W. "Ih = 2 in. -8 ft- - 8 ft- м, max (b)
The A992 steel beam shown in Fig. a is a W10 * 39. Determine the maximum bending stress in the beam and the beam’s maximum deflection if the weight W = 1.50 kip is dropped from a height h = 2 in. onto the beam. Est = 29(103) ksi.
Modulus of elasticity (E) A992 steel beam = 2987 ksi = 20.594 GPa
ho = 2 in
W = 1.5 kip
W10 * 39 beam dimensions, h = 9.87 in b = 8 in t = 0.5 in
A = 12.435 in2
L = 16 ft
V = A x L = 2387.52 in3
I = 204.838137625 in 4
The total energy of block = potential energy
Assumptions made in this analysis are
1) no energy is dissipated in impact
2) Block does not bounce off after striking.
Potential energy = mg(ho + δL)
where δL is deflection of beam at point C.
Since potential energy due to height δL is neglected.
Now, Assume equivalent load by impact load is P.
As, Single Load is applied on the centre of the simply supported beam, Reaction at support are equal.
RA = P/2. , RB = P/2
Maximum Bending moment in a simply supported beam with single point load is,
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