Question

The following observations were made of an axle-load survey on a road:

$\begin{array}{cc}Axleload\left(kN\right)& Repetitionsperday\\ 35-45& 800\\ 75-85& 400\end{array}$

The standard axle load is 80 kN. Equivalent daily number of repetitions for the standard axle load are

• A. 450
• B. 800
• C. 1200
• D. 480

Answer 1

The correct option is A 450

It is found that the fourth power rule applies in causing structural damage. The rule can be stated thus. The structural damage caused by an axle load varies at the fourth power of its ratio to the standard axle load. If F is the equivalence factor of an axle load L and if $L_s$ is the standard axle load
$Then,F={\left(\frac{L}{L_s}\right)}^4$

Here given standard axle load
$L_s=80kN$

Axle Load(kN)	Mid point in kN(L)	No. of repetitions per day (N)	${\left(\frac{L}{80}\right)}^4$	${\left(\frac{L}{80}\right)}^{4}XN$
35 - 45	40	800	1/16	50
75 - 85	80	400	1	400

$\sum =450$

Hence , number of repetitions corresponding to 80 kN standard load = 450 per day