Transcript Slide 1

McCallum set an NCAA
record for career allpurpose yards with 7,172
49ers linebacker Ken Norton Jr.
tackled McCallum and in the pileup
McCallum dislocated his knee,
tearing three ligaments, ripping his
calf and hamstring muscles from the
bone, and incurring nerve and artery
damage.
In surgery, doctors were concerned
that if the operation did not go well,
his leg could have to be amputated.
In the end, McCallum endured six
surgeries, including two knee
reconstructions. The rehabilitation
was as painful as any of the
surgeries, but now McCallum can
walk, even if he cannot run or ever
play again.
The change in length of a prismatic bar under applied load
P can be calculated for an elastic material using
L
P
P L
PL

   E 

 L 
L
A
EA L
EA
If the rod has intermediate loads as shown above then the
displacement can be determined for each section and then
summed to find the total displacement.
N1 L1 N 2 L2 N 3 L3
  1   2   3 


EA
EA
EA
If the rod has intermediate loads and multiple prismatic
elements then we have the more general formula
n
N i Li
 
i 1 Ei Ai
N x dx
N x dx
d 
    d  
EAx 
EAx 
0
0
L
L
If the rod cross-section varies continuously we can use
the more general form. This can be solved analytically or
numerically depending on the complexity if the
functions.
A composite steel bar of modulus 29 (103)
ksi is made from two segments AB and BD,
having cross-sectional areas of AAB=1 in2
and ABD=2 in2. Determine the vertical
displacement of B relative to C.
A  
 B/C 
PL 15* 2 *12 7 *1.5 *12  9 *1*12



 0.0127in
EA 29,000*1 29,000* 2 29000* 2
PBC LBC 7 *1.5 *12

 0.00217in
ABC E
29,000* 2