Solution to Problem 599 | Spacing of Rivets or Bolts in Built-Up Beams

Problem 599
A beam is formed by bolting together two W200 × 100 sections as shown in Fig. P-599. It is used to support a uniformly distributed load of 30 kN/m (including the weight of the beam) on a simply supported span of 10 m. Compute the maximum flexural stress and the pitch between bolts that have a shearing strength of 30 kN.
 

Wide Flange on top of the other and bolted together

 

Solution to Problem 597 | Spacing of Rivets or Bolts in Built-Up Beams

Problem 597
A plate and angle girder similar to that shown in Fig. 5-32 is fabricated by riveting the short legs of four 125 × 75 × 13 mm angles to a web plate 1000 mm by 10 mm to form a section 1020 mm deep. Cover plates, each 300 mm × 10 mm, are then riveted to the flange angles making the overall height 1040 mm. The moment of inertia of the entire section about the NA is I = 4770 × 106 mm4. Using the allowable stresses specified in Illustrative Problem 591, determine the rivet pitch for 22-mm rivets, attaching the angles to the web plate at a section where V = 450 kN.
 

From Illustrative Problem 591

τ = 100 MPa shear stress
σb = 220 MPa bearing stress for single shear rivet
σb = 280 MPa bearing stress for double shear rivet

 

Built-up Girder from Plate and Angles

 

Solution to Problem 596 | Spacing of Rivets or Bolts in Built-Up Beams

Problem 596
Three planks 4 in by 6 in., arranged as shown in Fig. P-596 and secured by bolts spaced 1 ft apart, are used to support a concentrated load P at the center of a simply supported span 12 ft long. If P causes a maximum flexural stress of 1200 psi, determine the bolt diameters, assuming that the shear between the planks is transmitted by friction only. The bolts are tightened to a tension of 20 ksi and the coefficient of friction between the planks is 0.40.
 

Three Planks Secured by Bolts

 

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.
 

595-box-beam-held-by-screws.jpg

 

Solution to Problem 594 | Spacing of Rivets or Bolts in Built-Up Beams

Problem 594
A distributed load of wo lb/ft is applied over a middle 6 ft of a simply supported span 12 ft long. The beam section is that in Prob. 593, but used here so that the 8-in dimension is vertical. Determine the maximum value of wo if fb ≤ 1200 psi, fv ≤ 120 psi, and the screws have a shear strength of 200 lb and a pitch of 2 in.
 

Solution to Problem 593 | Spacing of Rivets or Bolts in Built-Up Beams

Problem 593
A box beam, built up as shown in Fig. P-593, is secured by screws spaced 5 in. apart. The beam supports a concentrated load P at the third point of a simply supported span 12 ft long. Determine the maximum value of P that will not exceed fv = 120 psi in the beam or a shearing force of 300 lb in the screws. What is the maximum flexural stress in the beam?
 

Box Beam Secured by Screws

 

Solution to Problem 589 | Design for Flexure and Shear

Problem 589
A channel section carries a concentrated loads W and a total distributed load of 4W as shown in Fig. P-589. Verify that the NA is 2.17 in. above the bottom and that INA = 62 in4. Use these values to determine the maximum value of W that will not exceed allowable stresses in tension of 6,000 psi, in compression of 10,000 psi, or in shear of 8,000 psi.
 

Overhang beam loaded with contrated and rectangular loads