The beam shown in Figure Q.2 consists of a W610 × 140 structural steel wide-flange shape [E = 200 GPa; I = 1120 × 106 mm4]. If w = 68 kN/m and P = 121 kN , determine: Part A: The reactions at A, B, and D. Choose the reaction force at B as the redundant; therefore, the released beam is simply supported between A and D. a) Calculate the value of the deflection at point B due to uniformly distributed load w in the form ?? = ????????? / ?? Note: EI will cancel out in further calculations. Enter the numerator in the answer box below in kNm3 to three decimal places. Assume the positive direction of deflection in the positive direction of v axis. b) Calculate the value of the deflection at point B due to concentrated load P in the form ?? = ????????? / ?? Note: EI will cancel out in further calculations. Enter the numerator in the answer box below in kNm3 to three decimal places. Assume the positive direction of deflection in the positive direction of v axis. c) Calculate the vertical reaction at support B. When sketching FBD, assume the positive direction of all reactions in the positive direction of y axis. Enter your answer in kN to two decimal places. d) Calculate the vertical reaction at support D. Enter your answer in kN to two decimal places. e) Calculate the vertical reaction at support A. Enter your answer in kN to two decimal places. Part B. The magnitude of the maximum bending stress in the beam. f) Find the maximum bending moment in the beam. Enter your answer in kNm to two decimal places. g) Calculate the magnitude of the maximum bending stress in the beam. Enter your answer in MPa to two decimal places
Plane Trusses
It is defined as, two or more elements like beams or any two or more force members, which when assembled together, behaves like a complete structure or as a single structure. They generally consist of two force member which means any component structure where the force is applied only at two points. The point of contact of joints of truss are known as nodes. They are generally made up of triangular patterns. Nodes are the points where all the external forces and the reactionary forces due to them act and shows whether the force is tensile or compressive. There are various characteristics of trusses and are characterized as Simple truss, planar truss or the Space Frame truss.
Equilibrium Equations
If a body is said to be at rest or moving with a uniform velocity, the body is in equilibrium condition. This means that all the forces are balanced in the body. It can be understood with the help of Newton's first law of motion which states that the resultant force on a system is null, where the system remains to be at rest or moves at uniform motion. It is when the rate of the forward reaction is equal to the rate of the backward reaction.
Force Systems
When a body comes in interaction with other bodies, they exert various forces on each other. Any system is under the influence of some kind of force. For example, laptop kept on table exerts force on the table and table exerts equal force on it, hence the system is in balance or equilibrium. When two or more materials interact then more than one force act at a time, hence it is called as force systems.
The beam shown in Figure Q.2 consists of a W610 × 140 structural steel wide-flange shape [E = 200 GPa; I = 1120 × 106 mm4]. If w = 68 kN/m and P = 121 kN , determine:
Part A: The reactions at A, B, and D. Choose the reaction force at B as the redundant; therefore, the released beam is simply supported between A and D.
a) Calculate the value of the deflection at point B due to uniformly distributed load w in the form
?? = ????????? / ??
Note: EI will cancel out in further calculations.
Enter the numerator in the answer box below in kNm3 to three decimal places. Assume the positive direction of deflection in the positive direction of v axis.
b) Calculate the value of the deflection at point B due to concentrated load P in the form
?? = ????????? / ??
Note: EI will cancel out in further calculations.
Enter the numerator in the answer box below in kNm3 to three decimal places. Assume the positive direction of deflection in the positive direction of v axis.
c) Calculate the vertical reaction at support B. When sketching FBD, assume the positive direction of all reactions in the positive direction of y axis. Enter your answer in kN to two decimal places.
d) Calculate the vertical reaction at support D. Enter your answer in kN to two decimal places.
e) Calculate the vertical reaction at support A. Enter your answer in kN to two decimal places.
Part B. The magnitude of the maximum bending stress in the beam.
f) Find the maximum bending moment in the beam. Enter your answer in kNm to two decimal places.
g) Calculate the magnitude of the maximum bending stress in the beam. Enter your answer in MPa to two decimal places
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