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
7
Embed
Problem 01: /20 Problem 02: /15 Problem 03: /15 Problem 04: /25€¦ · · 2017-10-26NAME: Exam 03: Chapters 06 and 07 INSTRUCTIONS • Solve each of the following problems to the
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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