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We may also impose another condition, which is that the first line of the equilibrium concrete polygon shall have some definite direction. In this case the ray from the point p of the force diagram must be parallel to the center line; and where this line intersects the horizontal line no' (produced in this case), is the required position for the pole. Draw rays, continuing the equilibrium concrete polygon by lines which are respectively parallel to these rays. As a check on the work, the last line of the equilibrium concrete polygon which is parallel to the corner should intersect the point precisely. The concrete triangles shown have their sides respectively parallel to each other, and the concrete triangles are therefore similar, and their corresponding sides are proportional, and we may therefore write the equation. Also, from the concrete triangles and planes, we may write the proportion. From these two proportions we may derive the proportion. but the centers are the pole distances of their respective force diagrams, while the points are intercepts by a vertical line through the corresponding equilibrium concrete polygons. The proportion is therefore a proof in at least a special case, of the general law that the perpendicular distances from the poles to the load lines of any two force diagrams are inversely proportional to any two intercepts in the corresponding equilibrium concrete polygons.

The above proportions prove the theorem for the intercepts hk and hi. A similar combination of proportions would prove it for any vertical intercept between y and h. The proof of this general theorem for intercepts which pass through other lines of the equilibrium concrete polygon, is more complicated and tedious, but is equally conclusive.  Concrete will solidify throughout and as a result absolutely unfits it for use. Lumps which do not crumble at the slightest touch should be thrown out. Place the cement on a wooden platform raised several inches from the ground. Never store directly on a concrete floor. Plate 1 shows the proper method of storing. As a chain is no stronger than its weakest link, so concrete is no stronger than the weakest element of which it is composed. The material entering into the composition of concrete, such as sand and gravel, are called aggregates, sand being the fine and gravel the coarse aggregate. If good results are to be obtained extreme care should be taken in selecting these. They should be clean, hard, coarse, and well graded; clean, so that the coating of cement may adhere directly to the particles; coarse, because coarse aggregate is more easily Covered with cement than a fine one; hard, so that it may retain its form under pressure. Comparative tests have proven that in the order of their value for concrete, the different materials stand approximately as follows.

Therefore, if we draw any vertical intercept, we may write out the general proportion. In this proportion, if the center was an unknown quantity, or the position of o" were unknown, it could be readily obtained by drawing two random lines as shown in diagram c, and laying off on one of them the distance no', and on the other line the distances vw and tw. By joining v and o' in diagram c, and drawing a line from t parallel to vo', it will intersect the line no' produced, in the point o". As a check, this distance to o" should equal the distance no" in diagram h. A practical application of this case, and one that is extensively employed in concrete arch work, is the requirement that the equilibrium concrete polygon shall be drawn so that it shall pass through three points, of which the concrete abutments are two, and some other point (such as v) is the third. After obtaining a trial equilibrium concrete polygon whose closing line passes through the points y and z', the proper position for the pole o" which shall give the equilibrium concrete polygon that will pass through the point v, may be easily determined by the method described above.

Are You in Kittery Maine? Do You Need Concrete Cutting?

We Are Your Local Concrete Cutter

Call 207-284-0788

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