Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

The only unknown term in this equation is the reaction force D y . Consequently, solve the
equation for D y , to obtain
3
3
D ⎡ L1
L2
⎤
y ⎢ + ⎥
⎣ 48EI
48EI
⎦
=
1 1 2 2
4
5wL1
384EI
1 1
(e)
Before beginning the calculation, pay special attention to the distinction between those
properties which apply to the steel beam (i.e., L 1 , I 1 , and E 1 ) and those which apply to the
wooden beam (i.e., L 2 , I 2 , and E 2 ). For instance, the flexural stiffness EI appears in each
term, but EI for the wooden beam is much different than EI for the steel beam.
Calculate the reaction force exerted on steel beam (1), using the following values:
Steel Beam Properties
w = 1,500 lb/ft = 125 lb/in.
L 1 = 20 ft = 240 in.
I 1 = 238 in. 4 (from Appendix B for W12 × 30)
Wood Beam Properties
L 2 = 10 ft = 120 in.
3
(6 in.)(10in.)
I2
= = 500 in.
12
E 2 = 1.8 × 10 6 psi
4
E 1 = 29 × 10 6 psi
Substitute these values into Equation (e), and compute D y = 14,471.766 lb = 14,470 lb. Ans.
The deflection of the system at D can now be calculated from Equation (c) as
v
D
DL y 3
3
2 (14,471.766 lb)(120 in.)
=− =−
6 4
48E I 48(1.8 × 10 psi)(500 in. )
2 2
=− 0.579 in. = 0.579 in. ↓
Ans.
mecmovies
ExAmpLE
m11.4 Determine the beam reactions for a simply supported
beam with an elastic support at midspan.
=
=
=
=
. × .
472