=,,= _,_h= " =,=,,=,=,j=,,=,,,-,-Y'=,= 7m
250 =_ . = 217N/mm 2 1.1 5
Required cross.sectional area = design load design st ress
Liv~ lood ·2'DkN
7.4 x 103 217
O<zod lood • 3'DkN
= 34,1 mm 2
Figure 2.2
These different design methods all give similar results for the cross·sectional area.
(a) Load Factor Method Design load = load factor (dead load + live load) = 1.8 (3 .0 + 2.0) = 9.0 kN
Fewer calculations are required for the permissible stress and the load factor methods, so rcducing the chances of an arithmetical error. The limit state me thod provides much better control over the facto rs of safe ty , which are applied to each of U1 C variables. For convenience , the partial factors of safety in the example are the sume as those recommended in BS 8 1 10. Probably , in a practical design, higher rlCIOTS of safety would be preferred for a single supporting cable, in view of the consequences o f a failure.
design load Required cross·sect ional area = =~'""= y ield stress
• 9.0x 10' =36 mm2 250
, X"lnlllt1 2. 2
Illufl 2.3 Ahows 0 beom supported o n foundlitlOnJ lLt A and B. The loads sup1'01111.1 by the beam arc Its OW l! unlfonnly dlJlrlbutcu dCld weight of 20 kN/ m