Problem # 1: The two rods as shown in the figure are attached to each other and the aluminum rod is fixed at the wall. The rods are initially unstressed and then a 20, 000 lb horizontal force is applied to the end of the brass rod as shown. Additionally, the rods experience a temperature increase of 80 °F. Use Linear coefficient of Expansion: 13 x 10-6/°F Brass = 11 x 10-6/°F Aluminum Young's Modulus: EAluminum = 10 x 106 lb/in²; EBrass = 15 x 106 lb/in² Determine; a) the final stress that develops in the aluminum rod, b) the total displacement of point C. Aluminum 10 ft B Aal= 2in² Brass 6 ft A₁= 1in² Abr F = 20,000 lb

Problem # 1: The two rods as shown in the figure are attached to each other and the aluminum rod is fixed at the wall. The rods are initially unstressed and then a 20, 000 lb horizontal force is applied to the end of the brass rod as shown. Additionally, the rods experience a temperature increase of 80 °F. Use Linear coefficient of Expansion: 13 x 10-6/°F Brass = 11 x 10-6/°F Aluminum Young's Modulus: EAluminum = 10 x 106 lb/in²; EBrass = 15 x 106 lb/in² Determine; a) the final stress that develops in the aluminum rod, b) the total displacement of point C. Aluminum 10 ft B Aal= 2in² Brass 6 ft A₁= 1in² Abr F = 20,000 lb

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

At a temperature of 60°F, a 0.04-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; v = 0.32; α=α=12.5 x 10-6/°F] bar with a width of 2.5 in. and a thickness of 0.75 in. Bar (2) is a stainless steel [E = 28,000 ksi; v = 0.12; α=α=9.6 x 10-6/°F] bar with a width of 1.7 in. and a thickness of 0.75 in. The supports at A and C are rigid. Assume h1=2.5 in., h2=1.7 in., L1=31 in., L2=46 in., and Δ=Δ= 0.04 in. (A) Determine the lowest temperature, Tcontact, at which the two bars contact each other. (B) Find a geometry-of-deformation relationship for the case in which the gap is closed. Express this relationship by entering the sum δ1+δ2, where δ1 is the axial deflection of Bar (1), and δ2 is the axial deflection of Bar (2). δ1+δ2= _____in. (C) Find the force in the Bar (1), F1, and the force in Bar (2), F2, at a temperature of 225oF. By convention, a tension force is positive and a compression force is negative. IN KIPS (D) Find σ1 and σ2,…
A rigid bar, AB, is pinned at point B. Two other bars, AC and AD, are connected to point A to provide support for AB. We are investigating the behavior of this system under a specific load. Key Details: Bar properties: Material: Steel with Young's modulus (Esteel) of 200 GPa and coefficient of thermal expansion (a) of 11.7 x 10^-6 /°C. Cross-sectional area: AC: 1960 mm² AD: 1250 mm² Length: AC: √2 meters (square root of 2 meters) AD: 1 meter Inclination angles: AC: θ₁ (theta 1) = 30° from horizontal AD: θ₂ (theta 2) = 20° from horizontal Load on bar AB: Idealized linearly increasing load with a maximum value of 30 kN/m at point B. Problem Objectives: Determine the internal forces (axial forces) acting within bars AC and AD due to the applied load on AB. Calculate the displacement of point A in both horizontal (dA,x) and vertical (dA,y) directions.If the bar is cooled by 10°C, what would be the: Determine the internal forces (axial forces) acting within bars AC and AD…
Q.1 The yield stresses (oy) have been measured using steel and aluminum specimens of various grain sizes, as follows: Material D (µm) σΥ (MPa) Steel 60.5 160 136 128 Aluminum 11.1 235 100 223 (a) Determine the coefficients o and kỵ in the Hall- Petch for these two materials. (b) Determine the yield stress in each material for a grain size of d=26 um.
A 1.0 meter long A36 steel rod with a diameter of 40mm is lightly attached at both end of the rod, end A and end B. A collar is located in the center of the rod. The initial temp is 60 degrees C. The final temperature is 35 degrees C. Determine the force that must be applied to the collar so that the reaction at B is zero.Given:Delta T=25 degrees CE for A36 steel: 200 GPaCoeff of thermal expansion: 12(10^-6)/degree C
A steel bar is held by two fixed supports as shown in the figure and is subjected to an increased temperature of AT = 200°C. If coefficient of thermal expansion and young's modulus of elasticity of steel are 11 x 10-6/°C and 200 GPa respectively, the magnitude of thermal stress (in MPa) induced in the bar is
The rigid horizontal bar ABC of negligible mass is connected to two rods as shown in the figure. If the system is initially stress-free, calculate the temperature change that will cause a tensile stress of 90 MPa in the brass rod. Assume that both rods are subjected to the same change in temperature.
Problem # 2. At room temperature (20°C) a 0.5-mm gap exists between the ends of the rods shown. At a later time when the temperature has reached 140 °C, determine (a) the normal stress in the aluminum rod Ans: A -300 mm Aluminum A = 2000 mm² E = 75 GPa α = 23 x 16-6/°C 0.5 mm -250 mm Stainless steel A = 800 mm² B E = 190 GPa a = 17.3 x 10-6/°C
A 4 meter long steel plate with a rectangular cross section (10 mm x 50 mm) is resting on a frictionless surface under the sun. The plate temperature is measured to be at 40°C. The plate is then moved into a cold room and is left to rest on a frictionless surface. After several hours, the plate temperature is measured to be 5°C. The steel has a modulus of elasticity equal to 200 GPa and a coefficient of thermal expansion equal to 1.1x10-5/°C. a. What is the length of shrinkage b. What tension load is needed to return the length to the original value of 4 meters? c. What is the longitudinal strain under this load?
Three aluminum rods support the rigid L-shaped bracket BCF as shown in the figure. Determine the stress in rod DE (express answer in MPa) if rod FG is cooled by 50°C. All three rods have the same cross-sectional area of 1000 mm^2. Use 73.1 GPa and 23 x 10^-6/°C for the modulus of elasticity and the coefficient of thermal expansion of aluminum, respectively.
Problem 1 An aluminum rod is rigidly attached between a steel rod and a bronze rod as shown. Axial loads are applied at the positions indicated. Aluminum Steel A=800mm2 A=1000mm2 Bronze A=700mm? 4P 2P 500mm 600mm 700mm 1. What is the maximum value of P that will not exceed the axial stress bronze of 105 MPa? 2. What is the maximum value of P that will not exceed the axial stress in aluminum of 90 MPa? 3. If P=10KN, what is the axial force to be carried by the aluminum in KN? 4. If P is 5KN, what is the axial stress of steel?
At room temperature (20°C) a 0.7-mm gap exists between the ends of the rods shown. At a later time when the temperature has reached 150°C, determine: (a.)The normal stress in the aluminum rod, (b.) The change in length of the aluminum rod. 0.7 mm 300 mm A Aluminum A =2,000 mm² E= 75 GPa α = 23 x 106/°C 250 mm B Stainless steel A = 800 mm² E = 190 GPa a = 17.3 x 10-6/°C
Knowing that a 0.02in gap exists when the temperature is 75°F, determine (a) the temperature at which the normal stress in the aluminum bar will be equal to -11ksi, (b) the corresponding exact length (2 decimal places in 103 inches) of the aluminum bar. 0.02 in. 14 in. Bronze A = 2.4 in² E = 15 × 106 psi a = 12 x 10-6/°F 18 in. Aluminum A = 2.8 in² E = 10.6 × 106 psi a = 12.9 x 10-6/°F