NAME:

Exam 03: Chapters 06 and 07

INSTRUCTIONS

• Solve each of the following problems to the best of your ability. You may use your calculator and the provided formula sheet.

• Read and follow the directions carefully.• Solve using the method required by the problem statement.• Show all your work. Work as neatly as you can. If you need additional paper, blank sheets will be provided for you.• It is permissible to use your calculator to solve a system of equations directly. If you do, state this explicitly.• If you need to use an online solver (like Wolframα), please ask. You will be permitted to use a browser window on my

computer.• Express your answer as directed by the problem statement, using three significant digits. Include the appropriate units.

Your  work  will  be  scored  according  to  the  following  point  structure:Problem 01: /20

Problem 02: /15

Problem 03: /15

Problem 04: /25

Problem 05: /25

ENGR 2311: STATICS FALL 2017

Problem 01 (20 points)

The  truss  shown  is  supported  by  a  pins  at  A  and  E,  and  subjected  to  discrete  loads  P1 = 3kN  applied  at  point  B,  and  P2 = 2kN  applied  at  point  C.

A) Use  the  method  of  joints  to  determine  the  force  in  each  member  of  the  truss.    State  whether  each  member  is  in  tension  (T)  or  compression  (C).    (Hint:    Start  at  joint  C!)

A) Determine  the  reaction  forces  at  A  and  E.2m

√(13m)

Ax

Ex

Ay

EyE

C

FCD

FBC

2kN

FBCB

3kN

FBD

FAB

FBD FCD

FDE

FAD

D

ENGR 2311: STATICS FALL 2017

EXAM 03 PAGE 2/7

Problem 02 (15 points)

Use  the  method  of  sections  to  determine  the  force  in  members  CB,  CF,  and  EF  of  the  bridge  truss  and  state  if  these  members  are  in  tension  or  compression.

Ax

Ay D D

a

a

FEF

FBC

FCF

ENGR 2311: STATICS FALL 2017

EXAM 03 PAGE 3/7

Problem 03 (15 points)

Determine  the  horizontal  and  vertical  components  of  the  forces  at  pins  B  and  C.

Ax

Ay

BxBy

Cx

Cx

Cy

Cy

T

T

T

ENGR 2311: STATICS FALL 2017

EXAM 03 PAGE 4/7

Problem 04 (25 points)

Determine  the  reaction  force  at  A,  and  the  internal  normal  force,  shear  force,  and  bending  moment  at  points  E  and  F  in  the  beam.

Ax

AyT T

W

Ax

Ay

W1

NE

VE

T

W2

VFME

MF

↻

↺

ENGR 2311: STATICS FALL 2017

EXAM 03 PAGE 5/7

Problem 05 (25 points)

The  beam  shown  is  supported  by  a  pin  at  A  and  roller  at  B,  then  subjected  to  the  distributed  loads  shown.

A. Determine  the  reaction  forces  at  A  and  B.

B. Construct  the  shear  and  bending  moment  diagrams.

C. Write  the  equations  for  V(x)  and  M(x)  for  the  length  of  the  beam.

Work  from  left  to  right.    Mind  the  sign  convention!

Note:    I  used  Wolframα  to  solve  for  the  inOlection  points;    set  V(x) = 0  to  Oind  x=1.8  for  M(x)  =  maximum  (M=3.7  when  x=1.8).    Also  let  Wα  solve  M(x)=0  to  Oind  M=0  at  x=3.8.

If  you  labeled  your  curves  properly,  and  bent  them  in  the  right  directions,  I  did  not  subtract  for  not  calculating  the  precise  values  for  the  max  and  the  zeroes.

A B

W P

V

x

x

M

4.5

-3.5

6

-9

3.7

quadratic

cubic

x=1.8 x=3.8

ENGR 2311: STATICS FALL 2017

EXAM 03 PAGE 6/7

Sign Convention for Normal, Shear, Bending

Moment

Sign Convention for Normal, Shear, Bending

Moment

Cut end (point C) on the right:N > 0 = tensionV > 0 = downM > 0 = CCW

Cut end (point C) on the left:N > 0 = tensionV > 0 = upM > 0 = CW

Shear and Bending Moment DiagramsShear and Bending Moment Diagrams

If you’re not sure which way your quadratic or cubic curves, use your graphing calculator for a quick check!

w(x) = constantV(x) = linearM(x) = quadratic

w(x) = linearV(x) = quadraticM(x) = cubic

If you’re not sure which way your quadratic or cubic curves, use your graphing calculator for a quick check!

Boundary conditions:• Check endpoints• Check supports• Check points where

load changes• V=0 ⇒ M = max

ENGR 2311: STATICS FALL 2017

EXAM 03 PAGE 7/7