Iowa Public Television

Challenge Question Number 1 for Draftsperson #1201

This sketch illustrates a typical plate detail used in our towers. The plate would be used as a stiffener inside the fluted column. It is also a platform used to climb the ladders to the top of the tank. The dimensions in the center of the plate show the opening required for the ladder to go through the platform. The numerical dimensions are what we are typically given and the dimensions shown as letters are those that the drafter must calculate to complete the detail for the shop.

Clearly describe what you expect from the students:
Calculate the missing dimensions, length to the nearest 1/16”, angles to 4 decimal places.

A Overall angle of finished piece:
B Arc length of lower edge:
C Chord length of lower edge:
D Mid-ordinate distance of lower edge:
E Vertical dimension on side:
F Horizontal dimension of side:
G Overall piece width:
H Length of top tab:

In order to give the teacher some guidance in evaluating the student's project(s); list some tips that may help to assess the student's work:
A
Convert 14’-6 7/8” radius to inches.
14 x 12 = 168
168 + 6.875 (6 7/8) = 174.875

A = 72º - ( 2 x arcsin (1 / 174.875))
= 72º - 2 x arcsin (.0057)
= 72º - 2 x .3276º
= 71.3447º

B
Convert 14’-6 7/8” radius to inches. (174.875 from A)
B = 174.875 x  x Aº/180
= 174.875 x 3.14159 x 71.3447º/180º
= 217.7543

Convert to feet and inches.
217/12=18.08333  18 Feet
18 x 12 = 216
217.7543 – 216 = 1.7543 inches
= 18’-1 3/4”

C
Convert 14’-6 7/8” radius to inches. (174.875 from A)
C = 2 x (174.875 x sin(A/2)
= 2 x (174.875 x sin(71.3447º/2)
= 2 x (174.875 x sin(35.67235º)
= 2 x (174.875 x .5831)
= 2 x 101.9782
= 203.9564 (Convert to feet and inches.)
= 16’-11 15/16”

D
Convert 14’-6 7/8” radius to inches. (174.875 from A)
D = 174.875 – (174.875 x cos(A/2))
= 174.875 – (174.875 x cos(35.67235))
= 174.875 - (174.875 x .8124)
= 174.875 – 142.0623
= 32.8127 (Convert to feet and inches.)
= 2’-8 13/16”

E
Convert 1’-11 7/8” to inches. (23.875)
E = 23.875 x cos(A/2)
= 23.875 x .8124
= 19.3952 (Convert to feet and inches.)
= 1’-7 3/8”

F
Convert 1’-11 7/8” to inches. (23.875)
F = 23.875 x sin(A/2)
= 23.875 x .5831
= 13.9227 (Convert to feet and inches.)
= 1’-1 15/16”

G
G = D + E + 4
= 32.8127 + 19.3952 + 4
= 56.2079 (Convert to feet and inches.)
= 4’-8 3/16”

H
H = C – (2 x F)
= 203.9564 - (2 x 13.9227)
= 203.9564 – 27.8454
= 176.1110 (Convert to feet and inches.)
= 14’-8 1/8”