Question: The C-frame of a 100 kN capacity press is shown in Fig.2.2 The material of the frame is grey cast iron FG 200 and the factor of safety is 3. Determine the dimensions of the frame.
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Subject: Machine Design -I

Topic: Curved beams and Thin cylinder

Difficulty: High

md1(66) • 1.1k views
 modified 14 months ago by written 17 months ago by kiran.9870 • 10
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 written 14 months ago by kiran.9870 • 10
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Step 1: Calculation of permissible tensile stress:

$\tau_max=\frac{S_ut}{fs}=\frac{200}{3}=66.67N/mm^2$

Step 2: Calculation of eccentricity (e):

b_i=3t

h=3t

R_i=2t

R_o=5t

t_i=t

t=0.75t

$R_N=\frac{t_i(b_i-t)+th}{(b_i-t)log_e(\frac{R_i+t_i}{R_i})+tlog_e\frac{R_o}{R_i}}$

$R_N=\frac{t(3t-0.75t)+0.75t(3t)}{(3t-0.75t)log_e(\frac{2t+t}{2t})+0.75tlog_e\frac{5t}{2t}}$

$=2.8134t$

$R=R_i+\frac{0.5th^2+0.5t_i^2(b_i-t)}{th+t_i(b_i-t)}$

$R=2t+\frac{0.5*0.75t*3t^2+0.5t^2(3t-0.75t)}{0.75t*3t+t(3t-0.75t)}=3t$

$e=R-R_N=3t-2.8134t=0.1866t$

Step 3: Calculation of bending stress:

$h_i=R_N-R_i=2.8134t-2t=0.8134t$

$A=3t*t+0.75t*2t=4.5t^2 mm^2$

$M_b=100*10^3(1000+3t) N-mm$

bending stress at the inner fibre is given by,

$\sigma_bi=\frac{M_bh_i}{AeR_i}=\frac{100*10^3(1000+3t)(0.8134t)}{4.5t^2*0.1866t*2t}=\frac{100*10^3(1000+3t)(2.1795)}{4.5t^2} N/mm^2$

Step 4: Calculation of direct tensile stress

$\sigma_t=\frac{P}{A}=\frac{100*10^3}{4.5t^2} N/mm^2$

Step 5: Calculation of dimensions of cross-section

$\sigma_N+\sigma_t=\sigma_max$

$\frac{100*10^3(1000+3t)(2.1795)}{4.5t^2}+\frac{100*10^3}{4.5t^2}=66.67$

$t^3-2512.83t-726500=0$

Adding the two stresses and equating the resultant stress to permissible stress,

t=99.2mm or t=100mm