2.99 See Answer

Question: A cantilever beam AB with a circular

A cantilever beam AB with a circular cross section and length L = 750 mm supports a load P = 800 N acting at the free end (see figure). The beam is made of steel with an allowable bending stress of 120 MPa. (a) Determine the required diameter dmin (figure part a) of the beam, considering the effect of the beam’s own weight. (b) Repeat part (a) if the beam is hollow with wall thickness t = d/8 (figure part b); compare the cross-sectional areas of the two designs.
A cantilever beam AB with a circular cross section and length L = 750 mm supports a load P = 800 N acting at the free end (see figure). The beam is made of steel with an allowable bending stress of 120 MPa.
(a) Determine the required diameter dmin (figure part a) of the beam, considering the effect of the beam’s own weight.
(b) Repeat part (a) if the beam is hollow with wall thickness t = d/8 (figure part b); compare the cross-sectional areas of the two designs.





Transcribed Image Text:

8 B 'P -d- (а) (b) II


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> A fixed-end beam is loaded by a uniform load q = 15 kN/m and a point load P = 30 kN at mid span. The beam has a length of 4 m and modulus of elasticity of 205 GPa. (a) Find reactions at A and B. (b) Calculate the height of the beam if the displacement at

> A triangularly distributed load with a maximum intensity of qo = 10 lb/ft acts on propped cantilever beam AB. If the length L of the beam is 10 ft, find the reactions at A and B. go B IA

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> Beam ABC is fixed at support A and rests (at point B) upon the midpoint of beam DE (see part a of the figure). Thus, beam ABC may be represented as a propped cantilever beam with an overhang BC and a linearly elastic support of stiffness k at

> A continuous beam ABC with two unequal spans, one of length L and one of length 2L, supports a uniform load of intensity q (see figure). Determine the reactions RA, RB, and RC for this beam. Also, draw the shear-force and bending-moment diagrams, labelin

> A propped cantilever beam, fixed at the left-hand end A and simply supported at the right hand end B, is subjected to a temperature differential with temperature T1 on its upper surface and T2 on its lower surface (see figure). (a) Find all reactions for

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> A propped cantilever beam of a length 2L is loaded by a uniformly distributed load with intensity q. The beam is supported at B by a linearly elastic rotational spring with stiffness kR, which provides a resisting moment MB due to rotation θ

> A propped cantilever beam of a length 2L is loaded by a uniformly distributed load with intensity q. The beam is supported at B by a linearly elastic spring with stiffness k. Use the method of superposition to solve for all reactions. Also draw shear-for

> Two flat beams AB and CD, lying in horizontal planes, cross at right angles and jointly support a vertical load P at their midpoints (see figure). Before the load P is applied, the beams just touch each other. Both beams are made of the same material and

> The continuous frame ABCD has a pin support at B; roller supports at A, C, and D; and rigid corner connections at B and C (see figure). Members AB, BC, and CD each have flexural rigidity EI. Moment M0 acts counterclockwise at B and clockwise at C. Note:

> Beam AB has a pin support at A and a roller support at B. Joint B is also restrained by a linearly elastic rotational spring with stiffness kR, which provides a resisting moment MB due to rotation at B. Member AB has flexural rigidity EI. A moment M0 act

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> The continuous frame ABC has a pin support at A, roller supports at B and C, and a rigid corner connection at B (see figure). Members AB and BC each have flexural rigidity EI. A moment M0 acts counterclockwise at B. Note: Disregard axial deformations in

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> (a) A simple beam AB with length L and height h supports a uniform load of intensity q (see the figure part a). Obtain a formula for the curvature shortening l of this beam. Also, obtain a formula for the maximum bending stress σb in the beam

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> A beam of square cross section (a = length of each side) is bent in the plane of a diagonal (see figure). By removing a small amount of material at the top and bottom corners, as shown by the shaded triangles in the figure, you can increase the section m

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> A two-axle carriage that is part of an overhead traveling crane in a testing laboratory moves slowly across a simple beam AB (see figure). The load transmitted to the beam from the front axle is 2200 lb and from the rear axle is 3800 lb. The weight of th

> A “trapeze bar” in a hospital room provides a means for patients to exercise while in bed (see figure). The bar is 2.1 m long and has a cross section in the shape of a regular octagon. The design load is 1.2 kN applied

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> The wood joists supporting a plank floor (see figure) are 38 mm × 220 mm in cross section (actual dimensions) and have a span length of L = 4.0 m. The floor load is 5.0 kPa, which includes the weight of the joists and the floor. (a) Calculat

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> A simple beam of length L = 5 m carries a uniform load of intensity q = 5.8 kN/m and a concentrated load 22.5 kN (see figure). (a) Assuming σallow = 110 MPa, calculate the required section modulus S. Then select the most economical wide-flange

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> Solve the preceding problem for a bar of monel metal having the following properties: d1 = 1.0 in., d2 = 1.4 in., L1 = 20.0 in., L2 = 5.0 in., and E = 25 × 106 psi. Also, the bar lengthens by 0.0040 in. when the tensile load is applied. Da

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> Draw the shear-force and bending-moment diagrams for a cantilever beam AB carrying a uniform load of intensity q over one-half of its length (see figure). A B L 2

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2.99

See Answer