# Solution to Problem 560 | Built-up Beams

**Problem 560**

The wide-flange beam shown in Fig. P-560 is strengthened by bolting two cover plates 160 mm by 20 mm to the top and bottom flanges. If the maximum flexure stress is 140 MPa, compute the total force (a) in each cover plate and (b) in each flange. Neglect the weakening effect of the bolt holes.

**Solution 560**

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$\dfrac{f_c}{190} = \dfrac{140}{200}; \,\, f_c = 133 \, \text{MPa}$

$\dfrac{f_f}{170} = \dfrac{140}{200}; \,\, f_f = 119 \, \text{MPa}$

(a) Force in each cover plate

$F_c = f_c A_c = 133(160 \times 20)$

$F_c = 425\,600 \, \text{N}$

$F_c = 425.6 \, \text{kN}$ *answer*

(b) Force in each flange

$F_f = f_f A_f = 119(160 \times 20)$

$F_f = 380\,800 \, \text{N}$

$F_f = 380.8 \, \text{kN}$ *answer*

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