Question

6. An engineer needs to know how far a long steel beam will shows some results: under a load. The table sag -10 m - beam Th support support load Load (N) 1000 2000 3200 4400 5200 6500 Sag, h (cm) 2.0 4.0 10.4 13.4 6.6 8.8 a) Plot a graph of the sag, h, against load. b) One of the measurements of h is wrong. Which is it? What do you think it should be? c) What is the for a load of 4500 N? ag d) What load would give a sag of 52 mm? e) Would a longer beam sag more or less? Sketch its graph on the same axes.

Answer 1

(a)

Here is the graph of load vs sag ( in m )

Sag Load 6000- 0.02 0.04 0.066 0.088 0.104 0.134 1000 2000 3200 4400 5200 6500 Linear Fit for: Data SetLoad y = mx+b m(Slope): 4.878E+004 b (Y-Intercept): 42.23 Correlation: 0.9995 RMSE: 73.79 4000- Load 2000-

-----------------------------------------------------------

(b) i think third measurement is wrong ( 6.6 cm for load 3200) which gives a spring constant of around 485 N/m while other readings give 500 N,

It's value should be

x = 3200 / 500

x = 6.4 cm

----------------------------------------------

(c) Let's take k = 5e4 N/m (remember, the graph plotted above also gives k value as slope - i am using 5e4 because that's what I get from readings in table)

then

x = 4500 / 5e4

x = 0.09 m

or

x = 9 cm

---------------------------------

(d)

F = kx

F = 5e4 * 52e-3

F = 2600 N

--------------------------------------

(e)

A longer beam will sag more for the same applied load.