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5.28
The concrete [
E
= 29 GPa] pier shown in
Fig. P5.28 is reinforced using four steel [
E
=
200 GPa] reinforcing rods, each having a
diameter of 19 mm. If the pier is subjected to an
axial load of 670 kN, determine:
(a) the normal stress in the concrete and in the
steel reinforcing rods.
(b) the shortening of the pier.
Fig. P5.28
Solution
(a) Equilibrium:
Consider a FBD of the pier, cut around the upper
end.
The concrete will be designated member (1) and the reinforcing
steel bars will be designated member (2).
Sum forces in the vertical
direction to obtain:
12
670 kN
0
y
FF
F
Σ=
−−−
=
Geometry of Deformations:
δ
=
ForceDeformation Relationships:
11
2 2
FL
A
EA
E
δδ
==
Compatibility Equation:
Substitute Eqs. (c) into Eq. (b) to derive the compatibility equation:
A
E
=
(d)
Solve the Equations:
Solve Eq. (d) for
F
2
:
2
1
2
2
21
1
2
2 1 1
L
AE
L A E
F
A
EL
LAE
(e)
and substitute this expression into Eq. (a) to determine
F
1
:
122
1 1
1
211
1
670 kN
y
F
F
⎡⎤
⎡
⎤
−− =
−−
=
− +
=
⎢⎥
⎢
⎥
⎣⎦
⎣
⎦
(f)
Since
L
1
=
L
2
, the term
L
1
/
L
2
= 1 can be eliminated and Eq. (f) simplified to
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This note was uploaded on 02/09/2012 for the course MECHANICAL EM217 taught by Professor Joyce during the Spring '11 term at Naval Academy.
 Spring '11
 Joyce
 Stress

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