3) Determine the overall deformation (elongation) of the A-36 steel rod under the given
unaxial loads and determine the normal stress in section AB.
A 12in B 12in C 16in D
A-36 Steel
$E=29x10^3 Ksi$
$G=11x10^3 ksi$
$\sum F_x=0$
$A_{AC} = 0.9in^2$
$A_{CD}=0.3in^2$
Given:
Cross sectional area of AC = 0.9 $in^2$
$L_{AB} = 12 in$
$L_{BC} = 12 in$
Cross sectional area of CD = 0.3 $in^2$
$L_{CD} = 16 in$
With the following forces applied at the indicated points
$F_B = 75 kips$
$F_C = 45 kips$
$F_D = 30 kips$
Answer (5 pts each):
a) Draw FBDs for each section AB, BC and CD
b) Internal forces for: $F_{AB}$, $F_{BC}$ and $F_{CD}$?
75 kips, 45 kips, 30 kips
c) What is the elongation for sections: AB, BC and CD?
$AD=0.03in$; $BC=0.02in$; $CD=0.05in$
d) What is the total elongation for AD? = 0.11in
e) What is the normal stress ($\sigma$) in section AB = 83.33 $\frac{kip}{in^2}$
