There are few old sports stadiums left these days, but if you have attended a ga
ID: 1884800 • Letter: T
Question
There are few old sports stadiums left these days, but if you have attended a game at one of the remaining old fields, such as Fenway Park or Wrigley Field, you know that your view from the lower decks can be obstructed by columns that support the upper decks and canopies. Fortunately, better structural engineering has mitigated this problem in modern stadiums by using trusses to support the roof and some upper decks. The truss below is designed to support roofs over stadium seats in order to provide unobstructed views for the fans. (a) Determine the forces (and state if in tension or compression) in members EG, FG, FH (b) Determine the forces (and state if in tension or compression) in members IK, JK, JL Use whichever truss analysis approach (sections or joints) that you prefer. 1 kip 2 kips 2 kips 1 kip 6 ft 15 ft KL Not: IG, IK, and KM are each 5 ft in length, i.e. the 15 ft dimension in the figure is divided equally over the three membersExplanation / Answer
for the given problem
cosider method of sections
let normal reaction at M = Mx, My
normal reaction at N = Nx, Ny
From force balance
1 + 2 + 2 + 1 = My + Ny = 6 kips
Nx + Mx = 0
from moment balance about N
1*36 + 2*28 + 2*20 + 2*12 = My*12
My = 13 kips
Ny = -7 kips
also
Ny/Nx = -15/6
Nx = -6Ny/15 = 42/15 = 2.8 kips
Mx = -2.8 kips
consider section passing through EG, FG, FH
a. let tension in the members be T1, T2, T3
then from force balance
T1 + T3*cos(45) = Mx + Nx = 0
T1 = -T3*cos(45)
T2 + T3sin(45) + My + Ny = 0
T2 + T3sin(45) + 6 = 0
T2 - T1 + 6 = 0
from moemnnt balance
about N
T1*15 - T2*12 + T3*cos(45)*15 - T3*sin(45)*6 + 13*12 = 0
15T1 - 12T2 + 9cos(45)T3 = -156
15(T2 + 6) - 12T2 - 9(T2 + 6) = -156
-6T2 + 36 = -156
T2 = 32 kips ( tension)
T1 = 38 kips (tension)
T3 = -53.740 kips (copression)
similiarly
consider section IK, jK, JL
from force balance
T1 + T2*5/sqrt(25 + 16) + T3*5/sqrt(25 + 4) + My + Ny = 0
T1 + 5T2/sqrt(41) + 5T3/sqrt(29) = -6
T2*4/sqrt(41) + 2T3/sqrt(29) = 0
from moment balance about M
T2*5*5/sqrt(41) + T3*2*5/sqrt(29) - T3*5*2/sqrt(29) - Ny*12 = 0
25T2/sqrt(41) = Ny*12 = -84
T2 = -21.5144 kips (compression) Fjk
T3 = 36.1883 kips (tension) Fjl
T1 = -22.800 kips (compression) Fik
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