menu
bartleby
search
close search
Hit Return to see all results

A4momdir

Question

The beam is supported by a pin connection at A and a roller at B. Beam AB supports a uniformly distributed load of 7.5 kN/m over the first 4 meters (x=0 to x=4) and supports a distributed load that decreases from w2=4.5kN/m to w3=0kN/m. Over all beam length (x) is 10 meters. Neglecting the self-weight of member AB, find"

  • The reaction forces at A and B.
  • The internal shear and moment at mid-span (x=5m)
  • The equations for internal shear, V(x), and internal moment M(x), as a function of  location (x) in the region for x between 0 and 4m of the beam. 
A
4m
om
dir
help_outline

Image Transcriptionclose

A 4m om dir

fullscreen
check_circleAnswer
Step 1

Given:

The beam is

W1-7.5kn/m
W2=4.5kn/m
W3-0
A
6m
4m
X
help_outline

Image Transcriptionclose

W1-7.5kn/m W2=4.5kn/m W3-0 A 6m 4m X

fullscreen
Step 2

Calculation:

  1. The reaction forces at A and B

To calculate the support reactions replace the distributed load into equivalent concentrated loads.

Then,

R1
R2
W1=7.5kn/m
W2-4.5kn/m
W3-0
Ax
B
6m
4m
x-2m
x-4m
By
A
help_outline

Image Transcriptionclose

R1 R2 W1=7.5kn/m W2-4.5kn/m W3-0 Ax B 6m 4m x-2m x-4m By A

fullscreen
Step 3
7.5kn /mx 4m
R
R 30kN
=-x4.5kn /m x 6m
R 13.5kN
Σκ -
4 0
ΣΕν-0
4,B-RR 0
A, +B-30-13.5 = 0
4, +B43.5 0
A, B 43.5
ΣΜ.-0
Bx10-30x2-13.5 x 4 = 0
x10-60-54 0
B, x10-114 0
B x10 114
B, 11.4kN
Substitute the value in above equation then we get that
A,11.4 43.5
A, =43.5-11.4
A 32.1kN
help_outline

Image Transcriptionclose

7.5kn /mx 4m R R 30kN =-x4.5kn /m x 6m R 13.5kN Σκ - 4 0 ΣΕν-0 4,B-RR 0 A, +B-30-13.5 = 0 4, +B43.5 0 A, B 43.5 ΣΜ.-0 Bx10-30x2-13.5 x 4 = 0 x10-60-54 0 B, x10-114 0 B x10 114 B, 11.4kN Substitute the value in above equation then we get that A,11.4 43.5 A, =43.5-11.4 A 32.1kN

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Engineering

Civil Engineering

Solid Mechanics

Related Civil Engineering Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: 3.15 In a site consisting of normally consolidated clean sands, the water table is at 10 ft depth. T...

A: Given : 

question_answer

Q: subject : Geotechnical Design Book : PRINCIPLE OF FOUNDATION ENGINEERING

A: We have been given the following information:

question_answer

Q: Determine the maximum shear stress acting at section a-a of the cantilevered strut.

A: we have been given the following information:

question_answer

Q: Give one or two possible identifications for each of the following. Provide a group symbol and descr...

A: Solution to the given scenario:                 Soil having the particle size less than 75 micron is...

question_answer

Q: A storage tank if fabricated by bolting together two half cylindrical shells as shown. The tank is d...

A: Determine the required thickness of the cylindrical shell as shown below:The inner diameter of the t...

question_answer

Q: The W 10X15 cantilevered beam is made of A-36 steel and is subjected to the loading shown. Determine...

A: To find deflection:Remove all external loads and apply a unit vertical load at the point B. Consider...

question_answer

Q: The simply supported wood beam is loaded as shown.  Ewood=10 GPa What is the slope at A? What is th...

A: Determine the moment of inertia using the formula.

question_answer

Q: A member is made of the following materials: steel, brass and copper, the constants are listed below...

A: We are given the data of three materials namely steel, brass and copper.For steel, 

question_answer

Q: For the W14x53 (English units) section shown below, determine the First Moment of Outward Area at th...

A: For the section The properties of the section are given below:  

Sorry about that. What wasn’t helpful?