SQL Server adding field to table generates error timeout expired

I have a table with 12 million records in it.

I want to add a field. I made a backup of the database to try it first.
When I used the interface to modify the table and then added the field (an int), it said it would affect about 7 other tables and do I want to proceed. I said yes.

The response was that it updated all the other tables but when it got to the table I am altering, it errored with this:

Unable to modify table.  
Timeout expired.  The timeout period elapsed prior to completion of the operation or the server is not responding.

Am I never going to be able to add a field to that table? How do I do it?

Here is the script to create the original table from scratch if that's useful:

CREATE TABLE [dbo].[Log](
	[LogId] [int] IDENTITY(1,1) NOT NULL,
	[IPAddress] [nvarchar](50) NULL,
	[ClientId] [int] NULL,
	[UnitId] [int] NULL,
	[UserProfileId] [int] NULL,
	[SignOffUserProfileId] [int] NULL,
	[TrainingCourseId] [int] NULL,
	[TrainingWorkshopId] [int] NULL,
	[TrainingModuleId] [int] NULL,
	[TrainingModuleStepId] [int] NULL,
	[EmployeeTrainingModuleAttemptId] [int] NULL,
	[LogEvent] [nvarchar](50) NULL,
	[Note] [nvarchar](4000) NULL,
	[CreatedUserId] [int] NULL,
	[DateCreated] [datetime] NULL,
	[UpdatedUserId] [int] NULL,
	[DateUpdated] [datetime] NULL,
 CONSTRAINT [PK_Log] PRIMARY KEY CLUSTERED 
(
	[LogId] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, IGNORE_DUP_KEY = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
) ON [PRIMARY]

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thanks!