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 598 | Spacing of Rivets or Bolts in Built-Up Beams Jhun Vert Thu, 04/23/2020 - 01:44 pm

Problem 598
As shown in Fig. P-598, two C380 × 60 channels are riveted together by pairs of 19-mm rivets spaced 200 mm apart along the length of the beam. What maximum vertical shear V can be applied to the section without exceeding the stresses given in Illustrative Problem 591?
 

Bolted Back-to-back Channels

 

Solution to Problem 597 | Spacing of Rivets or Bolts in Built-Up Beams Jhun Vert Thu, 04/23/2020 - 01:41 pm

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 Jhun Vert Thu, 04/23/2020 - 01:39 pm

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 594 | Spacing of Rivets or Bolts in Built-Up Beams Jhun Vert Thu, 04/23/2020 - 01:31 pm

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 Jhun Vert Thu, 04/23/2020 - 01:28 pm

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 587 | Design for Flexure and Shear Jhun Vert Thu, 04/23/2020 - 12:23 pm

Problem 587
A beam carries two concentrated loads P and triangular load of 3P as shown in Fig. P-587. The beam section is the same as that in Fig. P-577. Determine the safe value of P if fb ≤ 1200 psi and fv ≤ 200 psi.
 

Overhang beam loaded with contrated and triangular loads

 

Solution to Problem 577 | Horizontal Shearing Stress Jhun Vert Wed, 04/22/2020 - 11:31 pm

Problem 577
A plywood beam is built up of 1/4-in. strips separated by blocks as shown in Fig. P-577. What shearing force V will cause a maximum shearing stress of 200 psi?
 

Built-up Plywood Beam

 

Solution to Problem 561 | Built-up Beams Jhun Vert Wed, 04/22/2020 - 08:41 pm

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 INA = 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?
 

T-beam strength Investigation