Question

A wood beam (1) is reinforced on its lower surface by a steel plate (2) as shown in the figure. Dimensions of the cross section are b 1 = 220 mm , d = 385 mm , b 2 = 190 mm , and t = 25 mm . The elastic moduli of the wood and steel are E 1 = 12.5 GPa and E 2 = 200 GPa , respectively. The allowable bending stresses of the wood and steel are 6.5 MPa and 130 MPa , respectively. This cross section is used for a simply supported beam that spans 8.3 m . What is the largest uniformly distributed load that can be applied to the beam?

​​​​​​

bi Wooden beam (1) N d Steel plate (2) b2 1 c!

part 1

Denote the wood as material (1) and denote the steel as material (2). Calculate the required width of a wood board, with the same thickness as the steel plate, that can be used for calculation purposes to replace the steel plate. In other words, transform the steel into an equivalent amount of wood, and find the width b 2 , trans of the wood.

b 2 , trans =

3040

mm

^^^ this is correct

part 2

Calculate the centroid location of the transformed section in the vertical direction measured upward from the bottom edge of the section.

y ¯ =

120.55

mm

^^^^ this is correct

part 3

Determine the area moment of inertia of the cross-section. As indicated, the numerical value you enter in the input field multiplied by the factor ( 10 6 ) equals the area moment of inertia in units of mm 4 .

I z =

× 10 6

mm 4

part 4

Based only on the allowable bending stress in the wood, determine the maximum allowable moment magnitude in the beam.

M allow , wood =

kN ⋅ m

part 5

Based only on the allowable bending stress in the steel, determine the maximum allowable moment magnitude in the beam.

M allow , steel =

kN ⋅ m

part 6

Determine the maximum allowable moment magnitude in the beam.

M allow =

kN ⋅ m

part 7

Calculate the maximum internal moment magnitude at any location along the simply supported beam due to a uniformly distributed load of magnitude w over the entire span. In the input field, enter the numerical value of the coefficient of w when the maximum moment is written as a function of w . Input the value assuming the moment has units of kN ⋅ m and w has units of kN / m . Since you’re entering a magnitude, enter a positive value.

M max =

w

kN ⋅ m

part 8

What is the largest uniformly distributed load magnitude w that can be applied to the beam?  Since you’re entering a magnitude, enter a positive value.

w =

kN / m

Answer 1

please upvote.