Problem 710 | Two simple beams at 90 degree to each other

Problem 710
Two timber beams are mounted at right angles and in contact with each other at their midpoints. The upper beam A is 2 in wide by 4 in deep and simply supported on an 8-ft span; the lower beam B is 3 in wide by 8 in deep and simply supported on a 10-ft span. At their cross-over point, they jointly support a load P = 2000 lb. Determine the contact force between the beams.
 

Solution to Problem 611 | Double Integration Method Jhun Vert Thu, 04/23/2020 - 04:11 pm

Problem 611
Compute the value of EI δ at midspan for the beam loaded as shown in Fig. P-611. If E = 10 GPa, what value of I is required to limit the midspan deflection to 1/360 of the span?
 

Simple Beam with Uniform Load to Half its Span

 

Area, moment of inertia, and radius of gyration of parabolic section

Situation
Given the parabola 3x2 + 40y – 4800 = 0.
 

Part 1: What is the area bounded by the parabola and the X-axis?
A. 6 200 unit2
B. 8 300 unit2
C. 5 600 unit2
D. 6 400 unit2
 

Part 2: What is the moment of inertia, about the X-axis, of the area bounded by the parabola and the X-axis?
A. 15 045 000 unit4
B. 18 362 000 unit4
C. 11 100 000 unit4
D. 21 065 000 unit4
 

Part 3: What is the radius of gyration, about the X-axis, of the area bounded by the parabola and the X-axis?
A. 57.4 units
B. 63.5 units
C. 47.5 units
D. 75.6 units
 

821 Rectangle minus semi-circle | Moment of Inertia Jhun Vert Mon, 04/20/2020 - 12:07 am

Problem 821
Find the moment of inertia about the indicated x-axis for the shaded area shown in Fig. P-821.
 

821-rectangle-minus-semi-circle.gif

 

820 Unsymmetrical I-section | Moment of Inertia Jhun Vert Mon, 04/20/2020 - 12:05 am

Problem 820
Determine the moment of inertia of the area shown in Fig. P-819 with respect to its centroidal axes.
 

Unsymmetrical I-section

 

818 Hollow square section | Moment of Inertia and Radius of Gyration Jhun Vert Sun, 04/19/2020 - 11:59 pm

Problem 818
A hollow square cross section consists of an 8 in. by 8 in. square from which is subtracted a concentrically placed square 4 in. by 4 in. Find the polar moment of inertia and the polar radius of gyration with respect to a z axis passing through one of the outside corners.
 

817 Hollow Tube | Moment of Inertia and Radius of Gyration Jhun Vert Sun, 04/19/2020 - 11:56 pm

Problem 817
Determine the moment of inertia and radius of gyration with respect to a polar centroidal axis of the cross section of a hollow tube whose outside diameter is 6 in. and inside diameter is 4 in.