Statics with MATLAB Dan B. Marghitu Mihai Dupac Nels H. Madsen
292 pág.

Statics with MATLAB Dan B. Marghitu Mihai Dupac Nels H. Madsen


DisciplinaMatlab495 materiais2.112 seguidores
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fs*subs(FA_, sl, nl);
FBn_ = fs*subs(FB_, sl, nl);
FCn_ = fs*subs(FC_, sl, nl);
Rtn_ = fs*Rn_;
Mtn_ = fs*Mn*uRn_;
quiver3...
(xA,yA,zA,FAn_(1),FAn_(2),FAn_(3),1,...
\u2019Color\u2019,\u2019k\u2019,\u2019LineWidth\u2019,2)
2.5 Examples 77
quiver3...
(xB,yB,zB,FBn_(1),FBn_(2),FBn_(3),1,...
\u2019Color\u2019,\u2019k\u2019,\u2019LineWidth\u2019,2)
quiver3...
(xC,yC,zC,FCn_(1),FCn_(2),FCn_(3),1,...
\u2019Color\u2019,\u2019k\u2019,\u2019LineWidth\u2019,2)
quiver3...
(xT,yT,zT,Rtn_(1),Rtn_(2),Rtn_(3),1,...
\u2019Color\u2019,\u2019r\u2019,\u2019LineWidth\u2019,2)
quiver3...
(xT,yT,zT,Mtn_(1),Mtn_(2),Mtn_(3),1,...
\u2019Color\u2019,\u2019G\u2019,\u2019LineWidth\u2019,2)
The vector representation with MATLAB is shown in Fig. 2.18b.
2.6 Problems
2.1 (a) Determine the resultant of the forces F1 = F1x \u131 + F1y j + F1z k, F2 =
F2x \u131 + F2y j + F2z k, and F3 = F3x \u131 + F3y j + F3z k, which are concurrent at
the point P(xP, yP, zP), where F1x = 2, F1y = 3.5, F1z = \u22123, F2x = \u22121.5,
F2y = 4.5, F2z = \u22123, F3x = 7, F3y = \u22126, F3z = 5, xP = 1, yP = 2,
and zP = 3. (b) Find the total moment of the given forces about the origin
O(0, 0, 0). The units for the forces are in Newtons and for the coordinates are
given in meters.
2.2 (a) Determine the resultant of the three forces shown in Fig. 2.19. The force
F1 acts along the x-axis, the force F2 acts along the z-axis, and the direction
of the force F3 is given by the line O3P3, where O3 = O(xO3 , yO3 , zO3) and
P3 = P(xP3 , yP3 , zP3). The application point of the forces F1 and F2 is the
origin O(0, 0, 0) of the reference frame as shown in Fig. 2.19. (b) Find the total
moment of the given forces about the point P3. Numerical application: |F1| =
F1 = 250 N, |F2| = F2 = 300 N, |F3| = F3 = 300 N, O3 = O3(1, 2, 3) and
P3 = P3(5, 7, 9). The coordinates are given in meters.
3
F2
O
z
y
xF1
F3
P
O
3
Fig. 2.19 Problem 2.2
78 2 Moments, Couples, Equipollent Systems
F2
d
z
y
x
F1
F3
O
1
A
Bd2
Fig. 2.20 Problem 2.3
2.3 Replace the three forces F1, F2, and F3, shown in Fig. 2.20, by a resultant force,
R, through O and a couple. The force F2 acts along the x-axis, the force F1 is
parallel to the y-axis, and the force F3 is parallel to the z-axis. The application
point of the forces F2 is O, the application point of the forces F1 is B, and
the application points of the force F3 is A. The distance between O and A is
d1 and the distance between A and B is d2 as shown in Fig. 2.20. Numerical
application: |F1| = F1 = 250 N, |F2| = F2 = 300 N, |F3| = F3 = 400 N,
d1 = 1.5 m and d2 = 2 m.
2.4 Two forces F1 and F2 and a couple of moment M in the xy plane are given. The
force F1 = F1x \u131 + F1y j + F1z k acts at the point P1 = P1(x1, y1, z1) and the
force F2 = F2x \u131+F2y j+F2z k acts at the point P2 = P2(x2, y2, z2). Find the
resultant force-couple system at the origin O(0, 0, 0). Numerical application:
F1x = 10, F1y = 5, F1z = 40, F2x = 30, F2y = 10, F2z = \u221230, F3x = 7,
F3y = \u22126, F3z = 5 , P1 = P1(0, 1, \u22121), P2 = P2(1, 1, 1) and M = \u221230
N·m. The units for the forces are in Newtons and for the coordinates are given
in meters.
2.5 Replace the three forces F1, F2, and F3, shown in Fig. 2.21, by a resultant
force at the origin O of the reference frame and a couple. The force F1 acts
along the x-axis, the force F2 is parallel with the z-axis, and the force F3
is parallel with the y-axis. The application point of the force F1 is at O, the
application point of the forces F2 is at A, and the application points of the force
F3 is at B. The distance between the origin O and the point A is d1 and the
distance between the point A and the point B is d2. The line AB is parallel with
the z-axis. Numerical application: |F1| = F1 = 50 N, |F2| = F2 = 30 N,
|F3| = F3 = 60 N, d1 = 1 m, and d2 = 0.7 m
F2
z
y
F1
F3
O
d
x
1
A
B
d2
Fig. 2.21 Problem 2.5
2.6 Problems 79
F2F1 F3
d
x
1 d2 d3 d4
2P1P 3PA B
Fig. 2.22 Problem 2.6
2.6 Three forces F1, F2 and F3 act on a beam as shown in Fig. 2.22. The directions
of the forces are parallel with y-axis. The application points of the forces are P1,
P2, and P3, and the distances AP1 = d1, P1P2 = d2, P2P3 = d3 and P3B = d4
are given. (a) Find the resultant of the system. (b) Resolve this resultant into two
components at the points A and B. Numerical application: |F1| = F1 = 30 N,
|F2| = F2 = 60 N, |F3| = F3 = 50 N, d1 = 0.1 m, d2 = 0.3 m, d3 = 0.4 m
and d4 = 0.4 m.
2.7 A force F acts vertically downward, parallel to the y-axis, and intersects the xz
plane at the point P1(x1, y1, z1). Resolve this force into three components
acting through the points P2 = P2(x2, y2, z2), P3 = P3(x3, y3, z3) and
P4 = P4(x4, y4, z4). Numerical application: |F| = F = 50 N, P1 =
P1(2, 0, 4), P2 = P2(1, 1, 1), P3 = P3(6, 0, 0), and P4 = P4(0, 0, 3).
The coordinates are given in meters.
2.8 Determine the resultant of the given system of forces F1, F2, and F3, shown in
the Fig. 2.23. The angle between the direction of the force F1 and the Ox axis
is \u3b81 and the angle between the direction of the force F2 with the x-axis is \u3b82.
The x and y components of the force F3 = |F3x| \u131 +
\u2223\u2223F3y
\u2223\u2223 j = F3x \u131 + F3y j
are given. Numerical application: |F1| = F1 = 250 N, |F2| = F2 = 220 N,
|F3x| = F3x = 50 N,
\u2223\u2223F3y
\u2223\u2223 = F3y = 120 N, \u3b81 = 30\u25e6, and \u3b82 = 45\u25e6.
2.9 The rectangular plate in Fig. 2.24 is subjected to four parallel forces. Determine
the magnitude and direction of a resultant force equivalent to the given force
system and locate its point of application on the plate. Numerical application:
FO = 700 lb, FA = 600 lb, FB = 500 lb, FC = 100 lb, a = 8 ft, and b = 10 ft.
Hint: the moments about the x-axis and y-axis of the resultant force, are equal
Fig. 2.23 Problem 2.8
1
F2
y
x
F1
F3
O
\u3b8 2\u3b8
80 2 Moments, Couples, Equipollent Systems
Fig. 2.24 Problem 2.9 z
y
x
A
O
B
C
FC
FB
a/2
a/2
b/2
b/2
FA
FO
Fig. 2.25 Problem 2.10 z
y
x
A
O
BC
FC
FB
a/2
a/2
b/2
b/2
FO
to the sum of the moments about the x-axis and y-axis of all the forces in the
system.
2.10 Three forces FO, FB, and FC , as shown in Fig. 2.25 , are acting on a rectan-
gular planar plate (FO||Oz, FB||Oy, FC ||Ox). The three forces acting on the
plate are replaced by a wrench. Find: (a) the resultant force for the wrench;
(b) the magnitude of couple moment, M, for the wrench and the point Q(y, z)
where its line of action intersects the plate. Numerical application: FO = 800 lb,
FB = FC = 500 lb, a = OA = 6 ft, and b = AB = 5 ft.
2.7 Programs
2.7.1 Program 2.1
% example 2.1
clear all; clc; close all
syms F theta a b real
rA_ = [a b 0];
2.7 Programs 81
FA_ = [F*cos(theta) F*sin(theta) 0];
MO_ = cross(rA_, FA_);
MOz= MO_(3);
sl = {F, theta, a, b};
nl = {5, pi/4, 1, 5};
fprintf(\u2019MOz = %s =\u2019,char(MOz))
fprintf(\u2019%6.3f (kN m)\n\u2019,subs(MOz,sl,nl))
% numerical values
rAn_ = double(subs(rA_,sl,nl));
Fn_ = double(subs(FA_,sl,nl));
Mn_ = subs(MO_,sl,nl);
% vector plotting
axis([0 5 0 10 -18 0])
xlabel(\u2019x\u2019), ylabel(\u2019y\u2019), zlabel(\u2019z\u2019)
hold on, grid on
% Cartesian axes
text(0,0,0,\u2019 O\u2019,\u2019fontsize\u2019,14,\u2019fontweight\u2019,\u2019b\u2019)
quiver3(0,0,0,4,0,0,1,\u2019Color\u2019,\u2019b\u2019)
text(4.1,0,0,\u2019x\u2019)
quiver3(0,0,0,0,9,0,1,\u2019Color\u2019,\u2019b\u2019)
text(0,9.4,0,\u2019y\u2019)
quiver3(0,0,0,0,0,5,1,\u2019Color\u2019,\u2019b\u2019)
text(0,0,5.5,\u2019 z\u2019)
line([0 0],[0 rAn_(2)],[0,0],\u2019LineStyle\u2019,\u2019--\u2019,...
\u2019Color\u2019,\u2019k\u2019,\u2019LineWidth\u2019,4)
line...
([0 rAn_(1)],[rAn_(2) rAn_(2)],[0,0],...
\u2019LineStyle\u2019,\u2019--\u2019,\u2019Color\u2019,\u2019k\u2019,\u2019LineWidth\u2019,4)
text(rAn_(1),rAn_(2),0,\u2019 A\u2019,...
\u2019fontsize\u2019,14,\u2019fontweight\u2019,\u2019b\u2019)
quiver3(0,0,0,rAn_(1),rAn_(2),0,1,...
\u2019Color\u2019,\u2019b\u2019,\u2019LineWidth\u2019,2)
text(rAn_(1)/2,rAn_(2)/2,0,...
\u2019 r_A\u2019,\u2019fontsize\u2019,14,\u2019fontweight\u2019,\u2019b\u2019)
quiver3(rAn_(1),rAn_(2),0,Fn_(1),Fn_(2),0,1,...
\u2019Color\u2019,\u2019r\u2019,\u2019LineWidth\u2019,2)
quiver3(rAn_(1),rAn_(2),0,Fn_(1),0,0,1,...
\u2019Color\u2019,\u2019k\u2019,\u2019LineWidth\u2019,1)
quiver3(rAn_(1),rAn_(2),0,0,Fn_(2),0,1,...
82 2 Moments, Couples, Equipollent Systems
\u2019Color\u2019,\u2019k\u2019,\u2019LineWidth\u2019,1)
Arthur
Arthur fez um comentário
Muito bom! achei que nunca ia achar um pdf desse livro, fazia tempo que estava procurando! muito obrigado!!!
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