Find the Laplace transform of f(t) =
2
s
2
s

t [0,2]
cfw_02otherwise
e2 s
Find the Laplace transform of f(t) = 1 2e2t
1
s
2
s+ 2

Find the Laplace transform of f(t) = t2e2tcos(3t)
2( s+ 2)( s 2+ 4 s23)
(s2 +4 s+ 13)3
Find the Laplace transform of f(t
4.31. Construct the shear force and bending moment diagrams for the beam
shown by the area method. Neglect the weight of the beam.
Required: Shear force and bending moment diagram using area method
Solution:
FBD:
+
+ MB = 0
Fy = 0
RA + RD 50 kN = 0
RA
SHEAR FORCE AND BENDING MOMENT
DIAGRAM: AREA METHOD
RHEA CARMONA
TRISHA PAHILANGA
ALJANE GRACE ROSAL
JIREH JAN VILLAMOR
PROBLEM 4.31
Construct the shear force and bending
moment diagrams for the beam shown
by the area method. Neglect the
weight of the bea
4.19 For the beam shown, derive the expressions for V and M, and draw the shear force and
bending moment diagrams. Neglect the weight of the beam.
Given:
1
A
288 kN
3
2.2 m
2.4 m
2.2 m
RA
2
B
C
D
RD
Required:
a. Expressions of V and M
b. Shear force and b
1.
Energy is added to a pistoncylinder arrangement, and the piston is withdrawn in such a way that the quantity PV
remains constant. The initial pressure and volume are 200 kPa and 2 m3, respectively. If the final pressure is 100 kPa,
calculate the work
The infinite series
A. sec x
B. cos x
corresponds to
C. ex*
D. 1 + sin2x
In an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative
value in five trials is
A. 1/32
C. 2/32
B. 3/32
D. 6/32*
Compute the increase in length of 50 m of copper wire when its temperature changes from 12C to 32C. For copper, =
1.7 x 105 C1
1.7 cm
A rod 3.0 m long is found to have expanded 0.091 cm in length after a temperature rise of 60C. What is for the material
vm/ s
=
4 x 1011
d km +6400
= arctan (
T
=
2
R sinL
H + R (1cosL)
(h+ R)3
4 x 10 5
Eb = PtTb
EIRP = Pt Lbo Lbf + At
Te = T(F1)
No = KTe
C
N
Eb
No
=
=
C
KT e
C
N
x
B
fb
)
rcos
d=
(r +h)2
r sin
Az = cos (1
G
Te
tan
tan
)
= GrdBi 10 log (Ta + Te)
Ta =
1.
Energy is added to a pistoncylinder arrangement, and the piston is withdrawn in such a way that the quantity PV
remains constant. The initial pressure and volume are 200 kPa and 2 m3, respectively. If the final pressure is 100
kPa, calculate the work
1.
When the input to an ideal nonlinear device is an AM waveform consisting of a carrier and its sidebands, the output of nonlinear
mixing produces the original intelligence because
A. The intelligence signal is one of its inputs.
B. A dc component is als
Compute the increase in length of 50 m of copper wire when its temperature changes from 12C to 32C. For copper, =
1.7 x 105 C1
1.7 cm
A rod 3.0 m long is found to have expanded 0.091 cm in length after a temperature rise of 60C. What is for the material
A copper bar is 80 cm long at 15C. What is the increase in length when it is heated to 35C? The linear expansion
coefficient for copper is 1.7 x 105 C1.
2.7 x 104 m
A cylinder of diameter 1 cm at 30C is to be slid into a hole in a steel plate. The hole
Shear Force and
Bending Moment
Sample Problem 4.19
Problem 4.19
For the beam shown, derive the expressions for V
and M, and draw the shear force and bending
moment diagrams. Neglect the weight of the
beam.
Required:
Expressions
Shear
of V and M
force and