# W Shape

## Solution to Problem 543 | Floor Framing

**Problem 543**

A portion of the floor plan of a building is shown in Fig. P-543. The total loading (including live and dead loads) in each bay is as shown. Select the lightest suitable W-shape if the allowable flexural stress is 120 MPa.

## For Girders (G - 2) | Solution to Problem 542

## For Girders (G - 2)

$S_{required} = \dfrac{M}{f_b} = \dfrac{120(1000^2)}{120}$

$S_{required} = 1000 \times 10^3 \, \text{mm}^3$

## For Beams (B - 3) | Solution to Problem 542

## For Beams (B - 3)

$M_{max} = \frac{1}{8}(20)(62)$

$M_{max} = 90 \, \text{kN}\cdot\text{m}$

$S_{required} = \dfrac{M_{max}}{f_b} = \dfrac{90(1000^2)}{120}$

$S_{required} = 750 \times 10^3 \, \text{mm}^3$

## For Beams (B - 2) | Solution to Problem 542

## For Beams (B - 2)

$\Sigma M_{R2} = 0$

$6R_1 = 20(4) + 10(2)(5) + 15(4)(2)$

$R_1 = 50 \, \text{kN}$

$\Sigma M_{R1} = 0$

$6R_2 = 20(2) + 10(2)(1) + 15(4)(4)$

$R_2 = 50 \, \text{kN}$

## For Girder (G - 1) | Solution to Problem 542

**For Girder (G - 1)**

$S_{live-load} = \dfrac{M}{f_b} = \dfrac{40(1000^2)}{120}$

$S_{live-load} = 333.33 \times 10^3 \, \text{mm}^3$

## Solution to Problem 542 | Floor Framing

## Solution to Problem 541 | Floor Framing

**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/in^{2}. If the beams have W10 × 30 sections, determine the center-line spacing using an allowable flexural stress of 18 ksi.

## Solution to Problem 536 | Economic Sections

**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.

## Solution to Problem 535 | Economic Sections

**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?

## Solution to Problem 534 | Economic Sections

**Problem 534**

Repeat Prob. 533 if the uniformly distributed load is changed to 5000 lb/ft.