Question

نقطتان (2) Determine for the plate area (a) .summation of area 150 mm 150 mm 50 mm) 300 mm 25 mm 25 mm إجابتك نقطة واحدة (b) The summation (XA) إجابتك تقطتان (2) (c) The summation (YA إجابتك

Answer 1

(a)

Let a1 and a2 be the area of the vertical and horizontal section of the T-shaped bea.

Now,a1 = a2 = 300*50 = 15000 sq. mm

Now,summation of area(a)= a1+a2

= 15000+15000

= 30000 sq. mm

(b)

Let x1 and x2 the position of centroid in the x direction.

As the beam is symmetrical along the y-axis.

So,

x1=x2= 0 mm

Hence,

Summation of (XA) = 0.

(c)

Now let y1 and y2 the distance of centroid of the vertical and horizontal axis respectively from the reference position shown .

Now,

y1 = 150 mm

y2 = 300+25 = 325 mm

Now,

Summation of YA= a1y1+a2y2

= (15000*150)+(15000*325)

= 7125000 cu. mm

(d)

Now centroid (y)

= summation YA/summation of area

= 7125000/30000

= 237.5 mm = 238 mm