Mechanical Engineering Chapter 4 Homework Summing the forces along the y axis by referring to Fig

368

SOLUTION

Resultant Force. Referring to Fig. a,

4–137.

Replace the three forces acting on the plate by a wrench.

Specify the magnitude of the force and couple moment for

the wrench and the point P(x, y) where the wrench intersects

the plate.

5 m 3 m y

yx

x

P

C

B

z

FC fi {200j} N

FB fi { 300k} N

369

Ans:

Referring to Fig. a,

4–137. Continued

370

SOLUTION

4–138.

Replace the loading by an equivalent resultant force and

couple moment acting at point O.

9 ft

O

50 lb/ft

50 lb

/

ft

Ans:

371

Ans:

4–139.

Replace the distributed loading with an equivalent resultant

force, and specify its location on the beam measured from

point O.

SOLUTION

O

3 m 1.5 m

3 kN/m

372

Ans:

SOLUTION

Equivalent Resultant Force. Summing the forces along the y axis by referring to

Fig. a

*4–140.

Replace the loading by an equivalent resultant force and

specify its location on the beam, measured from point A.

BA x

2 kN/m

5 kN/m

w

4 m 2 m

373

Ans:

4–141.

Currently eighty-five percent of all neck injuries are caused

by rear-end car collisions.To alleviate this problem, an

automobile seat restraint has been developed that provides

additional pressure contact with the cranium. During

dynamic tests the distribution of load on the cranium has

been plotted and shown to be parabolic. Determine the

equivalent resultant force and its location, measured from

point A.

A

w

B

x

wfi12(1 2x

2

)lb/ft

0.5 ft

12 lb/ft

18 lb/ft

SOLUTION

374

Ans:

SOLUTION

Equivalent Resultant Force. Summing the forces along the y axis by referring to

Fig.a,

4–142.

Replace the distributed loading by an equivalent resultant

force, and specify its location on the beam, measured from

the pin at A.

3 m3 m

AB

2 kN/m

4 kN/m

375

Ans:

SOLUTION

Equivalent Resultant Force. Summing the forces along the y axis by referring to

Fig. a,

4–143.

Replace this loading by an equivalent resultant force and

specify its location, measured from point O.

1.5 m2 m

6 kN/m

4 kN/m

O

376

Ans:

*4–144.

The distribution of soil loading on the bottom of a

building slab is shown. Replace this loading by an

equivalent resultant force and specify its location, measured

from point O.

SOLUTION

12 ft 9ft

100 lb/ft

50 lb/ft

300 lb/ft

O

377

Ans:

SOLUTION

Equivalent Resultant Force And Couple Moment About Point O. Summing the

forces along the y axis by referring to Fig. a,

Summing the Moment about point O,

4–145.

Replace the loading by an equivalent resultant force and

couple moment acting at point O.

1.5 m 0.75 m 0.75 m

5 kN/m

8 kN/m

O

378

Ans:

SOLUTION

Equivalent Resultant Force And Couple Moment About Point A. Summing the

forces along the y axis by referring to Fig. a,

4–146.

Replace the distributed loading by an equivalent resultant

force and couple moment acting at point A.

A

3

m3

m

6 kN/m 6 kN/m

3 kN/m

B

379

Ans:

SOLUTION

4–147.

Determine the length b of the triangular load and its

position a on the beam such that the equivalent resultant

force is zero and the resultant couple moment is 8 kN

#

m

clockwise.

a

9 m

4 kN/m

A

b

2.5 kN/m

380

SOLUTION

Also, from the back of the book,

*4–148.

The form is used to cast a concrete wall having a width

of 5 m. Determine the equivalent resultant force the wet

concrete exerts on the form AB if the pressure distribution

due to the concrete can be approximated as shown. Specify

the location of the resultant force, measured from point B.

A

B

4 m

p

fi (4 ) kPa

pz2

1

381

Ans:

4–149.

If the soil exerts a trapezoidal distribution of load on the

bottom of the footing, determine the intensities w1and w2of

this distribution needed to support the column loadings.

SOLUTION

3.5 m2.5 m

1

m1

m

60 kN 80 kN

50 kN

w2

382

4–150.

SOLUTION

Rep

l

ace t

h

e

l

oa

di

ng

b

y an equ

i

va

l

ent force an

d

coup

l

e

moment acting at point O.

O

7.5 m4.5 m

500 kN m

6kN/m15 kN