California College of the Arts | Department of Architecture
NAME: __________________________________________
Solution
Structures
LAB INSTRUCTOR: _____________________
LAB TIME: ____________________________
HW wk02 | due 01.31.2017 in Lecture | Free Body Analysis
+ Σ Ma = 0
0 = Rxa(0)+Rya(0)-433lbs(5')
+Ryb(10ft)
1. For the beam shown below, draw the free body diagram, and, using the equations of equilibrium,
0 = 0+0-2165ft-lbs+10ftRyb
determine the magnitude of the reactions due to the given loading (hint: to begin, determine the X and Y
from trigonometry
0 = -2165ft-lbs+10ftRyb
components of the 500 lbs. load).
Ryb = +2165ft-lbs/10ft
+
X-component = 500lbs(COS(60)) = 250lbs
Σ Fx = 0
Ryb
= +216.5 lbs
Y-component = 500lbs (SIN(60)) = 433 lbs
433lbs
Rxa+250lbs = 0
(direction assumed is correct)
500
Rxa = -250lbs
(direction assumed is wrong) +
60˚
REDRAW FINAL ANSWER
Σ Fy = 0
250lbs
0 = +Rya - 433lbs + Ryb
500 lbs
Rxa
Rya = 433 lbs - Ryb
Rya = 433 lbs - 215.6 lbs
250 lbs
Rya = +215.6 lbs
Ryb
(direction assumed is correct)
Rya
216.5 lbs
216.5 lbs
2. For the column shown below, draw the free body diagram, and, using the equations of equilibrium, determine
the magnitude of the reactions at the base of the ‘Endless Column’ due to the given loading.
REDRAW FINAL ANSWER
1
10000lbs
+
Σ Fx = 0
0 = Rxa+1200 lbs
Rxa = -1200 lbs
(direction assumed is wrong)
+ Σ Ma = 0
0 = Rxa(0)+Rya(0)+Ma
-1200lbs(50ft)+10000lbs(0)
0 = 0+0+Ma-60000ft-lbs+0
0 = Ma-180000ft-lbs
Ma = 180000ft-lbs
(direction assumed is correct)
50 ft
1200lbs
100 ft
12
50 ft
1200lbs
Rxa
Ma
60000ft-lbs
Rya
Beazley – Ratchye
10000lbs
+
Σ Fy = 0
0 = +Rya - 10000lbs
Rya = +10000lbs
(direction assumed is correct)
Spring 2017
California College of the Arts | Department of Architecture
Structures
3. For the cantilever beam shown below, draw the free body diagram, and, using the equations of equilibrium,
determine the magnitude of the reactions at the foundation for MVRDV’s cantilevered house.
(total length of house is 100 ft.)
6
12
Rxa
Ryb
Rya
+
Σ Fx = 0
0 = +Rxa
Rxa = 0
(no reaction in x-direction)
+ Σ Ma = 0
REDRAW FINAL ANSWER
60k
12k
2k
70k
Beazley – Ratchye
0 = Rxa(0)+Rya(0)-60k(50ft)+Rby(60ft)-12k(100ft)
0 = 0+0-60k(50ft)+Rby(60ft)-12k(100ft)
0 = -3000k-ft+60ftRby-1200k-ft
0 = +60ftRby-4200k-ft
Rby = 4200k-ft/60ft
Rby = 420k-ft/6ft
Rby = 70k
(direction assumed is correct)
+
Σ Fy = 0
0 = +Rya - 60k + Ryb - 12k
0 = +Rya+Ryb-60k
0 = +Rya +70k-60k-12k
0 = +Rya -2k
Rya = +2k
(direction assumed is correct)
Spring 2017