The cantilever beam (of type W8 × 15) made of A36 steel alloy has a depth d =8.11 in, as shown below. The moment of inertia I, is 48.0 in.4. 1, 400 lb 1, 400 lb 100 lb/ft d -5 ft -5 ft (a) Determine the maximum internal bending moment produced by the loading con- dition provided. (b) Determine the maximum normal stress, due to the bending mo- ment, and the corresponding factor of safety (using o y as the failure stress). (c) Draw a graph that shows the stress in the beam along the y-direction at the point chosen in part (a). (d) Calculate emax based on your answer to part (b). (e) Calculate the radius of curvature p based on your answer to part (d). (a) 26 kip-ft (you should find reaction force of 3.8 kip); (b) 26.4 ksi, 1.38; (c) o(y) = 6.5y ksi; (d) 9.10(10¬4); (e) 372 ft

The cantilever beam (of type W8 × 15) made of A36 steel alloy has a depth d =8.11 in, as shown below. The moment of inertia I, is 48.0 in.4. 1, 400 lb 1, 400 lb 100 lb/ft d -5 ft -5 ft (a) Determine the maximum internal bending moment produced by the loading con- dition provided. (b) Determine the maximum normal stress, due to the bending mo- ment, and the corresponding factor of safety (using o y as the failure stress). (c) Draw a graph that shows the stress in the beam along the y-direction at the point chosen in part (a). (d) Calculate emax based on your answer to part (b). (e) Calculate the radius of curvature p based on your answer to part (d). (a) 26 kip-ft (you should find reaction force of 3.8 kip); (b) 26.4 ksi, 1.38; (c) o(y) = 6.5y ksi; (d) 9.10(10¬4); (e) 372 ft

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 61 GPa] with a cross-sectional area of A₁ = 810 mm². Bar (2) is a bronze alloy [E = 103 GPa] with a cross-sectional area of A2 = 470 mm². Assume L₁=2.4 m, L₂=3.1 m, a=0.7 m, b=1.9 m, and c= 1.1 m. All bars are unstressed before the load P is applied; however, there is a 5.8-mm clearance in the pin connection at A. If a load of P = 44 kN is applied at B, determine: (a) the normal stresses 0₁, 0₂, in both bars (1) and (2). (b) the normal strains &1, 82, in bars (1) and (2). (c) determine the downward deflection VA of point A on the rigid bar. A Answers: (a) 0₁ = (STVA = a i i B 156.10 0.00256 b C MPa, 0₁ = με, €2 = mm L2 i i D 20.75 0.0002014 MPa. με.
The pin-connected structure consists of a rigid beam ABCD and two supporting bars. Bar (1) is an aluminum alloy [E = 79 GPa] with a cross-sectional area of A₁ = 700 mm². Bar (2) is a bronze alloy [E = 106 GPa] with a cross-sectional area of A₂ = 480 mm². Assume L₁=1.8 m, L₂=2.1 m, a=0.5 m, b=1.6 m, and c=0.8 m. All bars are unstressed before the load P is applied; however, there is a 3.4-mm clearance in the pin connection at A. If a load of P = 53 kN is applied at B, determine: (a) the normal stresses 01, 02, in both bars (1) and (2). (b) the normal strains 1, 2, in bars (1) and (2). (c) determine the downward deflection VA of point A on the rigid bar. (1) A Answers: (a) σ₁ = (b) 1 (c) VA = i a L₁ B b (2) L2 MPa, 0₁ = με, €2 = mm. i i D MPa. με.
The pin-connected structure consists of a rigid bar ABCD and two axial members. Bar (1) is bronze [E = 90 GPa] with a cross-sectional area of A1 = 510 mm². Bar (2) is an aluminum alloy [E = 68 GPa] with a cross-sectional area of A2 = 320 mm². A concentrated load of P - 75 kN acts on the structure at D. Assume L1-840 mm., L2-420 mm., a-650 mm., b-260 mm., and c-1070 mm. Determine: (a) the normal stresses o1,02 in both bars (1) and (2). (b) the downward deflection vp of point D on the rigid bar. L2 B b D Answers: (a) oi = i MPa, 02 = i MPa (b) VD - i mm.
The compound shaft consists of a solid aluminum segment (1) and a hollow brass segment (2) that are connected at flange B and securely attached to rigid supports at A and C. Aluminum segment (1) has a diameter of 0.55 in., a length of L₁ = 40 in., a shear modulus of 3800 ksi, and an allowable shear stress of 5.8 ksi. Brass segment (2) has an outside diameter of 0.45 in., a wall thickness of 0.15 in., a length of L₂ = 30 in., a shear modulus of 6400 ksi, and an allowable shear stress of 8.2 ksi. Determine: (a) the allowable torque Te that can be applied to the compound shaft at flange B. (b) the magnitudes of the internal torques in segments (1) and (2). (c) the rotation angle of flange B (relative to support A) that is produced by the allowable torque TB. L₁ L2 TB (1) Answer: (a) TB= (b) T₁ = T2= (c) OB= B lb-ft lb-ft lb-ft rad (2) C
A beam ABC with an overhang from B toC supports a uniform load of 200 lb/ft throughout itslength (see figure). The beam is a channel section withdimensions as shown in the figure. The moment of inertiaabout the z axis (the neutral axis) equals 8.13 in4.(a) Calculate the maximum tensile stress σt andmaximum compressive stress σc due to theuniform load.(b) Find the required span length a that results inthe ratio of larger to smaller compressive stressbeing equal to the ratio of larger to smaller tensilestress for the beam. Assume that the totallength L =a + b = 18 ft remains unchanged.
The steel bar AB has a diameter of 30mm and is connected to the brass bar BC. The two bars are fixed to unyielding supports at the top (point A) and bottom (point C) ends. If there is a temperature rise of 50°C, calculate the compressive force induced in the rods (ABC). Note: For steel (E = 200 GPa, as = 11.7 x 106 °C) and for brass (E = 105 GPa, qb= 20.9 x 10-6/ °C). 250 mm 300 mm A B -30-mm diameter -50-mm diameter
A rigid bar ABCD is supported by two bars as shown in the figure. There is no strain in the vertical bars before load P is applied. After load P is applied, the normal strain in rod (1) is -1350 µm/m. Determine the normal strain in rod (2) if there is a 1-mm gap in the connection at pin C before the load is applied. A 240 mm B (1) O 1281 um/m O 1877 µm/m O 1141 µm/m O 1358 µm/m O 999 µm/m 360 mm (2) Rigid bar 900 mm C 140 mm, 1,500 mm
b. Discuss how the figure below and determine the rigid bar BDE as used to support by two link AB and CD. 0.4 m 0.3 m B D 0.4 m 30 kN E 0.2 m The Link AB is made of aluminum (E = 70 GPa) and has a cross-sectional area of 500 mm2. Link CD is made of steel (E = 200 GPa) and has a cross- sectional area of (600 mm2). For the 30-kN force shown, determine the deflection a) of B, b) of D, and c) of E.
3) The rigid link is supported by steel wire (1) with an unstretched length of 200 mm and cross-sectional area of 22.5 mm?. Member (2) is a short aluminum of initial length 50 mm and cross-sectional area of 40 mm?. The modulus of elasticity of the steel wire is 200 GPa and the aluminum block is 70 GPa. a) Draw the deflected shape of the rigid member and clearly label the deformation of members (1) and (2). b) Write the equilibrium and compatibility equations needed to solve the problem along with the supporting sketches. Hint: Be sure to carefully consider if the members are elongating or shortening; this must be represented mathematically. c) Calculate the internal forces in both axial members and clearly indicate tension or compression. [Ans. to Check: F2 = 535 N]
Question 3 of 5 -/ 20 E View Policies Current Attempt in Progress A steel [E = 200 GPa] bar (1) supports beam AB. The cross-sectional area of the bar is 580 mm2. If the stress in the bar must not exceed 330 MPa and the maximum deformation in the bar must not exceed 13 mm, determine the maximum load P that may be supported by this structure. Use dimensions of a = 4 m, b 2.4 m, and c = 5.2 m. %3! C (1) a Answer: kN P = Attempts: 0 of 1 used Sub Save for Later B.
The compound shaft consists of a solid aluminum segment (1) and a hollow brass segment (2) that are connected at flange B and securely attached to rigid supports at A and C. Aluminum segment (1) has a diameter of 0.95 in., a length of L1 = 50 in., a shear modulus of 3800 ksi, and an allowable shear stress of 6.7 ksi. Brass segment (2) has an outside diameter of 0.85 in., a wall thickness of 0.13 in., a length of L2 = 38 in., a shear modulus of 6400 ksi, and an allowable shear stress of 8.0 ksi. Determine:(a) the allowable torque TB that can be applied to the compound shaft at flange B.(b) the magnitudes of the internal torques in segments (1) and (2).(c) the rotation angle of flange B (relative to support A) that is produced by the allowable torque TB.
Q4: For the figure below, determine the principal stresses and show them on a sketch of a properly oriented element. Also, find the maximum shear stresses and show them on a sketch of a properly oriented element. (Consider only the in-plane stresses.) -30MPA 90 MPa -34MPA