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

Equation (c) for the beam slope and Equation (d) for the elastic curve can now be
completed:
EI dv
dx
90 kN/m
579 kN
90 kN/m
=− x − 0m + x − 2m + x − 12 m
6
2
6
639 kN
2 2
+ x −12 m −1,880 kN⋅m
2
3 2 3
90 kN/m
579 kN
90 kN/m
EIv =− x − 0m + x − 2m + x − 12 m
24
6
24
639 kN
3 2 3
+ x −12 m − (1,880 kN ⋅ m) x + 3,820 kN ⋅m
6
4 3 4
(h)
(i)
(b) Beam Deflection at A
The beam deflection at A (x = 0 m) is computed from Equation (i):
EIv
A
= 3,820 kN⋅m
3
3,820 kN⋅m
∴ vA
=
120,000 kN⋅m
3
2
= 0.031833 m = 31.8 mm ↑
Ans.
(c) Beam Deflection at C
From Equation (i), the beam deflection at C (x = 7 m) is computed as follows:
EIv
C
∴ v
90 kN/m 579 kN
=− (7 m) + (5 m) − (1,880 kN⋅ m)(7 m) + 3,820 kN⋅m
24
6
3
=−6,281.250 kN⋅m
C
4 3 2 3
3
6,281.250 kN⋅m
= −
=− 0.052344 m = 52.3 mm ↓
2
120,000 kN⋅m
Ans.
pRoBLEmS
p11.12 A propped cantilever beam is loaded as shown in Figure
P11.12. Assume that EI = 200,000 kN · m 2 , and use discontinuity
functions to determine
(a) the reactions at A and C.
(b) the beam deflection at B.
v
A B C
FIGURE p11.12
7 m
150 kN
5 m
p11.13 A propped cantilever beam is loaded as shown in Figure
P11.13. Assume that EI = 200,000 kN · m 2 , and use discontinuity
functions to determine
x
(a) the reactions at A and B.
(b) the beam deflection at C.
v
A B C
FIGURE p11.13
5 m
2.5 m
750 kN.m
p11.14 A propped cantilever beam is loaded as shown in Figure
P11.14. Assume that EI = 100,000 kip ⋅ ft 2 , and use discontinuity
functions to determine
(a) the reactions at A and E.
(b) the beam deflection at C.
x
459