Masonry Magazine January 1969 Page.23
Stress paths in web section
Center of gravity C comparative- for solid section PeCa Reaction line at 4 of face shell R
Equations: PX X+X Ra Por P-R XX 2R 2 A
Stress diagram for web section at A-A At web section at B-B At core section at A-A & B-B (a) Axial compression Stress diagram at B-B for e 6 (b) Eccentric compression Unit stresses calculated from, -, where P PeC A Cross-sectional area of face shells Moment of inertia of face shells about center of gravity () of wall Fig. 3 Unit Stress Diagrams for Hollow Block Walls Laid with Face Shell Mortar Bedding. Stress diagram (c) Eccentric compression Approximate method of calculating distribution of P to the face shells and the unit face-shell stresses
loading applied at the centerline of a wall is true axial loading only when the wall section is geometrically and elastically symmetrical about the centerline. In order to obtain uniform fiber stress in all parts of the section in bearing the load line must coincide with the center of resistance of the section.
Referring to Fig. 4, section (a) is both geometrically and elastically symmetrical. Therefore centerline loading produces the same intensity of stress in both face shells and is true axial loading. In section (b) the solid and hollow units are assumed to be of the same material, therefore the section is symmetrical as regards the stiffness of the materials but it manifestly is geometrically unsymmetrical. The centroidal axis, which in this case is also the center of resistance, is located to the left of the centerline and the load actually is eccentric instead of axial as might be assumed. The unit stresses vary as indicated, being greater in the hollow unit than in the solid unit tier. Section (c) is the transformed area of section (b) assuming that the modulus of elasticity of the material in the brick tier is greater than that of the material in the block tier. The transformation utilizes the well known transformed area principle of reinforced concrete to give a theoretical section in which elastically different masonry materials can be treated as though they were similar in locating the center of resistance in compression and the neutral axis in bending. The center of resistance of the actual section becomes the geometric centroidal axis of the transformed area and this axis it will be noted has moved farther to the left, compared with section (b), thus increasing the eccentricity of the centerline load. Making the usual assumptions that sections that are plane before bending remain plane after bending and that stress is the product of strain times the elastic modulus, the fiber stresses will vary somewhat as depicted in the diagram. The brick tier being solid and stiffer may carry the larger portion of the total load although the load line is substantially eccentric toward the block tier. The abrupt break in the fiber stresses at mid point in the diagram corresponds to the change from the low modulus block to the high modulus brick.
Effect of Block Strength
As previously mentioned, strength of masonry unit is the most important factor influencing wall strength. Evaluation of research data supports the general conclusion that compressive strength of typical story-height walls is approximately 50 percent of the strength of units of which the wall is constructed. Recognition of this property is reflected in new criteria which bases allowable stress, fm, pri-