# Unsymmetrical Beam

## Solution to Problem 595 | Spacing of Rivets or Bolts in Built-Up Beams

**Problem 595**

A concentrated load *P* is carried at midspan of a simply supported 12-ft span. The beam is made of 2-in. by 6-in. pieces screwed together, as shown in Fig. P-595. If the maximum flexural stress developed is 1400 psi, find the maximum shearing stress and the pitch of the screws if each screw can resist 200 lb.

## Solution to Problem 564 | Unsymmetrical Beams

**Problem 564**

Repeat Prob. 563 using 2-in. by 10-in. pieces.

## Solution to Problem 563 | Unsymmetrical Beams

**Problem 563**

A box beam is made from 2-in. by 6-in. pieces screwed together as shown in Fig. P-563. If the maximum flexure stress is 1200 psi, compute the force acting on the shaded portion and the moment of this force about the NA. Hint: Use the results of Prob. 562.

## Solution to Problem 562 | Unsymmetrical Beams

**Problem 562**

In any beam section having a maximum stress f_{b}, show that the force on any partial area A' in Fig. P-562 is given by F = (f_{b}/c)A'(barred y') , where (barred y') is the centroidal coordinate of A'. Also show that the moment of this force about the NA is M' = f_{b} I'/c, where I' is the moment of inertia of the shaded area about the NA.

## Solution to Problem 558 | Unsymmetrical Beams

### Problem 558

In Prob. 557, find the values of x and w_{o} so that w_{o} is a maximum.

## Solution to Problem 557 | Unsymmetrical Beams

**Problem 557**

A cast-iron beam 10 m long and supported as shown in Fig. P-557 carries a uniformly distributed load of intensity w_{o} (including its own weight). The allowable stresses are f_{bt} ≤ 20 MPa and f_{bc} ≤ 80 MPa. Determine the maximum safe value of w_{o} if x = 1.0 m.

## Solution to Problem 556 | Unsymmetrical Beams

**Problem 556**

A T beam supports the three concentrated loads shown in Fig. P-556. Prove that the NA is 3.5 in. above the bottom and that I_{NA} = 97.0 in^{4}. Then use these values to determine the maximum value of P so that f_{bt} ≤ 4 ksi and f_{bc} ≤ 10 ksi.

## Solution to Problem 555 | Unsymmetrical Beams

**Problem 555**

A beam carries a concentrated load W and a total uniformly distributed load of 4W as shown in Fig. P-555. What safe value of W can be applied if f_{bc} ≤ 100 MPa and f_{bt} ≤ 60 MPa? Can a greater load be applied if the section is inverted? Explain.

## Solution to Problem 554 | Unsymmetrical Beams

**Problem 554**

Determine the maximum tensile and compressive stresses developed in the overhanging beam shown in Fig. P-554. The cross-section is an inverted T with the given properties.

## Solution to Problem 553 | Unsymmetrical Beams

**Problem 553**

Determine the maximum tensile and compressive bending stresses developed in the beam as shown in Fig. P-553.