{Contributed by P. R. Strong)

Pillars

As already seen, vertical reinforcement is employed in the construction of pillars, its use being to help to distribute the load past weak points in the concrete, and to give to the concrete more uniform properties, and at the same time to reduce the cross section of the concrete by assisting in carrying the load. The hooping of concrete has a further use.

As stated when considering beams, the reinforcement in compression must be strained to the same extent as the concrete which surrounds it, and the stress upon it will therefore be cr, where c = stress upon concrete and r = Es/Ec

The safe load for a rectangular pillar is thus SL = bdc+acr=c {bd+ar), where b and d are the dimensions of the section of the pillar, and a = sectional area of reinforcement.

The above value may be allowed for pillars up to a length of about 15 b. Thus, taking a safe load of 400 lbs. per square inch, a pillar 12 feet long and 10 inches square with 2 square inches of vertical reinforcement will carry a safe load of 400 (102 + 2 x 10) = 48,000 lbs.

Having proportioned a pillar by the above formulae, the safety of long pillars against flexure is usually supposed to be calculated by Euler's formulae, in which safe load = Ec1π2, where Ec = modulus of elasticity for Sk concrete, S = factor of safety; while k = 1/2 for pillars with both ends fixed, 1 when both ends are hinged, and 1/√2 when one end is fixed and the other hinged.

The moment of inertia, I, for a reinforced section, may be taken as bd3/12 + ary2, where y = distance of reinforcing bars from the central axis of section.

Euler's formula, however, is only accurate for very long pillars, and is not at all suitable for use in the case of concrete.

An adaptation of Rankine's formula? would be more suitable -

SL = Ac

1+kl2/r2 where A = bd + ar

c = safe load per square inch on concrete = say,

400 lbs. 1= length in the common unit.

- r2 = 1 = bd3/12+ary2

A bd+ar

The value of coefficient k may be taken as 1.

40,000

According to this formula the safe load for a pillar r2 = 104/12 + 2x10x 32 =8.4

20 feet long, 10 by 10 inches with 2 square inches of vertical reinforcement, the centres of rods being 2 inches from outer surface or 3 inches from axis, is found as follows -

A= 10x 10 + 2 x 10 = 120 square inches.

102 + 2 x 10

120x400 =40,975lbs

SL.

1+1. . (20x12)2.

40,000 8.4

Hooped Concrete

All solid materials will resist an unlimited pressure so long as the part subjected to the load is prevented from expanding or escaping either laterally or vertically. Thus in considering the bearing resistance, or resistance to local compression, of steel, a considerably larger value was allowed than was done for ordinary compression; for in this case the metal was prevented from escaping laterally by the metal on either side. This result may be obtained with concrete by simply winding it round with steel wire, producing M. Considere's "Hooped Concrete." In this way an ultimate resistance on the concrete of over 10,000 lbs. per square inch may be obtained (see Fig. 60).

In order to more effectually confine the concrete and to prevent it from escaping laterally, vertical rods are also used, producing a network, the vertical rods transmitting the thrust caused by the swelling of the concrete to the helical binding, while in long pillars their use is further necessary in the resistance to flexure.

According to M. Considere, the resistance of hooped concrete = the resistance of the vertical rods and the concrete at their elastic limits + 2.4 x the resistance that would be offered by the metal in the hooping if it were used as vertical reinforcement in place of spiral binding. He also states that the hooping should be spaced with a pitch of 1/7 to 1/10 of diameter of the winding.

Only concrete within the hooping may be considered as resisting compression; that outside the hooping acting merely as a protection. Besides the greatly increased resistance offered by this method of construction, it has the further advantage that any signs of distress in the material are at once made evident by the breaking away of the outer protecting skin of concrete, which takes place long before the ultimate resistance is reached.

Fig. 60.

The wire ties in the pillars shown in Figs. 36, 68, etc., besides holding the reinforcement in position while the concrete is being filled in, act to some extent as do the hoopings mentioned above, while the nearer they are placed together the greater resistance will the resultant material have.

Fig. 61.

Walls

The thickness of a wall, together with the extent of its reinforcement, must largely be a matter of practical consideration, for the thrusts that it may be called upon to meet as a general rule cannot be even approximately arrived at.

Fig. 61 shows the method of reinforcing a wall according to the Hennebique system, the wall being constructed as a slab capable of resisting thrust from either side.

Foundations

Concrete always finds an important place in foundation work, and the nature of armoured concrete makes it particularly suitable for use in this position, while the moulds, which usually form a considerable portion of the cost of armoured concrete, are here reduced to a minimum.

Fig. 62.

Fig. 63.

Armoured concrete may be economically used for all

Armoured or Reinforced Concrete for Various Uses 43 the methods of forming foundations mentioned in reference to steel frame buildings in Chapter XVI (Building Stone. Sandstones). Part II. Volume IV., while there is greater certainty of the thorough protection of steelwork than in the case of the grillage of steel beams.