Express the shear and moment in terms of x for 0 < x < 3 m and 3 m < x < 4.5 m, and then draw the shear and moment diagrams for the simply supported beam. 300 N/m 1.5 m

The 304 stainless steel tube has a thickness of 10 mm. If the allowable shear stress is Ï allow = 80 MPa, determine the maximum torque T that it can transmit. Also, what is the angle of twist of...

Draw the shear and moment diagrams for the shaft. The bearings at A and B exert only vertical reactions on the shaft. Also, express the shear and moment in the shaft as a function of x within the...

Draw the shear and moment diagrams for the overhanging beam.

Draw the shear and moment diagrams for the compound beam. 5 kN/m I||||..|||| 2 m m

If the compound beam in Prob. 642 has a square cross section of side length a, determine the minimum value of a if the allowable bending stress is allow = 150 MPa.

If the applied distributed loading of w = 4 kN/m can be assumed to pass through the centroid of the beams cross-sectional area, determine the absolute maximum bending stress in the joist and the...

The wooden section of the beam is reinforced with two steel plates as shown. If the beam is subjected to a moment of M = 30 kN · m, determine the maximum bending stresses in the steel and...

A wood beam is reinforced with steel straps at its top and bottom as shown. Determine the maximum bending stress developed in the wood and steel if the beam is subjected to a moment of M = 150 kN...

Determine the maximum uniform distributed load w0 that can be supported by the reinforced concrete beam if the allowable tensile stress for the steel is (Ï st ) allow = 28 ksi and the allowable...

The curved bar used on a machine has a rectangular cross section. If the bar is subjected to a couple as shown, determine the maximum tensile and compressive stresses acting at section aa. Sketch the...

The curved member is subjected to the moment of M = 50 kN · m. Determine the percentage error introduced in the calculation of maximum bending stress using the flexure formula for straight...

The Douglas Fir beam is reinforced with A-36 steel straps at its sides. Determine the maximum stress in the wood and steel if the beam is subjected to a bending moment of M z = 4 kN · m....

The shaft is supported by a thrust bearing at A and a journal bearing at B. If the shaft is made from a material having an allowable shear stress of Ï allow = 75 MPa, determine the maximum value...

The wood beam has an allowable shear stress of Ï allow = 7 MPa. Determine the maximum shear force V that can be applied to the cross section. 50 mm 50 mm +100 mm- 50 mm 200 mm 50 mm

The compound beam consists of two segments that are pinned together at B. Draw the shear and moment diagrams if it supports the distributed loading shown. - -1/3 L- - 2/3 L-

Determine the maximum bending stress in the handle of the cable cutter at section aa. A force of 45 lb is applied to the handles. 45 Ib 5 in. 4 in. 3 in. 0.75 in. 0.50 in. 45 lb

The stressstrain diagram for a titanium alloy can be approximated by the two straight lines. If a strut made of this material is subjected to bending, determine the moment resisted by the strut if...

Determine the shape factor for the beam. 3 in. 6 in. 1.5 in! 3 in. 1.5 in!

The beam is made of an elastic perfectly plastic material. Determine the plastic moment M p that can be supported by a beam having the cross section shown. Ï Y = 30 ksi. 2 in. 1 in 10 in `1 in....

Determine the maximum shear stress in the strut if it is subjected to a sheer force of V = 20 kN. 12 mm 60 mm 12 mm 20 mm 80 mm 20 mm

The beam is made from a polymer and is subjected to a shear of V = 7 kip. Determine the maximum shear stress in the beam and plot the shear-stress distribution over the cross section. Report the...

Plot the shear-stress distribution over the cross section of a rod that has a radius c. By what factor is the maximum shear stress greater than the average shear stress acting over the cross section?

If the beam is made from wood having an allowable shear stress Ï allow = 400 psi, determine the maximum magnitude of P. Set d = 4 in. 2P 2 ft- 2 ft- -2 ft- 2 in.

The beam has a rectangular cross section and is subjected to a load P that is just large enough to develop a fully plastic moment M p = PL at the fixed support. If the material is elastic perfectly...

The beam in Fig. 648f is subjected to a fully plastic moment M p . Prove that the longitudinal and transverse shear stresses in the beam are zero. Hint: Consider an element of the beam shown in Fig....

The beam is constructed from two boards fastened together at the top and bottom with three rows of nails spaced every 4 in. If a sheer force of V = 900 lb is applied to the boards, determine the...

The double T-beam is fabricated by welding the three plates together as shown. If the weld can resist a shear stress tallow = 90 MPa, determine the maximum shear V that can be applied to the beam. 20...

The beam is subjected to a shear force of V = 50 kip. Determine the maximum shear flow in the cross section. 1 in. 5 in. 1 in. 5 in. 1 in. 9 in. 12 in.

A pressurized spherical tank is made of 0.5-in.-thick steel. If it is subjected to an internal pressure of p = 200 psi, determine its outer radius if the maximum normal stress is not to exceed 15 ksi.

The simply supported beam is built up from three boards by nailing them together as shown. If P = 12 kN, determine the maximum allowable spacing s of the nails to support that load, if each nail can...

The box beam is constructed from four boards that are fastened together using nails spaced along the beam every 2 in. If each nail can resist a shear force of 50 lb, determine the largest force P...

Determine the maximum shear stress acting at section aa in the beam. 8000 lb 150 lb/ft B. 4 ft 4 ft 1.5 ftT1.5 ft

The member is subject to a shear force of V = 2 kN. Determine the shear flow at points A, B, and C. The thickness of each thin-walled segment is 15 mm. 200 mm 100 mm 300 mm V = 2 kN

The member consists of two plastic channel strips 0.5 in. thick, glued together at A and B. If the distributed load has a maximum intensity of w0 = 3 kip>ft, determine the maximum shear stress...

The member consists of two plastic channel strips 0.5 in. thick, glued together at A and B. If the glue can support an allowable shear stress of Ï allow = 600 psi, determine the maximum...

The beam is made from four boards nailed together as shown. If the nails can each support a shear force of 100 lb, determine their required spacing s­¢ and s if the beam is subjected to a...

The beam is made from three polystyrene strips that are glued together as shown. If the glue has shear strength of 80 kPa, determine the maximum load P that can be applied without causing the glue to...

The plate has a thickness of 20 mm and the force P = 3 kN acts along the centerline of this thickness such that d = 150 mm. Plot the distribution of normal stress acting along section aa. 200 mm

Determine the maximum force P that can be exerted on each of the two pistons so that the circumferential stress in the cylinder does not exceed 3 MPa. Each piston has a radius of 45 mm and the...

The thin-walled cylinder can be supported in one of two ways as shown. Determine the state of stress in the wall of the cylinder for both cases if the piston P causes the internal pressure to be 65...

The bar has a diameter of 40 mm. Determine the state of stress at point A and show the results on a differential volume element located at this point. 200 mm y 200 mm 1200 N 15 800 N

The wall hanger has a thickness of 0.25 in. and is used to support the vertical reactions of the beam that is loaded as shown. If the load is transferred uniformly to each strap of the hanger,...

The 20-kg drum is suspended from the hook mounted on the wooden frame. Determine the state of stress at point F on the cross section of the frame at section bb. Indicate the results on an element. 50...

Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibrium described in Sec. 9.1. 65 MPa 30 B 20 MPa

Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibrium described in Sec. 9.1. A 400 psi 650 psi 60

The sign is subjected to the uniform wind loading. Determine the stress components at points C and D on the 100-mm-diameter supporting post. Show the results on a volume element located at each of...

The sign is subjected to the uniform wind loading. Determine the stress components at points A and B on the 100-mm-diameter supporting post. Show the results on a volume element located at each of...

Solve Prob. 97 using the stress transformation equations developed in Sec. 9.2. 60 MPa 80 MPa 50 40 MPa

Determine the stress components acting on the plane AB. Solve the problem using the method of equilibrium described in Sec. 9.1. 80 MPa 30 MPa 30 40 MPa

The man has a mass of 100 kg and center of mass at G. If he holds himself in the position shown, determine the maximum tensile and compressive stress developed in the curved bar at section aa. He is...

The stress along two planes at a point is indicated. Determine the normal stresses on plane bb and the principal stresses.

The frame supports the distributed load shown. Determine the state of stress acting at point D. Show the results on a differential element at this point. 4 kN/m 20 mm 60 mm BA 20 mm D. 50 mm |-1.5...

Solve Prob. 92 using Mohrs circle. Data from 9-2 65 MPa A. /30 20 MPa

Solve Prob. 96 using Mohrs circle. Data from 9-6 Determine the stress components acting on the inclined plane AB. B 8 ksi 5 ksi 40 3 ksi

A rod has a circular cross section with a diameter of 2 in. It is subjected to a torque of 12 kip · in. and a bending moment M. The greater principal stress at the point of maximum flexural...

Determine the principal stress at point D, which is located just to the left of the 10-kN force. 10 kN ,100 mm D30 -1m+1m: |B 2 m 300 mm 100 mm 100 mm

The post is fixed supported at its base and a horizontal force is applied at its end as shown, determine (a) the maximum in-plane shear stress developed at A and (b) the principal stresses at A. K3...

The post is fixed supported at its base and the loadings are applied at its end as shown. Determine (a) the maximum in-plane shear stress developed at A and (b) the principal stresses at A. 1900 lb...

Determine the equivalent state of stress on an element which represents (a) the principal stresses, and (b) the maximum in-plane shear stress and the associated average normal stress. Also, for each...

Determine the equivalent state of stress if an element is oriented 40° clockwise from the element shown. Use Mohrs circle. 10 ksi 6 ksi

A sample of gas has a mass of 0.205 g. Its volume is 0.112 L at a temperature of 25 C and a pressure of 740 mmHg. Find its molar mass.

Prove that the sum of the normal strains in perpendicular directions is constant, i.e., x + y = x + y .

The state of strain at the point on the arm has components of õ x = 200 (10 -6 ), õ y = -300 (10-6), and ó xy = 400(10 -6 ). Use the strain transformation...

The state of strain at the point on the leaf of the caster assembly has components of õ x = - 400 (10 -6 ), õ y = 860(10 -6 ), and ó xy = 375(10 -6 ). Use the...

A two-story light storage warehouse has interior columns that are spaced 12 ft apart in two perpendicular directions. If the live loading on the roof is estimated to be 25 lb/ft 2 , determine the...

The steel shaft has a radius of 15 mm. Determine the torque T in the shaft if the two strain gages, attached to the surface of the shaft, report strains of ε x² = -80(10 -6 ) and...

Air is pumped into the steel thin-walled pressure vessel at C. If the ends of the vessel are closed using two pistons connected by a rod AB, determine the increase in the diameter of the pressure...

The thin-walled cylindrical pressure vessel of inner radius r and thickness t is subjected to an internal pressure p. If the material constants are E and ν, determine the strains in the...

Determine the reactions on the beam. Neglect the thickness of the beam. 20 kN 26 kN 20 kN 13 12 B - 3 m- -6 m- -6 m-

The state of strain at the point on the spanner wrench has components of ε x = 260(10 -6 ), ε y = 320(10 -6 ), and γ xy = 180(10 -6 ). Use the strain...

Determine the horizontal and vertical components of reaction at the supports A and B. Assume the joints at C and D are fixed connections. 40 kN 30 kN 20 kN 12 kN/m 4 m B - 6 m- - 8 m

Determine the horizontal and vertical components force at pins A and C of the two-member frame. 200 N/m (B 3 m -3 m

Determine the resultant forces at the pins A, B, and C of the three-hinged arched roof truss. 4 kN 4 kN 3 kN 2 k 5 kN B -3 m- -3 m- -3 m- 2 m im1 m

The three-hinged spandrel arch is subjected to the loading shown. Determine the internal moment in the arch at point D. 8 kN 8 kN 6 kN 6 kN 3 kN 4 kN 3 kN 2 m 2 m 2 m 4 kN 2 m2 m 2 m IB 5 'm 3'm -8...

Determine the internal normal force, shear force, and bending moment in the beam at points C and D. Assume the support at A is a pin and B is a roller. 6 kN 20 kN m B_I! |-1 m-|--1 m-- 2 m 2 m-

Draw the influence lines for (a) The vertical reaction at B, (b) The shear just to the right of the rocker at A, and (c) The moment at C. Solve Prob. 65 using Muller-Breslaus principle. 6 ft 6 ft 6 ft

Draw the influence lines for (a) The vertical reaction at A, (b) The moment at A, and (c) The shear at B. Assume the support at A is fixed. Solve Prob. 63 using the Muller-Breslau principle. 5 ft 5 ft

Draw the influence line for (a) The moment at B, (b) The shear at C, and (c) The vertical reaction at B. Solve this problem using the basic method of Sec. 61.The support at A resists only a...

Draw the influence lines for (a) The vertical reaction at B, (b) The shear just to the right of the rocker at A, and (c) The moment at C. Solve this problem using the basic method of Sec. 61. 6 ft 6...

The beam is used to support a dead load of 800 N/m, a live load of 4 kN/m, and a concentrated live load of 20 kN. Determine (a) The maximum positive (upward) reaction at B, (b) The maximum positive...

Where should the beam ABC be loaded with a 300 lb/ft uniform distributed live load so it causes (a) The largest moment at point A and (b) The largest shear at D? Calculate the values of the moment...

Draw the influence line for (a) The shear in panel BC of the girder, and (b) The moment at D. 'F 21 2 m - 2m - 2 m - 2 m 2 m

Draw the influence line for the force in (a) Member KJ and (b) Member CJ. 8 ft lo0880 JoBo Pon- Fonfont F 6 ft--6 ft 6 ft- - 6 ft--6 ft

Draw the influence line for the force in member KJ.

Draw the influence line for the force in (a) Member JI, (b) Member IE, and (c) Member EF. K 550. 8 ft l0 880 lo0880 A 8800 fonfonfonFonT F 6 ft--6 ft -+ 6 ft- 6 ft-+6 ft -6 ft -

Draw the influence line for the force in (a) Member EH and (b) Member JE. L. 3 m IC |D -4 m--4 m--4 m- |F E4 m--4 m--4 m-

The beam is subjected to a uniform dead load of 1.2 kN/m and a single live load of 40 kN. Determine (a) The maximum moment created by these loads at C, and (b) The maximum positive shear at C. Assume...

A uniform live load of 300 lb/ft and a single live concentrated force of 1500 lb are to be placed on the beam. The beam has a weight of 150 lb/ft. Determine (a) The maximum vertical reaction at...

The beam is used to support a dead load of 0.6 k/ft, a live load of 2 k/ft and a concentrated live load of 8 k. Determine (a) The maximum positive (upward) reaction at A, (b) The maximum positive...

The beam is used to support a dead load of 400 lb/ft, a live load of 2 k/ft, and a concentrated live load of 8 k. Determine (a) The maximum positive vertical reaction at A, (b) The maximum positive...

Determine the maximum positive moment at the splice Con the side girder caused by the moving load which travels along the center of the bridge. 8 kN 4 kN B

Determine the absolute maximum shear in the beam due to the loading shown. 20 kN 40 kN 25 kN B' 1.5 m -12 m-

The truck has a mass of 4 Mg and mass center at G 1 , and the trailer has a mass of 1 Mg and mass center at G 2 , Determine the absolute maximum live moment in the bridge in Problem 669 if the...

The cart has a weight of 2500 lb and a center of gravity at G. Determine the maximum positive moment created in the side girder at C as it crosses the bridge. Assume the car can travel in either...

The state of strain at the point on a boom of a shop crane has components of ε x = 250(0 -6 ), ε y = 300(10 -6 ), and γ xy = -180(10 -6 ). Use the strain...

Draw (approximately) the moment diagram for girder PQRST and column BGLQ of the building frame. All columns have the same cross-sectional area. Use the cantilever method. 6k k 10 ft L. k J| 10 ft...

Use the portal method and determine (approximately) the reactions at supports A,B,C, and D. K 9 kN 4 m F 12 kN 4 m D - 5 m- 5 m -

Determine the slope and displacement at C. EI is constant. Use the moment-area theorems. 15 k B 30 ft 15 ft-

Determine the elastic curve for the simply supported beam using the x coordinate 0 ¤ x ¤ L/2, Also determine the slope at A and the maximum deflection of the beam. EI is constant. Wo