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14) What is the median of the list of numbers: 35, 20, 30, 25, 20?
10. A football team played 160 games and won 65 percent of them. How many games did it
win?
📕What is BODMAS Rule?📕
✅BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. The BODMAS is used to explain the order of operation of a mathematical expression. In some regions, the BODMAS is also known as PEDMAS which stands for Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction.
✅According to BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEDMAS rule is followed to solve it.
📕Example Question Using BODMAS Rule:
👉🏾Example 1: 5 + 3 x 2 - 4
Using BODMAS, we first do the multiplication (3 x 2 = 6), then the addition and subtraction in order from left to right:
5 + 6 - 4 = 7
👉🏾Example 2: (4 + 2) x 3 - 5
Using BODMAS, we first do the calculation inside the brackets (4 + 2 = 6), then the multiplication (6 x 3 = 18), and finally the subtraction:
18 - 5 = 13
👉🏾Example 3: 10 ÷ 2 x 3
Using BODMAS, we first do the division (10 ÷ 2 = 5), then the multiplication:
5 x 3 = 15 Example 1: Simplify the expression by using the BODMAS rule: [18 - 2(5 + 1)] ÷ 3 + 7
Solution:
The given expression is [18 - 2(5 + 1)] ÷ 3 + 7
Step 1: We begin with solving the innermost bracket first. Starting with 5 + 1 = 6. Thus, [18 - 2(6)] ÷ 3 + 7
Step 2: Next, we work with the order, thereby multiplying 2 (6) or 2 × 6 = 12. Thus, [18 - 12] ÷ 3 + 7
Step 3: There is one bracket left, [18 - 12] = 6. So, 6 ÷ 3 + 7
Step 4: After B and O comes D, hence, 6 ÷ 3 = 2. So, 2 + 7
Step 5: And finally, addition, 2 + 7 = 9
∴ The expression is simplified and the answer is 9.
Example 2: Evaluate using the order of operati
8. Simplify the numerical expression: [36 ÷ (-9)] ÷ [(-24) ÷ 6]
5. Evaluate using the order of operations using the BODMAS rule: (1 + 20 - 16 ÷ 4²) ÷ {(5 - 3)² + 12 ÷ 2}
6️⃣1️⃣A steel column with a length of 5 m and a rectangular cross-section has a width of 200 mm and a height of 300 mm. The column is subjected to an axial compressive load of 1000 kN. The modulus of elasticity of the steel is 200 GPa. Determine the maximum compressive stress in the column.
a) 50 MPa
b) 75 MPa
c) 100 MPa
d) 125 MPa
6️⃣2️⃣A beam with a rectangular cross-section has a width of 150 mm and a height of 250 mm. The beam is subjected to a uniformly distributed load of 30 kN/m over its entire span of 4 m. The modulus of elasticity of the beam material is 180 GPa. Determine the maximum deflection of the beam.
a) 4.86 mm
b) 6.48 mm
c) 8.10 mm
d) 9.72 mm
6️⃣3️⃣A steel rod with a diameter of 20 mm and a length of 2 m is subjected to a tensile load of 50 kN. The modulus of elasticity for steel is 200 GPa. Calculate the elongation of the rod.
a) 0.1 mm
b) 0.25 mm
c) 0.5 mm
d) 1.0 mm
🟢7️⃣0️⃣Practice Exam 🇪🇹 MCQs
📚 Engineering 👆👆
✅️Course: Strength of Materials
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4️⃣7️⃣What is the formula for calculating the equivalent axial stress in a compound bar consisting of multiple materials?
a) σ = (P × L) / (A × E)
b) σ = (P × L) / (A × σy)
c) σ = (P × ΔL) / (A × E)
d) σ = (P × ΔL) / (A × σy)
4️⃣8️⃣Which of the following factors does NOT affect the fatigue strength of a material?
a) Mean stress
b) Surface finish
c) Temperature
d) Density of the material
4️⃣9️⃣The phenomenon of creep refers to:
a) The sudden fracture of a material under stress
b) The gradual deformation of a material over time under a constant load
c) The elastic behavior of a material under stress
d) The permanent deformation of a material under stress due to cyclic loading
5️⃣0️⃣A rectangular beam with a width of 100 mm and a height of 200 mm is subjected to a bending moment of 5000 Nm. The moment of inertia of the beam is 8.33 × 10^6 mm^4. What is the maximum bending stress in the beam?
a) 24 MPa
b) 30 MPa
c) 36 MPa
d) 42 MPa
5️⃣1️⃣A steel rod with a diameter of 20 mm and a length of 1.5 m is subjected to a tensile load of 10 kN. The modulus of elasticity for steel is 200 GPa. What is the elongation of the rod?
a) 0.75 mm
b) 1.25 mm
c) 1.75 mm
d) 2.25 mm
5️⃣2️⃣A simply supported beam with a span of 4 m is subjected to a uniformly distributed load of 20 kN/m. The modulus of elasticity of the beam material is 200 GPa and the moment of inertia of the beam is 1.33 × 10^6 mm^4. What is the maximum deflection of the beam?
a) 4.8 mm
b) 6.4 mm
c) 8.0 mm
d) 9.6 mm
5️⃣3️⃣A circular steel shaft with a diameter of 50 mm and a length of 2 m is subjected to a torque of 500 Nm. The polar moment of inertia of the shaft is 6.25 × 10^6 mm^4. What is the maximum torsional shear stress in the shaft?
a) 25 MPa
b) 50 MPa
c) 75 MPa
d) 100 MPa
5️⃣4️⃣A cantilever beam with a length of 3 m is subjected to a point load of 15 kN at the free end. The modulus of elasticity of the beam material is 150 GPa and the moment of inertia of the beam is 3.75 × 10^6 mm^4. What is the maximum deflection of the beam at the free end?
a) 2.25 mm
b) 3.75 mm
c) 5.63 mm
d) 7.50 mm
5️⃣5️⃣A rectangular column with a width of 150 mm and a height of 300 mm is subjected to a compressive load of 500 kN. The effective length of the column is 4 m. The modulus of elasticity of the column material is 180 GPa. What is the buckling load of the column?
a) 750 kN
b) 1000 kN
c) 1250 kN
d) 1500 kN
5️⃣6️⃣A steel plate with a thickness of 10 mm is subjected to a tensile load of 50 kN. The width of the plate is 200 mm. If the ultimate strength of the steel is 400 MPa, what is the factor of safety for the plate?
a) 2.0
b) 2.5
c) 3.0
d) 3.5
5️⃣7️⃣A cylindrical pressure vessel with a diameter of 500 mm and a wall thickness of 20 mm is subjected to an internal pressure of 10 MPa. The tensile yield strength of the material is 400 MPa. What is the factor of safety against yielding for the pressure vessel?
a) 5.0
b) 7.5
c) 10.0
d) 12.5
5️⃣8️⃣A steel beam with a rectangular cross-section has a width of 150 mm and a height of 250 mm. The beam is subjected to a bending moment of 6000 Nm. The modulus of elasticity of the steel is 200 GPa, and the maximum allowable bending stress is 180 MPa. Will the beam fail under this loading condition?
a) Yes, the beam will fail.
b) No, the beam will not fail.
5️⃣9️⃣A circular shaft with a diameter of 100 mm is subjected to a torque of 10 kNm. The shaft is made of a material with a shear modulus of 80 GPa. What is the maximum angle of twist experienced by the shaft over its length of 2 meters?
a) 0.031 radians
b) 0.047 radians
c) 0.063 radians
d) 0.079 radians
6️⃣0️⃣A cantilever beam with a length of 3 m and a rectangular cross-section is subjected to a point load of 20 kN at its free end. The width of the beam is 150 mm, and the height is 250 mm. The beam materi
al has a modulus of elasticity of 200 GPa. What is the maximum bending stress in the beam?
a) 32 MPa
b) 48 MPa
c) 64 MPa
d) 80 MPa
2️⃣6️⃣What is the formula for calculating the deflection of a cantilever beam under a point load?
a) δ = (P × L^3) / (3 × E × I)
b) δ = (P × L^3) / (4 × E × I)
c) δ = (P × L^3) / (6 × E × I)
d) δ = (P × L^3) / (8 × E × I)
2️⃣7️⃣Which of the following materials exhibits a linear relationship between stress and strain within the elastic limit?
a) Ductile materials
b) Brittle materials
c) Non-elastic materials
d) Viscoelastic materials
2️⃣8️⃣The ability of a material to resist indentation or penetration is known as:
a) Hardness
b) Toughness
c) Elasticity
d) Resilience
2️⃣9️⃣Which of the following is NOT a factor affecting the torsional shear stress in a shaft?
a) Torque
b) Shaft diameter
c) Length of the shaft
d) Material's density
3️⃣0️⃣What is the formula for calculating the total strain energy stored in a material under axial loading?
a) U = (1/2) × σ × ε
b) U = (1/2) × σ × δ
c) U = (1/2) × F × ε
d) U = (1/2) × F × δ
3️⃣1️⃣Which type of stress causes a change in shape or size of a material?
a) Tensile stress
b) Compressive stress
c) Shear stress
d) Bending stress
3️⃣2️⃣What is the formula for calculating the polar moment of inertia of a circular cross-section?
a) J = (π × d^4) / 32
b) J = (π × d^3) / 32
c) J = (π × d^4) / 64
d) J = (π × d^3) / 64
3️⃣3️⃣The ratio of ultimate stress to yield stress is known as:
a) Resilience
b) Toughness
c) Ductility
d) Rupture strength
3️⃣4️⃣What is the formula for calculating the thermal stress in a material due to a change in temperature?
a) σ = α × ΔT
b) σ = ΔT / α
c) σ = E × ΔT
d) σ = ΔT / E
3️⃣5️⃣Which of the following is a failure criterion used for ductile materials?
a) Maximum principal stress criterion
b) Maximum shear stress criterion
c) Maximum distortion energy criterion
d) Maximum strain energy criterion
3️⃣6️⃣The ability of a material to recover its original shape after deformation is known as:
a) Ductility
b) Resilience
c) Elasticity
d) Toughness
3️⃣7️⃣What is the formula for calculating the bending stress in a beam?
a) σ = (M × c) / S
b) σ = (M × S) / c
c) σ = (M × c) / I
d) σ = (M × I) / c
3️⃣8️⃣Which of the following is a type of beam that is supported at one end and free at the other end?
a) Simply supported beam
b) Cantilever beam
c) Overhanging beam
d) Fixed beam
3️⃣9️⃣What is the formula for calculating the maximum deflection of a simply supported beam under a uniformly distributed load?
a) δ = (5 × w × L^4) / (384 × E × I)
b) δ = (w × L^4) / (384 × E × I)
c) δ = (5 × w × L^4) / (256 × E × I)
d) δ = (w × L^4) / (256 × E × I)
4️⃣0️⃣Which theory is used to analyze the stress distribution in a thin-walled pressure vessel?
a) Lame's theory
b) Saint-Venant's theory
c) Tresca's theory
d) Rankine's theory
4️⃣1️⃣Which of the following assumptions is NOT made in the theory of pure bending of beams?
a) The material is isotropic.
b) The beam is initially straight.
c) The neutral axis remains neutral during bending.
d) The strain distribution is linear across the section.
4️⃣2️⃣What is the formula for calculating the radius of gyration of a rectangular cross-section?
a) k = (h^2 + b^2) / (2√3)
b) k = √[(h^2 + b^2) / 12]
c) k = √[(h^2 × b^2) / 12]
d) k = (h + b) / 2
4️⃣3️⃣The slope of the shear diagram corresponds to:
a) The bending moment
b) The shear force
c) The deflection
d) The axial stress
4️⃣4️⃣Which of the following methods is NOT used for determining the principal stresses and their orientations?
a) Mohr's circle
b) Strain transformation equations
c) Principal stress transformation equations
d) Principal stress distribution diagrams
4️⃣5️⃣What is the formula for calculating the buckling load of a long column?
a) P = (π^2 × E × I) / (L^2)
b) P = (π^2 × E × I) / (L^4)
c) P = (π^2 × E × I) / (L^3)
d) P = (π^2 × E × I) / (L^6)
4️⃣6️⃣The phenomenon of stress concentration occurs:
a) Only in brittle materials
b) Only in ductile materials
c) Only in elastic materials
d) In both brittle and ductile materials
