Determine the resultant force and specify where it acts on the beam measured from A. Assume p = 230 lb/ft.

1.Determine the magnitude of the resultant force.

2.Determine the distance between A and the resultant’s line of action.

Determine the resultant force and specify where it

Answer

General guidance

Concepts and reason

The concepts required to solve this problem are Resultantforce, Moment, Uniformly distributed load, uniformly varying load and Free body diagram. Resultant force: A resultant force is the single force which is obtained by combining a system of forces acting on a rigid body. The effect of the resultant force is the same as the original system of forces. Moment: Moment is the turning effect of a force and is written as an expression that involves the product of the distance and the physical quantity. Uniformly distributed load: It is a type of distributed load spread across a region of beam. It has constant magnitude throughout its length of application. Uniformly varying load: It is a type of distributed load in which load varies uniformly over a region of beam from minimum at one end to maximum at other end. Free body diagram (FBD): It is a diagram of the member, representing all external forces and moments acting on it, considering all the support reactions on that member. It helps us to analyze the forces and moments acting on the system. Sketch the free body diagram of the beam. Determine the expression for total resultant force by adding the expression of resultant force due to uniformly distributed load and the expression of resultant force due to uniformly varying load. Use moment equilibrium equation at the point 2f89f8d319ea

to calculate the distance between point e3c4d2b45b2a

and the resultant’s line of action.

Fundamentals

Expression to find theresultant force on beam carrying uniformly distributed load R= Px …… (1) Here, 1f407a35575f is the resultant force on the beam acting in downward direction, 6324eba60007 is the load on beam per unit length of the beam and 73ca227d2141 is the length of the portion of the beam on which uniformly distributed load is applied. Expression to find theresultant force on beam carrying linearly varying load 7ea2f3089ebf …… (2) Here, 1f407a35575f is the resultant force on the beam acting in downward direction, 6324eba60007 is the load acting on beam per unit length and ad96f74ceb60 is the length of the portion of the beam on which linearly varying load is applied. General sign convection for moment: The moment is considered positive in counter-clockwise direction and negative in clockwise direction Expression for the equilibrium of the rigid body: Net force acting on a body is equal to zero. Also, the sum of the moment of all the forces at any point is equal to zero. In b95d75ea4281 plane, ΣF = 0 ΣΕ, = 0 And ΣMς = 0 Here, 57f53fec7d61 is the force acting on the rigid body in af31cf09baf8 direction, e8d98d10cad4 is the force acting on the rigid body in 06a11431914e direction and 0ebdff051dec is the moment of forces acting at point 91a00f560019 . Point of application of resultant force for uniformly distributed load RUDL
AAAAAAM Resultant force (RUDI) lies at f83e19d25a9e distance from left hand side. Point of application of resultant force for linearly varying load: AOA A
A
A
A.
1 Resultant force (RU) lies at dec0558a9d6a distance from left hand side or low end side of the triangle.

Step-by-step

Step 1 of 2

(1) Free body diagram of the beam, 85fdf2cb2282 Here, d72920b82657 is the distance between point ad7b57c268dc and point b6a9c0dedb3b , 5a5550488ca7 is the distance between point 0eb730641953 and point 777cb5827354 and 35a741bedc8c is load per unit length acting on the beam. From the above figure, the beam is carrying linearly varying load from point 3be6b543c484 to point and the beam is carrying uniformly distributed load from point to point a49b92511a35 . Calculate the magnitude of the resultant force. Add equation (1) and equation (2) to calculate total resultant of force 58fdff165888 acting on the beam. +ਬ = Substitute 230 lb/ft for 12738b4d6da4 , 0d7bb136cb86 for d8d466bb2ce1 and 09fdd0f125ae for e29277d2ec75 . R=(230 Ibn) (8 ), (230 1b/n)(6)
= 2530 Ib The magnitude of the resultant force is 2530 lb .

Part 1

The magnitude of the resultant force is 2530 lb .

Determine the expression for total resultant force by adding the expression of resultant force due to uniformly distributed load and uniformly varying load. Substitute the values of d8d466bb2ce1 , e29277d2ec75 and 1ab5aaf60a0d .Then calculate the total resultant force on the beam.

Step 2 of 2

(2) Calculate the distance between point A and the resultant’s line of action. || L.KY Here, 17c589a6733e is the resultant force acting due to uniformly varying load on member 58f74edd95f5 of the beam, 322208b63e2c is the resultant force acting due to uniformly distributed load on member 2b71fc13b891 of the beam, cb35531b6129 is the net resultant force acting at 44f904751344 from point 1c9e3867d6e4 . 6d53888b2de4 is the distance between point 3be6b543c484 and point b6a9c0dedb3b and 975c6217031b is the distance between point 0eb730641953 and point a49b92511a35 . Distance between and line of action of 9e1367304ecf For uniformly varying load at member a0d1ce0fde6e , 16178930f3e5 acts at 76a31d7fe9d5 from point 1c9e3867d6e4 . Distance between and line of action of 76ac091f1da8 For uniformly distributed load at member 0c3648db2f93 , 34260089d59b acts at 60a22b924236 from point . Calculation for resultant force 1ecd02519087 acting on member e3066483e540 . R, = Px Here, 17c6b2191aa4 is load acting per unit length and c28ade0d9a11 is the length of member 9f9c90a7d9c3 . Substitute 230 lb/ft for 12738b4d6da4 and 0d7bb136cb86 for d8d466bb2ce1 R, = (230 lb/ft)(8 ft)
= 1840 lb Calculate resultant force 974bd11f8a3e acting on member fcafe5d33920 . 105f6d634455 Here, 17c6b2191aa4 is load acting per unit length and ec7516294f23 is the length of member 734fb6f445b7 . Substitute for and 5736f41ef99c for 30e94e6ce91e (230 lb/ft)(6 ft)
= 690 lb Use moment equilibrium equation at point 2d254870788e . 0=W3 Thus, aea21118a08d Rd=R (* + x2]+R/2TO Substitute 2530 lb for bbef37ab5fb0 , 1840 lb for 207add1873ba , 690 lb for 86a40492729a , 0d7bb136cb86 for d8d466bb2ce1 and for

2530d = 1848 ()0++ 69020
d=21160
2530
= 8.363 ft

Part 2

The distance between point A and the resultant line of action is 8.363 ft .

Calculate the values of b02aaadae14f and a40da0a11db1 . Determine the point of application of and . Apply moment equilibrium equation at point 2d254870788e . Substitute the values of b9d360992bed and 9b7cff439ca5 in moment equilibrium equation. Solve for the distance between point and resultant’s line of action.