$M_{max} = \frac{1}{8}(20)(62)$
$M_{max} = 90 \, \text{kN}\cdot\text{m}$
$S_{required} = \dfrac{M_{max}}{f_b} = \dfrac{90(1000^2)}{120}$
$S_{required} = 750 \times 10^3 \, \text{mm}^3$
$\Sigma M_{R2} = 0$
$6R_1 = 20(4) + 10(2)(5) + 15(4)(2)$
$R_1 = 50 \, \text{kN}$
$\Sigma M_{R1} = 0$
$6R_2 = 20(2) + 10(2)(1) + 15(4)(4)$
$R_2 = 50 \, \text{kN}$
For Girder (G - 1)
$S_{live-load} = \dfrac{M}{f_b} = \dfrac{40(1000^2)}{120}$
$S_{live-load} = 333.33 \times 10^3 \, \text{mm}^3$
Problem 542
Select the lightest W shape sections that can be used for the beams and girders in Illustrative Problem 537 of text book if the allowable flexural stress is 120 MPa. Neglect the weights of the members.
Problem 541
The 18-ft long floor beams in a building are simply supported at their ends and carry a floor load of 0.6 lb/in2. If the beams have W10 × 30 sections, determine the center-line spacing using an allowable flexural stress of 18 ksi.
Problem 536
A simply supported beam 10 m long carries a uniformly distributed load of 20 kN/m over its entire length and a concentrated load of 40 kN at midspan. If the allowable stress is 120 MPa, determine the lightest W shape beam that can be used.
Problem 535
A simply supported beam 24 ft long carries a uniformly distributed load of 2000 lb/ft over its entire length and a concentrated load of 12 kips at 8 ft from left end. If the allowable stress is 18 ksi, select the lightest suitable W shape. What is the actual maximum stress in the selected beam?
Problem 534
Repeat Prob. 533 if the uniformly distributed load is changed to 5000 lb/ft.
Problem 533
A beam simply supported on a 36-ft span carries a uniformly distributed load of 2000 lb/ft over the middle 18 ft. Using an allowable stress of 20 ksi, determine the lightest suitable W shape beam. What is the actual maximum stress in the selected beam?
