
The steel beam ABCD shown is simply supported at C as shown and supported at B and D by shoulder steel bolts, each having a diameter of 8 mm. The lengths of BE and DF are 50 mm and 65 mm, respectively. The beam has a second area moment of 21(103) mm4. Prior to loading, the members are stress-free. A force of 2 kN is then applied at point A. Using procedure 2 of Sec. 4–10, determine the stresses in the bolts and the deflections of points A, B, and D.
Problem 4–102

The stresses in the bolts.
The deflection at point A.
The deflection at point B.
The deflection at point D.
Answer to Problem 102P
The stress in the bolt
The deflection at point A is
The deflection at point B is
The deflection at point D is
Explanation of Solution
The Figure (1) shows the free body diagram of the steel beam ABCD.
Figure (1)
Here, the applied load at point
Refer to procedure 2 from Sec. 4–10.
Write the expression for the net force in the beam
Write the expression for the net moment about point
Here, the length of the beam is
The Figure (2) shows the beam at section (1).
Figure (2)
Write the expression for the bending moment at section (1).
Here, the bending moment at section (1) is
Write the expression for the bending moment in terms of elastic equation.
Here, the modulus of elasticity is
Substitute
Integrate the above expression.
Further integrate the above expression.
Write the expression for the area of the bolt.
Here, the area of the bolt is
Write the expression for elongationin the steel boltat point B.
Here, the elongation is
Write the expression for elongation in the steel bolt at point D
Here, the elongation is
Applying Boundary conditions.
At
Substitute
At
Substitute
At
Substitute
Write the expression for the normal stress in section BE.
Here, the normal stress is
Write the expression for the normal stress in section DF.
Here, the normal stress is
Conclusion:
Refer to Table A-5 “Physical Constants of Materials”, obtain the properties of modulus of elasticity for steel as
Substitute
Substitute
Substitute
Substitute
Write Equation (I), Equation (II), Equation (XIV), Equation (XV), and Equation (XVI) in matrix form.
Solve the above matrix Equation to obtain reactions as follows.
Solve the above matrix to obtain the constants.
Substitute
Thus, the stress in the bolt
Substitute
Thus, the stress in the bolt
Calculate deflection at point
Substitute
Thus, the deflection at point
Calculate deflection at point
Substitute
Thus, the deflection at point
Calculate deflection at point
Substitute
Thus, the deflection at point
Want to see more full solutions like this?
Chapter 4 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
- The steel eyebolt shown in the figure is loaded with a force F = 75 lb. The eyebolt is formed from round wire of diameter d = 0.25 in to a radius R₁ = 0.50 in in the eye and at the shank. Estimate the stresses at the inner and outer surfaces at section A-A. Notice at the section A-A: r₁ = 0.5 in, ro = 0.75 in rc = 0.5 + 0.125 = 0.625 in Ri 200 F FAarrow_forwardI have the fallowing question and solution from a reeds naval arc book. Im just confused as to where this answer came from and the formulas used. Wondering if i could have this answer/ solution broken down and explained in detail. A ship of 7000 tonne displacement has a waterplane areaof 1500 m2. In passing from sea water into river water of1005 kg/m3 there is an increase in draught of 10 cm. Find the Idensity of the sea water. picture of the "answer" is attachedarrow_forwardProblem A2 long steel tube has a rectangular cross-section with outer dimensions of 20 x 20 mm and a uniform wall thickness of 2. The tube is twisted along its length with torque, T. The tube material is 1045 CD steel with shear yield strength of S,, =315 MPa. Assume shear modulus, G = 79.3GPa. (a) Estimate the maximum torque that can be applied without yielding (b) Estimate the torque required to produce 5 degrees total angle of twist over the length of the tube. (c) What is the maximum torque that can be applied without yielding, if a solid rectangular shaft with dimensions of 20 x 20 is used? You may use the exact solution.arrow_forward
- A simply supported beam is loaded as shown. Considering symmetry, the reactions at supports A and B are R₁ = R₂ = wa 2 Using the singularity method, determine the shear force V along the length of the beam as a function of distance x from the support A. A B Ir. 2a За W C R₁₂ x 2. Using the singularity method, determine the bending M along the length of the beam as a function of distance x, from the support A. 3. Using the singularity method, determine the beam slope and deflection along the length of the beam as a function of the distance x, from the support A. Assume the material modulus of elasticity, E and the moment of inertia of the beam cross-section, I are given.arrow_forwardA steel tube, 2 m long, has a rectangular cross-section with outer dimensions of 20 × 30 mm and a uniform wall thickness of 1 mm. The tube is twisted along its length with torque, T. The tube material is 1018 CD steel with shear yield strength of Ssy =185 MPa. Assume shear modulus, G = 79.3GPa. (a) Estimate the maximum torque that can be applied without yielding.- (b) Estimate the torque required to produce 3 degrees total angle of twist over the length of the tube. (c) What is the maximum torque that can be applied without yielding, if a solid rectangular shaft with dimensions of 20 x 30 mm is used? You may use the exact solution:arrow_forward|The typical cruising altitude of a commercial jet airliner is 10,700 m above sea level where the local atmospheric temperature is 219 K, and the pressure is 0.25 bar. The aircraft utilizes a cold air-standard Brayton cycle as shown with a volume flow rate of 1450 m³/s. The compressor pressure ratio is 50, and the maximum cycle temperature is 1700 K. The compressor and turbine isentropic efficiencies are 90%. Neglect kinetic and potential energy effects in this problem. Assume constant specific heats with k=1.4, Ra=0.287 kJ/kg- K, Cp=1.0045 kJ/kg-K, and cv = 0.7175 kJ/kg-K. a) Draw a T-s diagram for this cycle on the diagram provided. b) Fill in the table below with the missing information. T[K] Heat exchanger Heat exchanger State P [bar] 1 0.25 2s 2 3 4s 4 Turbine c) (5pts) Determine the inlet air density in [kg/m³] (at state 1), and the system mass flowrate in [kg/s]. d) (10pts) Determine the net power developed in [MW]. Be sure to draw each component you are analyzing, define the…arrow_forward
- On the axis provide, draw a corresponding T-s diagram for the Brayton cycle shown given the following information: iv. V. vi. Compressor 1 is reversible, but Compressor 2 and the turbine are irreversible. The pressure drops through the regenerator are combustors are negligible. The pressures at state (1) and state (10) are equal to the atmospheric pressure. T 8 Regenerator fmm mmm Qin Combustor Compressor Compressor Turbine W cycle Intercooler mm Courarrow_forwardFor parts a) through e), consider the two power cycles shown in the diagram at the right, Cycle A: 1-2-3-4-1, and Cycle B: 1-2-3-4-1. a) What type of power cycles are shown? b) Which of cycles has a higher efficiency? c) Which of the cycles has a higher work output? d) For either cycle, would increasing the maximum cycle temperature (3) increase or decrease the efficiency? Cycle A: 1-2-3-4-1 3 3 Cycle B: 1-2-3-4-1 1 e) For either cycle, would decreasing the minimum cycle temperature (1) increase or decrease the efficiency? f) On the axis provide, draw a corresponding T-s diagram for the Rankine cycle shown given the following information: i. All turbines and pumps in the system are irreversible. ii. 111. The turbine inlet conditions (states 1 and 2) are superheated, while the 2nd stage turbine outlet is a saturated mixture. The condenser outlet state (4) and the CFWH outlet state (7) are saturated liquid. 2 Steam generator Condenser www Closed feedwater heater (1-y) T Pump Trap 8 (y) Sarrow_forwardProblem 4 A glass sphere with a 30 mm diameter is pressed against a flat carbon steel plate with a force of 5 N. Assume. For glass: E = 46.2 GPa, -0.245 and for steel E, 207 GPa, (a) Determine the radius of the contact surface. -0.292 (4 (b) Determine the maximum pressure at the contact surface. (4 (c) Calculate the principal stresses d., and a, in the glass sphere at the depth=0.037 mm. (d) Maximum shear stress in the glass sphere at the depth: 0.037 mm. (t (4 (e) Draw the Mohr circles for the stresses and show the point corresponding to the maximum shear stress. (3arrow_forward
- Steam is the working fluid in the vapor power cycle with reheat shown in the figure. The mass flow rate is 0.5 kg/s, and the turbines and pump operate isentropically. The temperature at the inlet of both turbine stages (i.e. states 1 and 3) is 400 °C The condenser outlet is saturated liquid. 1. Fill in the table below with the missing information. Reheat section High- pressure turbine State P [bar] h [kJ/kg] s [kJ/kg-K] x [-] Steam generator 1 140 Condenser Pump 2 40 5 3 4 4 5 6 2.Draw a T-s diagram for this cycle on the diagram provided 3. Determine the net power output of this cycle in [kW]. Be sure to draw the component(s) you are analyzing, define the system, and apply conservation of energy in the space below. 4.Determine the total heat transferred into the system in [kW]. Be sure to draw the component you are analyzing, define the system, and apply conservation of energy in the space bel 5.Determine the cycle efficiency. Low-pressure turbinearrow_forwardCalculate the moment of F about axis AB. Express the moment as a Cartesian vector, and then state its magnitude. The radii of the curved sections are all 0.5 m. F acts on the bottom center of the hook, and the hook lies in the yz plane.arrow_forwardDetermine the moment created by the force FAB about the point E. Assume FAB = 800 lbs. Express your answer as a Cartesian vector (ME) and state the magnitude of the moment.arrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
