Basic design
7.5.4 Loss of prestress
(a) The mean effective prestressing force Pm,t, is the force at the active end of the tendon less the relevant losses, which should be calculated on the basis of experience and data relating to the materials and methods used. As a result, only the types of
losses to be taken into account are indicated below. National practice conforming to the National Application Document should be adopted.
(b) The losses to be considered are anchorage slip, elastic shortening, friction in ducts, creep of concrete, shrinkage of concrete and relaxation of steel.
7.5.5 Anchorage (a) Pre-tensioned members
The transmission length is given by lbp=βb , when is the nominal size of the tendon and βb is obtained, in the absence of other more accurate data, from the Table below.
The design value of lbp should be taken as either 0.8lbp or 1.2lbp whichever is more critical. The length over which the stresses across the section of concrete gradually disperse to a linear distribution may be taken as
If the principal tensile stress at the ultimate limit state does not exceed 0.7fctm the anchorage is considered satisfactory. If not, the following should be satisfied.
[(Msd/z)+(Vsd/2)] (X/lbpd) Po Ap0.1k/1.15, where X is the distance of a section from the support.
(b) Post-tensioned members
The bearing stress behind anchorage plates caused by the force Apfck should not exceed
where Ac1 is the maximum area having the same centre of gravity and shape as the loaded area Aco, which it is possible to inscribe within the total area of member Ac.
Tensile stresses caused by the concentrated forces should be assessed by strut-and-tie model or other appropriate idealization and the anchorage zone should be reinforced accordingly.
Table 7.5 Minimum dimensions for fire resistance of rectangular or circular reinforced (normal weight) concrete columns Standard fire resistance
Column width b/axis distance a (both in mm)
Column exposed on more than one side Column exposed on one side
R 30 150/10 100/10
The ratio of the design effect of actions in the fire to the cold resistance of the structural element is assumed to be 0.7.
Table 7.6 Minimum dimensions for fire resistance of load-bearing reinforced (normal weight concrete walls made with siliceous aggregate
Standard fire resistance Wall thickness/axis distance (both in mm)
Exposed on one side Exposed on two sides
REI 30 120/10 120/10
NOTEThe ratio of the design effect of actions in the fire to the cold resistance of the structural element is assumed to be 0.7.
Table 7.7 Minimum dimensions for fire resistance of simply supported reinforced concrete (normal weight) beams Standard fire
resistance (mm) Possible combinations of the average axis distance a and the beam width b (both in
mm) Web thickness bw of
I-beams (mm)
R 30 a=25 b=80 a=15 b=120 a=10 b=160 a=10 b=200 80
R 60 a=40 b=120 a=35 b=160 a=30 b=200 a=25 b=300 100
R 90 a=55 b=150 a=45 b=200 a=45 b=250 a=35 b=400 100
R 120 a=65 b=200 a=55 b=240 a=50 b=300 a=45 b=500 120
R 180 a=80 b=240 a=70 b=300 a=65 b=400 a=60 b=600 140
R 240 a=90 b=280 a=80 b=350 a=75 b=500 a=70 b=700 160
ast=a+10 mm (see note below) ast=a (see note below)
ast=increased axis distance of the outermost bar (tendon, wire) from the side surface of the cross-section, where steel is in a single layer NOTES
1. For prestressed members, the axis distances should be increased by 10 mm for prestressing bars and by 15 mm for wires or strands.
2. The table applies to beams exposed to fire on three sides.
3. For beams exposed to fire on all four sides, the height should at least equal the minimum dimension bmin in the table for the required fire resistance and its cross-sectional area should be at least 2bmin2.
4. The minimum axis distance to any individual bars should not be less than that required for R 30 in the table nor less than half the average axis distance.
Table 7.8 Minimum dimensions for fire resistance of continuous reinforced concrete (normal weight) beams Standard fire resistance
(mm) Possible combinations of the average axis distance a and the beam width b
(both in mm) Web thickness bw of
I-beams (mm)
R 30 a=12 b=80 a=20 b=200 80
R 60 a=25 b=120 a=12 b=200 a=25 b=300 100
R 90 a=35 b=150 a=45 b=250 a=25 b=400 100
R 120 a=45 b=200 a=35 b=300 a=35 b=500 120
R 180 a=50 b=240 a=50 b=600 140
R 240 a=60 b=280 a=60 b=700 160
ast=a+10 mm (see note below) ast=a (see note below)
ast=increased axis distance of the outermost bar (tendon, wire) from the side surface of the cross-section, where steel is in a single layer NOTES
1. For prestressed members, the axis distances should be increased by 10 mm for prestressing bars and by 5 mm for wires or strands.
2. The table applies to beams exposed to fire on three sides.
3. For beams exposed to fire on all four sides, the height should at least equal the minimum dimension bmin in the table for the required fire resistance and its cross-sectional area should be at least 2bmin2.
4. The minimum axis distance to any individual bars should not be less than that required for R 30 in the table nor less than half the average axis distance.
5. For R 90 and above, the top reinforcement over each intermediate support should extend at least 0.3leff from the centre of support, where the effective span leff>4 metres and leff/h>20, h being the beam depth. In other cases, this minimum may be reduced to 0.15leff. 6. If the above detailing requirement is not met and the moment redistribution in the analysis exceeds 15%, each span of the continuous
beam should be assessed as a simply supported beam.
7. In a continuous I-beam, bw should not be less than b for a distance of 2h from an intermediate support unless a check for explosive spalling is carried out.
8. In two-span I-beam systems with no rotational restraint at the end, with predominantly concentrated loading with Msd/Vsd between 2.5 and 3, and with Vsd>2/3Vrd2, the minimum width of the beam web between the concentrated loads should be: 220 mm for R 120.
400 mm for R 180 and 600 mm for R 240.
Table 7.9 Minimum dimensions for fire resistance for solid (normal weight) reinforced concrete slabs spanning one and two ways Standard fire resistance Slab thickness hs (mm) Average axis distance span a (mm)
One way Two way
Standard fire resistance Slab thickness hs (mm) Average axis distance span a (mm)
One way Two way
ly/lx<1.5 1.5<ly/lx<2
REI 180 150 55 30 40
REI 240 175 65 40 50
lx and ly are the spans of a two-way slab (two directions at right-angles) where ly is the longer span NOTES
1. For prestressed members, the axis distances should be increased by 10 mm for prestressing bars and by 15 mm for wires or strands.
2. The minimum cover to any bar should not be less than half the average axis distance.
3. The table values of axis distance for two-way slabs apply to slabs supported on all four edges. For all other support conditions, the values for one-way slabs should be used.
4. The table values of slab thickness and cover for two-way slabs with ly/lx<1.5 should be used.
5. For R 90 and above, the top reinforcement over each intermediate support should extend at least 0.3leff from the centre of support, where the effective span leff >4 metres and leff/h>20, h being the beam depth. In other cases, this minimum may be reduced to 0.15leff. 6. If the above detailing requirement is not met and the moment redistribution in the analysis exceeds 15%, each span of the continuous
slab should be assessed as a simply supported slab.
7. Minimum top reinforcement of 0.005/Ac should be used over intermediate supports when the reinforcement has “normal” ductility, when there is not rotational restraint at ends of two-span slabs, and when transverse redistribution of load effects cannot occur.
Table 7.10 Minimum dimensions for fire resistance of reinforced and prestressed (normal weight) concrete slabs Standard fire resistance Slab thickness hs (mm), excluding finishes Axis distance a (mm)
REI 30 150 10
1. For prestressed members, the axis distances should be increased by 10 mm for prestressing bars and by 15 mm for wires or strands.
2. It is assumed that the moment redistribution in this analysis does not exceed 15%. If it does exceed 15%, the axis distances in this table should be replaced by those for one-way slabs.
3. Over intermediate supports in each direction, at least 20% of the total top reinforcement calculated for cold design should extend over the full span, in the column strips.