STRUCTURAL DESIGN FOR ARCHITECTURE

Fig. 4.32 Failure of an unreinforced concrete beam. The

unreinforced beam fails as a result of the formation of a

crack situated at the location of the highest tensile stress

and at right angles to the direction of maximum tension.

Fig. 4.33 Crack pattern in a reinforced concrete beam.

The reinforced beam carries significantly more load than

the unreinforced beam. Tensile cracks form, always at right

angles to the direction of maximum tension (given by the

principal stress lines) in those locations at which the

tensile strength of the concrete is exceeded. The beam

continues to carry load, however, so long as each crack is

effectively crossed by the reinforcement.

Figure 4.32 shows the behaviour of an

unreinforced concrete beam which is subjected

to increasing load. The symmetrical pattern of

tensile and compressive stresses shown in Fig.

4.31c becomes established when the load is

applied, with the maximum stresses occurring

at the mid-span position. As the load

increases, the magnitudes of the stresses

increase and eventually the tensile strength of

the concrete is exceeded at the lower extreme

fibre (the location of the highest level of

tensile stress). A crack forms at right angles to

the direction of maximum tension and this

rapidly propagates up through the beam which

breaks into two halves. Because the compres-

sive strength of the concrete is at least ten

times greater than its tensile strength, the

concrete in the top of the beam is relatively

understressed when the tensile failure occurs.

The failure can be prevented if steel

reinforcement is placed close to the lower

surface of the beam (shown diagrammatically

in Fig. 4.33). In the reinforced beam the tensile

failure of the concrete at the mid-span position

still occurs but the beam as a whole does not

fail because the crack which forms is now

crossed by the reinforcement. The reinforcing

bar carries the tensile load and the beam

continues to function so long as the cross-

sectional area of the steel bar is sufficient to

prevent it from becoming over-stressed in

tension and it does not pull out of the

concrete on either side of the crack. The

frictional stress between the concrete and the

surface of the bar (bond stress), is therefore an

important consideration in determining the

ability of the two materials to act compositely;

this is the reason that special surface textures

are often applied to reinforcement (Fig. 4.30).

If more load is applied to the beam than was

required to cause the first crack to appear, the

stress everywhere will increase and the point

on the principal tensile stress line at which the

tensile strength of the concrete is exceeded

progresses along the line, in both directions,

from the mid-span position. More cracks form

(Fig. 4.33), always at right angles to the direc-

tion of maximum tension, but failure of the

beam as a whole does not occur so long as the

cracks are effectively crossed by the steel bar

and the compressive strength of the concrete

is not exceeded in the top half of the beam. As

the tensile failure points move towards the

ends of the beam the cracks, which always

form at right angles to the direction of

maximum tension, become more and more

inclined to the beam axis and are less effec-

tively crossed by the reinforcement.

Failure eventually occurs due to the forma-

tion of a diagonal crack which is not crossed by

the reinforcement (Fig. 4.34). This type of

failure is called a shear failure because the

degree of inclination of the principal stress

lines causes a shearing action on the cross-

section rather than a simple bending action.

Shear failure can be prevented by shaping the

reinforcing bar so that it conforms to the

128 profile of the line of the principal tensile

Structural Design for Architecture