Imagine a downward static load of 3500N uniformly spread acc

Imagine a downward static load of 3500N uniformly spread accross the upper surface. Assume the lugs behave as the simple supports shown below. Spread the supports symmetrically towards the ends of the beam from a separation of 0mm until they are a total of 440mm apart. Plot the centerline and end deflections as function of support separation. Determine the vertical deflection at the beam ends and centerline. Is the centerline deflection ever equal to the end deflection? If so, what is the support separation (approximately)?

Centerline End Load Load Beam

Solution

solution:

1) here UDL of 3500 N is acting on beam of 440 mm long and it is initially supported at centerline means it is condition of cantilever beam of length 220 mm on both side and as we increase separation means we are are providing simply supported beam between two support and after that beam is cantilever,in this way we do analysis of beam for support separation

2) for cantilever beam deflection at end is given by

dc=wlc^4/8EI

for simply supported beam deflection is given by

ds=(5/384)wls^4/EI

3)case,support at center hence

cantilver length=lc=220 mm

simply supported length=ls=0 mm

hence deflection at vertical support

dc=102.48*10^10/EI mm

deflection at centerline

ds=0 mm

4)if support are 100 mm apart then

lc=170 mm and ls=100 mm

then deflection are

dc=36.54*10^10/EI mm

ds=.4557*10^10/EI mm

5) if support are 200 mm apart then

lc=120 mm and ls=200 mm

then deflection are

dc=9.07*10^10/EI mm

ds=7.29*10^10/EI mm

6) if support are 300 mm apart then

lc=70 mm and ls=300 mm

then deflection are

dc=1.05*10^10/EI mm

ds=36.91 *10^10/EI mm

7)if support are 400 mm apart then

lc=20 mm and ls=400 mm

then deflection are

dc=.007*10^10/EI mm

ds=116.66*10^10/EI mm

8)if support are 440 mm apart then

lc=0 mm and ls=440 mm

then deflection are

dc=0 mm

ds=170.81*10^10/EI mm

8)hence centerline deflection will not be equal to vertical end deflection and support separation means conversion of support from cantilver type to simply supported beam.