STRUCTURES: PURPOSE AND FUNCTION
1.7 TYPES OF INTERNAL FORCE
directions perpendicular to each other, and the frame can be stabilized by adding a diagonal member.
by the material. Actually, however, most building compression elements fall between a very slender (pure buckling) form and a very squat (pure crushing) form, and their behavior thus has some aspects of both forms of response. (See Figure 1.17 and consider the middle portion of the graph.) Compression can be transferred between elements by simple con- tact, as in the case of a footing resting on soil (see Figure 1.26). However, if the contact surface is not perpendicular to the compressive force, a side-slip failure might occur. Some form of engagement or restraint is thus usually desirable.
Shear
In its simplest form, shear is the tendency for slipping of adjacent objects.
This may occur at the joint between elements or within a material, such as a grain split in wood (see Figure 1.27). If two wooden boards in a floor are connected at their edges by a tongue-and-groove joint, shear stress is developed at the root of the tongue when one board is stepped on and the other is not. This type of shear also develops in bolts and hinge pins.
A more complex form of shear is that developed in beams. This can be visualized by considering the beam to consist of a stack of loose boards.
The horizontal slipping that would occur between the boards in such a structure is similar to the internal shear that occurs in a solid beam. If the boards are glued together to form a solid beam, the horizontal slipping ef- fect—beam shear—is what must be resisted at the glue joints.
Figure 1.26 Considerations of tension and compression actions.
Bending
Tension, compression, and shear are all produced by some direct force effect. Actions that cause rotation or curvature are of a different sort. If the action tends to cause straight elements to curve, it is called bending.
If it tends to twist elements, it is called torsion (see Figure 1.28). When a
TYPES OF INTERNAL FORCE 41
Figure 1.27 Effects of shear.
Figure 1.28 Effect of torsion.
pendicular to it. This is the basic condition of an ordinary beam. As shown in Figure 1.29, the internal force acting in the beam is a combi- nation of bending and shear. Both of these internal stress effects pro- duce lateral deformation of the straight, unloaded beam, called sag or deflection.
Bending involves a combination of force and distance, most simply visualized in terms of a single force and an operating moment arm (see Figure 1.30). It may also be developed by a pair of opposed forces, such as two hands on a steering wheel. The latter effect is similar to how a beam develops an internal bending resistance—by the opposing of com- pressive stresses in the top part of the beam to tension stresses in the bottom part.
Figure 1.29 Internal effects in beams.
Since the development of moment is a product of force times dis- tance, a given magnitude of force can produce more moment if the mo- ment arm is increased. The larger the diameter of a steering wheel, the less force required to turn it—or, with a given limited force, the more moment it can develop. This is why a plank can resist more bending if it is turned on its edge as a joist. Figure 1.31 shows the effect of form change on a constant amount of material used for the cross section of a beam. For each shape, the numbers indicate the relative resistance to bending in terms of strength (as a stress limit) and stiffness (as a strain limit producing deflection).
In addition to the bending created when flat spanning members are transversely loaded, there are other situations in buildings that can pro- duce bending effects. Two of these are shown in Figure 1.32. In the upper figures, bending is produced by a compression load not in line with the axis of the member or by a combination of compressive and lateral load- ing. In the lower figure, bending is transmitted to the columns through the rigid joints of the frame.
TYPES OF INTERNAL FORCE 43
Figure 1.30 Development of moments.
Figure 1.31 Relation of cross-sectional geometry to bending resistance.
Figure 1.32 Conditions resulting in internal bending.
Torsion
Torsion is similar to bending in that it is a product of force and distance.
As with bending, the form of the cross section of the member resisting the torsion is a critical factor in establishing its strength and stiffness. A round hollow cylinder (pipe shape) is one of the most efficient forms for resis- tance to torsion. However, if the cylinder wall is slit lengthwise, its resis- tance is drastically reduced, being approximately the same as that for a flat plate made by flattening out the slit cylinder. Figure 1.33 shows the effect on torsional resistance of variations in the cross-sectional shape of a lin- ear member with the same amount of material (area) in the cross section.
Often in designing structures, it is a wiser choice to develop resistance to torsion by bracing members against the twisting effect. Thus, the tor- sion is absorbed by the bracing, rather than by stresses in the member.
Combinations of Internal Forces
The individual actions of tension, compression, shear, bending, and tor- sion can occur in various combinations and in several directions at a sin- gle point in a structure. For example, as illustrated previously, beams ordinarily sustain a combination of bending and shear. In the columns of the frame shown in the lower part of Figure 1.32, the loading on the beam will produce a combination of compression, bending, and shear. In the ex- ample shown in Figure 1.34, the loading will produce a combination of in- ternal compression, shear, torsion, and bending in two directions.
Structures must be analyzed carefully for the various internal force combinations that can occur and for the critical situations that may
TYPES OF INTERNAL FORCE 45
Figure 1.33 Relation of cross-sectional geometry to torsional resistance.
produce maximum stress conditions and maximum deformations. In ad- dition, the external loads often occur in different combinations, with each combination producing different internal force effects. This frequently makes the analysis of structural behaviors for design a quite laborious process, making us now very grateful for the ability to utilize computer- aided procedures in design work.