For the beam and loading shown, determine the magnitude of...

Name: For the beam and loading shown, determine the magnitude of the vertical reaction at A (lb) provided that a=161, b=102 and c=6.2. Do not round off in any intermediate steps. Round off only on the final anwer expressed in 3 decimal places. a lb/ft b lb/ft A B c ft
Uploaded: 2021-10-22T14:50:16-08:00
Duration: 9 min 11 s
Channel: Ahmad Reda
Description: For the beam and loading shown, determine the magnitude of the vertical reaction at A (lb) provided that a=161, b=102 and c=6.2. Do not round off in any intermediate steps. Round off only on the final anwer expressed in 3 decimal places. a lb/ft b lb/ft A B c ft

For the beam and loading shown, determine the magnitude of the vertical reaction at A (lb) provided that a=161, b=102 and c=6.2. Do not round off in any intermediate steps. Round off only on the final anwer expressed in 3 decimal places. a lb/ft b lb/ft A B c ft

Transcript

00:01 In this problem we have beam ab like this that is hinged at a and we have a roller in b and it's loaded like this we have load intensity here as a which is equal 161 pound per foot and the intensity here is 102 pound per foot and of course the load direction is in the gravity direction we want to find the vertical reaction at a if this distance is given as c which is equal to 6 .2 feet we have here a reaction at a and we have a reaction at b this beam is in equilibrium then we we know that sigma moments at any point equal to zero sigma moments at point b equal to zero and we can take any direction and state it as positive i take this direction which is counterclockwise as the positive direction i took the moments about point b to get rid of the reaction at b i'm interested in the reaction at a, then i take the moments at b because the r of the reaction here is 0, then its moment is 0.

02:12 Now we have a challenge to calculate the moments of this type of load.

02:19 We can use the principle of superposition and divide this as a uniform load within tenacity 102 pound their foot and a triangle we can get the reaction due to the uniform load and added to their action due to this triangle then let's get the moment new to the uniform load the uniform load has a result on at its center then in the middle of its length we have the resultant of the uniform load this uniform load as a resultant of 102 multiplied by the length which is 6 .2 and it in it is in the middle or the center of the beam this load makes a moment about point b as a total load multiplied by its arm this is the arm the arm is 6 .2 divided by 2 then when we get the moments about point b we start by the uniform load and it makes a moment about point b and it rotates about b like this it's the same as the positive direction indicated here then we have 102 multiplied by 6 .2 this is the total load due to the uniform load multiply by its arm which is 3 .1 feet plus we add to it the load due to the triangle here if we have a triangle like this and we want to get the total load of it this value isn't 161 it's 161 minus 102 then we will make this intensity to be 61 minus 2 which is 59 pound per feet because we have already taken 102 in the infirm load then if we have a load like this we want to get its resultant it's just the area of this triangle we have here side of 59 and this side is 6 .2 then the total load will be 59 multiplied by 6 .2 multiplied by half because the area of the triangle is half by base by half.

05:57 This is the load...

Question

For the beam and loading shown, determine the magnitude of the vertical reaction at A (lb) provided that a=161, b=102 and c=6.2. Do not round off in any intermediate steps. Round off only on the final anwer expressed in 3 decimal places. a lb/ft b lb/ft A B c ft

Please give Ace some feedback