PLOTTING BY COORDINATES

PLOTTING ANGLES FROM TANGENTS - 14070_145

Mistakes in Computations - 14070_147

Engineering Aid 1 - Advanced Structural engineering guide book
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and an engineer’s scale, just to have a general idea of where to start. Make sure that the figure will fit proportionately on the paper of the desired size. Starting at point A, you draw the meridian line lightly. Then you lay off AO, 10 inches (or any convenient round-figure length) along the referenced meridian. Now, from O you draw a line OP perpendicular to AO. Draw a light line OP as shown. In a trigonometric table, look for the natural tangent of the bearing angle 26°90', which equals to 0.49098. Find the distance OP as follows: OP = AO tan 26°09' = 4.9098, or 4.91 inches. You know that OP is equal to 4.91 inches. Draw AP extended; then you lay off the distance AB to scale along AP. Remember that unless you are plotting a closed traverse, it is always advantageous to start your offsets from the referenced meridian. The reason is that, after you have plotted three or more lines, you can always use this referenced meridian line for checking the bearing of the last line plotted to find any discrepancy. The bearing angle, used as a check should also be found by the same method (tangent-offset method). Now to plot the directions of lines from deflection angles larger than 45°, you have to use the com- plementary angle (90° minus the deflection angle). To plot the direction of line BC in figure 7-37, draw a light perpendicular line towards the right from point B. Measure off again a convenient round-figured length, say 10 inches, representing BOJ. The complement of the deflection angle of BC is 90° – 78°25' = 11°35'. The natural tangent value of 11°35’ is equal to 0.20497. From O1 draw OIP1 perpendicular to BOI. Solving for OIPl, you will have O]PX = BO] tan 11°35' = 2.0497, or 2.05 inches. Now lay off the distance OIPA Draw a line from B through PI extended; lay off the distance BC to scale along this line. The remaining sides, CD and DA, are plotted the same way. Make sure that the angles used for your computations are the correct ones. A rough sketch of your next line will always help to avoid major mistakes. When the deflection angle is less than 45°, the procedure of plotting by tangent is as shown in figure 7-38. Here you measure off a convenient round-figure length (say 500.00 feet) on the extension of the initial traverse line to locate point O, and from O, draw OP perpendicular to AO. The angle between BO and BC is, Figure7-38.—Plotting by tangent-offset method from deflection angle smaller than 45°. Figure 7-39.—Plotting by coordnates. in this case, the deflection angle. Assume that 23°21'. The formula for the length of OP is this is OP = BO tan 23°21' = 500 x 0.43170= 215.85 feet. PLOTTING BY COORDINATES.— A common and accurate method of plotting by coordinates is shown in figure 7-39. Here you simply locate each station by its coordinates and have no angular measurements to bother about. To plot station B, for instance, you would layoff from O on the Y axis a distance equal to the Y coordinate of B (847.60 feet). Draw a light line from this point perpendicular to the Y axis, and measure off on this line a distance equal to the X coordinate of B (125.66 feet). The remaining points are plotted in the same way. 7-26

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