## 721 Increasing the width of flange to lower the centroid of inverted T-beam

**Problem 721**

Refer again to Fig. P-714. To what value should the 6-in. width of

the flange be changed so that the centroid of the area is 2.5 in. above the base?

**Problem 721**

Refer again to Fig. P-714. To what value should the 6-in. width of

the flange be changed so that the centroid of the area is 2.5 in. above the base?

**Problem 572**

The T section shown in Fig. P-572 is the cross-section of a beam formed by joining two rectangular pieces of wood together. The beam is subjected to a maximum shearing force of 60 kN. Show that the NA is 34 mm from the top and the I_{NA} = 10.57 × 10^{6} mm^{4}. Using these values, determine the shearing stress (a) at the neutral axis and (b) at the junction between the two pieces of wood.

**Problem 561**

A T section has the dimensions given in Fig. P-561. Show that the neutral axis is 3 inches below the top and that I_{NA} = 166.7 in4. If the tensile stress at the bottom of the flange is 1000 psi, calculate (a) the total tensile force in the flange and (b) the total compressive force in the cross section. Also compute (c) the moment of the compressive force about the NA, and (d) the moment of the total tensile force about the NA. (e) How does the sum of (c) and (d) compare with the total applied bending moment as computed from the flexure formula?

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

**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.

**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.

**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.

**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.

**Problem 553**

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

**Problem 552**

A cantilever beam carries the force and couple shown in Fig. P-552. Determine the maximum tensile and compressive bending stresses developed in the beam.