Civil Engineering Reference
In-Depth Information
Figure 4.3
Plain concrete beam
to the beam it would break in tension and collapse. However, the compressive
stress of +5 units is well below the crushing strength of the material.
Now assume that a steel bar is passed through the centre of the beam and
is stressed by jacks reacting against the beam. Thus the bar is put into tension
and the beam is compressed by the same amount. Assume that the uniform
compressive stress in the beam due to this prestress is +5 units, Figure 4.4. When
this compressive stress is combined with the bending stresses caused by the load of
w
kN/m, they produce a compressive stress of 5 + 5 = 10 units on the top fi bre
and 5 - 5 = 0 units on the bottom fi bre.
A further load of
w
kN/m may now be added to the beam, giving a total of
2
w
kN/m, creating additional bending stresses of ±5 units at the top and bottom
fi bres, taking the combined stresses to +15 units on the top fi bre and -5 units on
the bottom fi bre. Thus the load that can be carried by the beam without exceeding
the maximum allowable tensile stress has been doubled, but at the cost of tripling
the compressive stress on the top fi bre. Alternatively, the load may be kept at
w
kN/m, but the span increased by a factor of
2 = 1.41.
In a further rationalisation, the prestressing bar may be displaced downwards,
placing it closer to the bottom fi bre to increase its effectiveness. For instance, if it
were displaced by just one-sixth of the depth of the section to the lower edge of
the 'middle third' (
5.4
), it would create stresses that were zero on the top fi bre, and
+10 units of compressive stress on the bottom fi bre. This would allow the load
carried by the beam to be increased to a total of 3
w
kN/m before the bottom fi bre
stress attained the safe limit of -5 units, or the span to be increased by a factor of
√
√
3 = 1.73. The top fi bre stress would be +15 units once again, Figure 4.5.
Thus in this explanation, prestressing is a technique that enhances the capacity of
a beam made of a material that is weak in tension but strong in compression to carry
