SP - 5

Statically indeterminate rod
(Strength of Materials - I, Mid-term Exam-44-5)
Problem :
Two cylindrical rods, CD made of steel (E = 29 × 10 6 psi) and AC made of aluminum
(E = 10.4 × 10 6 psi), are joined at C and restrained by rigid supports at A and D.
Determine (a) the reactions at A and D, (b) the deflection of point C. (1 kips = 1000 lb)
Solution :
Internal forces
F1 = RA
F2 = RA − 18000
F3 = RA − 32000
The compatibility relation of deformation
∆ε1 + ∆ε2 + ∆ε3 = 0
l
l
l
RA + (RA − 18000) + (RA − 32000) = 0
AE 1
AE 2
AE 3
The cross-sectional areas
A1 = A2 = π
4
A3 = π
1
4
5
8
1 1
8
2
2
= 0.994 02 mm 2
= 2. 073 9 mm 2
1
0.994 02 × 10.4 × 106 (8RA
10
+ 10 (RA − 18000)) + (RA − 32000)
= 0
2. 073 9 × 29 × 106 Prof. Dr. M. Kemal APALAK 1

The deflection of the point C
18RA − 18 × 10 4 + (RA − 32000) × 1.71875 = 0
19. 719RA = 2. 35 × 10 5
RA = 11917 lb
RA + RD = 32000
RD = 32000 − 11917
RD = 20083 lb
∆ε3 =
l
10
δC = RD = 20083 ×
AE 3
2. 073 9 × 29 × 106 ∆ε3 = δC = 3. 339 2 × 10 −3 in (→)
Prof. Dr. M. Kemal APALAK 2