Determine the reactions at the supports of the beam which is...

Determine the reactions at the supports of the beam which is loaded as shown. Assume $w_1 = 840$ N/m, $w_2 = 360$ N/m, a = 5.0 m, b = 1.6 m. Answers $A_x = 0$ N $A_y = 1779.03$ N $B_y = 1779.03$ N

Transcript

00:01 Hi, in this question a beam that is an overhanging beam is given and this beam is loaded with a trapecidal load and an udl that is uniformly distributed load.

00:14 This trapecidal load, the maximum magnitude is given as 840 newton per meter and the minimum load is given as 360 newton per meter and the udl is 360 newton per meter and the udl is 360 newton.

00:30 Per meter.

00:31 First of all, we need to determine the center of gravity of this trapecidal loading system.

00:40 Let the distance between the total load of this trapecidal load and the point a as x.

00:50 We need to find the distance x.

00:53 The total load of the trapecidal system, trapicidal loading system will be acting at the central gravity of this trapecidal loading system.

01:02 Therefore, we need to find the value of x bar.

01:07 This x bar can be determined, x bar, or simply we can say x is equal to h by 3, multiply with 2a plus b divided by a plus b.

01:28 Where this a is the smaller side of the trapecide and b is the larger side of the trapecide.

01:36 Now let us plug the given values and determine the value of x.

01:43 H is 5 meters by 3 multiply with 2 times 360, 2 times 360 newton per meter, that is 720.

02:00 B is 840 divided by 360 plus 840.

02:14 On calculation we obtained the value of x is equal to 2 .17 meters.

02:25 Now let us determine the total load of the trapezoidal system and the uniformly distributed load.

02:32 W1 and w2 we need to find w1 is equal to this total udl plus the triangular load we can say.

02:48 So we can consider this trapecidal loading system into two parts.

02:54 One is up to here it is udl above this it is triangular loading system.

03:00 Therefore, we can write 360 multiply with 5, we are considering udl plus if we consider this triangle, we can write 1 by 2, 840 minus 360 multiply with 5 multiply with 5 meters length.

03:31 On calculation we obtained, the total load of the trapecidal loading system is equal to 3 ,000 newtons.

03:42 This 3 ,000 newtons acts at the center of gravity of this loading system, that is at a distance of x.

03:49 Now coming to the uniformly distributed load.

03:53 The total load of the uniformly distributed load, w2, is equal to 360.

04:04 Is acting for a distance of 1 .6 meters plus 1 .6 meters therefore 3 .2 meters...

Question

Determine the reactions at the supports of the beam which is loaded as shown. Assume $w_1 = 840$ N/m, $w_2 = 360$ N/m, a = 5.0 m, b = 1.6 m. Answers $A_x = 0$ N $A_y = 1779.03$ N $B_y = 1779.03$ N

Please give Ace some feedback