Question

Exercise 6.1.14 The L-shaped steel plate shown below is d = 8 mm thick (i.e., the member extends from Z = 0 to Z = -8 into the page). Determine a. its mass m b. the location of its center of mass (XM, YM, ZM). Assume: H = 730 mm, h = 70 mm, L = 460 mm, l = 75 mm. Material is homogeneous (Pstoel = 7830 kg/m3). H L a. M kg b. XM mm

Answer 1

Volume of the plate is

V = (H - h) (d) + (L)(h) (d)

$V = 0.6536 \times 10^{-3} m^3$

so the mass is

ա-

$m = (7830)(0.6536\times 10^{-3})$

Center of mass

Let P and Q be the center of mass of the horrizontal arm and vertical arm respectively so

$P = \left ( \frac{L}{2},\frac{h}{2},-\frac{d}{2} \right )$

$P = \left ( 230,35,-4 \right )$

$Q = \left ( \frac{l}{2},\frac{H-h}{2},-\frac{d}{2} \right )$

$Q = \left ( 37.5,330,-4 \right )$

m_H = mass of horrizontal arm

m_V = mass of vertical arm

m_H = 2.02 kg

m_V= 3.10 kg

S0,

$X_{cm} = \frac{m_H(230)+m_V(37.5)}{m_H+m_V}$

$Y_{cm} = \frac{m_H(35)+m_V(330)}{m_H+m_V}$

$Z_{cm} = \frac{m_H(-4)+m_V(-4)}{m_H+m_V}$